MSU ‘ RETURNING MATERIALS: Place in book drop to LIBRARJES remove this checkout from ” your record. FINES will - , be charged if book is returned after the date stamped below. SCATTERING OF ELECTROMAGNETIC WAVES BY HUMAN BODY AND ITS APPLICATIONS By Devendra K. Misra A DISSERTATION Submitted to Michigan State University in partial.fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering and Systems Science 1984 ABSTRACT SCATTERING OF ELECTROMAGNETIC WAVES BY HUMAN BODY AND ITS APPLICATIONS By Devendra K. Misra This dissertation presents a study on the scattering of electro- magentic waves by the human body alongwith some related applications. After introducing the aim and scope of this study in Chapter 1, the responses of three orthogonally aligned E-field probes, near a cylindrical model of human body illuminated by TE and TM waves, are determined theoretically in Chapter 2. In Chapter 3, theoretical results of the probe responses are verified experimentally using a cylindrical di- electric shell filled with saline solution and at the frequencies of ZGHz, 2.456Hz and 3GHz. The theoretically computed results are also compared with the experimentally recorded probe responses when the shell is empty. An excellent agreement is found between the theory and the experiments. Some additional theoretical results of the response of the probe near the biological body are also presented in this chapter. A large shadow region behind the body and the difference in the probe response with and without the presence of the body are noted. In Chapter 4, the expressions for the backscattered electric fields from a cylindrical and a spherical body illuminated by plane EM waves are obtained and their behaviours are studied when the body- radius changes with time. It is observed that the phase of the return signal changes approximately linearly with change in the radius, while the magnitude of this signal is not linearly affected. Two different techniques for detecting the breathing and heart beats of humans from large distances are presented in Chapter 5 using a magic tee in one and a circulator in the other. Detection of the breathing and heart beats from about 100 feet and also through a con- crete wall is reported in this chapter. Finally, Chapter 6 summarizes the whole work and Appendices A to D present the computer programs and the printouts. To My Father Sri Koshadhish Misra ACKNOWLEDGEMENTS The author expresses his gratitude to his major professor Dr. K.M. Chen, for his sincere guidance and encouragement throughout the course of this work. He also wishes to thank the members of his guidance committee, Dr. D.P. Nyquist, Dr. D.K. Reinhard and Dr. B. Drachman, for their assistance and constructive criticisms. Thanks are also due to Li Sheng Sun, H. Chuang and H. Wang for the assistance during the experimental phases of the work. The research reported in this thesis was supported in part by the Naval Medical Research and Development Command under contract NOOOl4-82-K-0355. Finally, an expression of appreciation is reserved for my wife, Ila and son, Shashank for their patience and understanding. TABLE OF CONTENTS Page LIST OF FIGURES ....................... vi Chapter l INTRODUCTION .................. l 2 RESPONSE OF E-FIELD PROBES IN THE PROXIMITY OF HUMAN BODY-THEORETICAL CONSIDERATIONS . . . . 3 2.l Human body exposed to a TE-polarized EM wave . ................. 3 2.l.l. Determination of scattered EM fields ............. 4 2.1.2. Equivalent voltage induced in a receiving probe .......... ll 2.2 Human body exposed to a TM-polarized EM wave .................. 14 2.2.l. Determination of the scattered EM field .............. 14 2.2.2. Equivalent voltage induced in an azimuthally aligned receiving probe ............... 20 2.2.3. Equivalent voltage induced in a radially aligned receiving probe ............... 26 3 RESPONSE OF E-FIELD PROBES IN THE PROXIMITY OF HUMAN BODY-EXPERIMENTAL VERIFICATION ..... 3l 3.l Set-up of the experimental system ..... 31 3.2 Results and inference ........... 33 3.3. Some theoretically computed results for the cylindrical biological body ..... 6l 4 SCATTERING 0F EM WAVES BY SIMPLE MODELS OF HUMAN BODY ................... 73 4.1 Scattering of a TE-polarized EM wave by a circular cylinder of complex permittivity ............... 73 4.2 Scattering of plane EM wave by a sphere of complex permittivity .......... 79 TABLE OF CONTENTS (Continued) Chapter Page 4.2.1. Solution to the vector Helmholtz equation in the spherical co- ordinate system .......... 81 4.2.2. Transformation of the plane wave into spherical coordinate system. . . 82 4.2.3. Construction of solution and computed results .......... 85 5 THE DISTANT LIFE DETECTION SYSTEM DESIGN AND TESTING ..................... 96 Analysis of the magic tee system ...... 96 Analysis of the circulator system ...... 102 The magic tee system for life detection . . . 105 The circulator system for life detection . . . 113 Effects of clutter cancellation, polarization, and the clothing of the human subject on the system performance . . . 121 5.6 Detection of breathing and heart signals 010101010: 01-5de through a concrete wall .......... 1293 6 SUMMARY ..................... 132 REFERENCES ................... 134 APPENDICES A Computer program for determining the response of an orthogonally connected E-probe system near the cylindrical body .............. 136 B The probe response near the cylindrical body - computer printouts ............... 149 C Computer program and the printouts for the back- scattered electric field from a cylindrical body of varying radius, illuminated by the plane EM waves ...................... 177 D Computer program and the printouts for the back- scattered electric field from a spherical body of varying radius, illuminated by the plane EM waves .................... 134 Figure 2.1.1 2.2.1 3.1.1 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 LIST OF FIGURES A TE-polarized plane wave illuminates a vertical receiving probe located near a long sheathed conducting cylinder ........ A TM-polarized plane wave illuminates a horizontal receiving probe located near a long sheathed conducting cylinder for (a) the probe oriented azimuthally and (b) the probe oriented radially ........... Experimental set-up for recording the response of E-field probe near the cylindrical body ...................... Response of an axially aligned E-probe near a sheathed conducting cylinder illuminated by a TE polarized plane wave at 3.00GHz ..... Response of an axially aligned E-probe near a conducting cylinder illuminated by a TE polarized plane wave at 3.00GHz ......... Response of an axially aligned E-probe near a sheathed conducting cylinder illuminated by a TE polarized plane wave at 2.4SGHz ...... Response of an axially aligned E-probe near a conducting cylinder illuminated by a TE polarized plane wave at 2.45GHz ......... Response of an axially aligned E-probe near a sheathed conducting cylinder illuminated by a TE polarized plane wave at 2.00GHz ...... Response of an axially aligned E-probe near a conducting cylinder illuminated by a TE polarized plane wave at 2.00GHz ......... Response of an azimuthally aligned E-probe near a sheathed conducting cylinder illuminated by a TM polarized plane wave at 3.006Hz ...... vi Page 15 32 34 35 37 38 39 40 41 Figure 3.2.8 3.2.9 3.2.10 3.2.11 3.2.12 3.2.13 3.2.14 3.2.15 3.2.16 3.2.17 3.2.18 vii LIST OF FIGURES (Continued) Response of an azimuthally aligned E-probe a conducting cylinder illuminated by a TM polarized plane wave at 3.00GHz ......... Response of an azimuthally aligned E-probe a sheathed conducting cylinder illuminated a TM polarized plane wave at 2.4SGHz ...... Response of an azimuthally aligned E-probe a conducting cylinder illuminated by a TM polarized plane wave at 2.4SGHz ......... Response of an azimuthally aligned E-probe a sheathed conducting cylinder illuminated a TM polarized plane wave at 2.00GHz ...... Response of an azimuthally aligned E-probe a conducting cylinder illuminated by a TM polarized plane wave at 2.006Hz ......... Response of a radially aligned E-probe near sheathed conducting cylinder illuminated by a TM polarized plane wave at 3.00GHz ....... Response of a radially aligned E-probe near conducting cylinder illuminated by a TM polarized plane wave at 3.00GHz ......... Response of a radially aligned E-probe near sheathed conducting cylinder illuminated by a TM polarized plane wave at 2.45GHz ...... Response of a radially aligned E-probe near conducting cylinder illuminated by a TM polarized plane wave at 2.456Hz ......... Response of a radially aligned E-probe near sheathed conducting cylinder illuminated by a TM polarized plane wave at 2.00GHz ...... Response of a radially aligned E-probe near conducting cylinder illuminated by a TM polarized plane wave at 2.00GHz ......... near near by near near by near a a a a a a Page 42 43 44 45 46 47 49 50 51 52 54 Figure 3.2.19 3.2.20 3.2.21 3.2.22 3.2.23 3.2.24 3.2.25 3.2.26 3.2.27 3.3.1 3.3.2 viii LIST OF FIGURES (Continued) Response of an axially aligned E-probe near a cylindrical dielectric shell illuminated by a TE polarized plane wave at 3.00GHz ...... Response of an axially aligned E-probe near a cylindrical dielectric shell illuminated by a TE polarized plane wave at 2.45GHz ..... Response of an axially aligned E-probe near a cylindrical dielectric shell illuminated by a TE polarized plane wave at 2.006Hz ...... Response of an azimuthally aligned E-probe near a cylindrical dielectric shell illumi- nated by a TM polarized plane wave at 3.00GHZ ...... Response of an azimuthally aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.45GHz ....... Response of an azimuthally aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.00GHz ....... Response of a radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 3.00GHz ....... Response of a radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.456Hz ...... Response of a radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.00GHz ....... Response of an orthogonally connected E-probe system and its individual components near a biological body illuminated by a plane wave of polarization angle a = 45° at 3.006Hz . . . . Response of an orthogonally connected E-probe system and its individual components near a biological body illuminated by a plane wave of polarization angle 9 = 45° at 2.456Hz ..... Page 55 56 57 58 59 6O 62 63 64 66 67 Figure 3.3.3 4.2.2 ix LIST OF FIGURES (Continued) Response of an orthogonally connected E-probe system and its individual components near a biological body illuminated by a plane wave of polarization angle a = 45° at l.SGHz ..... Response of an orthogonally connected E-probe system near a biological body illuminated by plane waves of different polarization angles, 0, at 3.00GHZ .................. Response of an orthogonally connected E-probe system near a biological body illuminated by plane waves of different polarization angles, a, at 2.4SGHz .................. Response of an orthogonally connected E-probe system near a biological body illuminated by plane waves of different polarization angles, 9, at 1.56Hz .................. Relative probe response as a function of spacing between the probe and the body at 2.4SGHz ..................... Coefficients Q and P as a function of koa (f = 3.0GHz) ................ Phase and square of the magnitude of the back- scattered field E; from a cylinder as a function of koa at 3GHz at a distance of 30.48 m ..................... Phase and square of the magnitude of the back- scattered field E; from a cylinder as a function of koa at lOGHz at a distance of 30.48 m ..................... Coordinate system for the sphere ........ Normalized backscattering cross section (a), and phase of backscattered field EBS (b) from a sphere as a function of koa at BGHz . . . Page 68 69 7O 71 72 76 77 78 8O 93 Figure 4.2.3 LIST OF FIGURES (Continued) Phase and square of the magnitude of the backscattered field EBS from a sphere as a function of koa at 3GHz at a distance of 30.48 m ................... Phase and square of the magnitude of the backscattered field EBS from a sphere as a function of koa at 10GHz at a distance of 30.48 m .................... Circuit diagram of an interferometer using a magic tee .................. Circuit diagram of an interferometer using a circulator .................. Schematic diagram of the X-band life detection system ................ Heart and breathing signals measured by the X-band life detection system .......... Recorded heart and breathing signals from a human subject lying on the ground at a distance of 100 feet. The life detection system uses a magic tee and the radiated power is 5 mN or 2.5 mw at 10GHz ........ L-band life detection system .......... Recorded heart signal of a human subject at a distance of 20 feet. The antenna radiated with a power of 0.5 N at ZGHz ......... Circuit diagram of the distant life detection system (without signal processing system) . . . . Heart and breathing signals of a human subject lying on the ground measured at a distance of 100 feet with a power of 45 mw at lOGHz . . . . Heart and breathing signals of a human subject lying on the ground measured at a distance of 100 feet with a power of 11.25 mw at lOGHz (Amplified gain increased) ........... Page 94 95 97 103 106 109 110 111 112 114 116 117 Figure 5.4.4 5.4.5 5.5.1 5.5.2 5.5.3 5.5.4 5.6.1 xi LIST OF FIGURES (Continued) Heart and breathing signals of a human subject lying on the ground at a distance of 100 feet measured with a microwave beam with a power of 4.5 mw at lOGHz. (Amplifier gain further increased) ............ Recorded heart and breathing signals of a human subject lying on the ground at a distance of 100 feet. The life detection system uses a circulator and the radiated power is 5 mw or 2.5 mN at lOGHz ........ Performance of the system as a function of signal power level (heart signal plus clutter) input to the mixer. . . . . . . . . . . . . . . Effect of microwave preamplifier saturation on the system performance. The output of the preamplifier was 80 mH and the pre- amplifier was saturated due to a large un- cancelled clutter. Under this condition, the heart signal was obscure even though the breathing signal was detectable. A 3 dB attenuator connected after the pre- amplifier can not recover the heart Signal. The attenuator connected before the pre- amplifier can neither recover the heart signal because it reduced both the clutter and the body-scattered signal input to the preamplifier .................. Measured breathing and heart signals from a human subject lying on the ground at a distance of 100 feet with a microwave beam of 20 mw at lOGHz with different polarizations; (l) circular polarization, (2) linear-vertical polarization and (3) linear-horizontal polarization .................. Effect of clothing of the human subject on the performance of the distant life detection system ................ Measured breathing and heart signals from a human subject sitting behind a concrete wall (6" thick) at various distances. The antenna of the life detection system was located at the other side of the wall and radiated with a power of 20 mN at lOGHz . . . . Page 118 120 123 124 126 128 130 CHAPTER 1 INTRODUCTION Many reports and papers are available in the scientific literature dealing with the interaction of EM field with the biological systems. These studies were motivated by the controversy over the potential health hazards due to non-ionizing EM radiation and increasing medical ap- plications in therapeutic and diagnostic treatment involving EM energy. For that purpose, theoretical methods of calculating the internal EM field accurately in an irradiated body have been developed [1]. However, the EM field scattered by the biological body,which is the subject of this thesis, has not been studied thoroughly so far [2,3]. In the present work, the scattered EM field near as well as away from the simplified models of human body, has been studied and some of its pos- sible applications have been demonstrated. In Chapter 2, the human body is modeled as two concentric cylinders of infinite length, illuminated by a linearly polarized plane EM wave. The responses of single and orthogonal E-field probes near the body are determined by solving the boundary value problem. These re- sults are experimentally verified in Chapter 3 using a cylindrical dielectric shell filled with saline water. A few computed results for the probe response under various conditions are also presented in this chapter. An expression for the backscattered electric field from a cylindrical body illuminated by a plane wave with electric field parallel to its axis, is first obtained in Chapter 4. The behaviour of this field is then studied when the radius of the cylinder changes with time. In the latter part of this chapter, an expression for the backscattered electric field from a spherical body exposed to the plane EM waves is obtained and the effect of the change in the radius of the sphere on the magnitude and phase of the field is studied. Chapter 5 presents two different techniques, one using a magic tee and the other using a circulator, to detect the breathing and heart signals of the human beings from the long distances (~ 100 feet or so) as well as through a concrete wall. These techniques may be useful for remotely detecting the physiological status of humans at distance or trapped living beings behind barriers. _ Finally, Chapter 6 summarizes the whole work and the computer programs are given in Appendices A to D alongwith the computed results. CHAPTER 2 RESPONSE OF E-FIELD PROBES IN THE PROXIMITY OF HUMAN BODY - THEORETICAL CONSIDERATIONS An E-field probe is often carried by a man on his body surface for sensing the intensity of the EM field he is exposed to. It is, therefore, worthwhile to study the response of these probes in the proximity of human body. In this chapter, the two cases - TE and TM polarized incident fields are considered. For simplicity, the human body is assumed as circular cylinder of infinite length with complex permittivity. The equivalent voltages induced in the receiving probes have been determined after obtaining the expressions for the scattered fields from a two-layer concentric cylindrical model. The experimental verification is presented in the following chapter using a cylindrical dielectric shell filled with saline water. 2.1 Human body exposed to a TE-polarized EM wave In order to determine the equivalent voltage induced in the receiving probe near the human body, the total fields at the location are required. Since, by superposition, total field is sum of the in- cident and scattered fields, the expression for the latter is first obtained in the following section and then the expression for induced voltage is obtained. 2.1.1 Determination of scattered EM fields The geometry and the coordinate systems related to the problem are shown in Figure 2.1.1 Specialized form of Maxwell's equations suitable for the present system are, 1 3E2 . -3Ez . r or o r 3¢ jwuo z ' ° . - 3 - = with the assumption of 52'* 0 and Er ~ E¢ 0, and 2 _ 2 . J1 k — w 1105(1-3 006) (2.1.4) The time dependence exp(jwt) is assumed and suppressed throughout. The expression for i-polarized incident plane wave is assumed to be A E1 = 2 EOZ exp(-jk0x) = 2 E02 exp(-jk0r cos ¢) (2.1.5) From equations (2.1.1) - (2.1.3), the partial differential equation for Ez(r,¢) is obtained as, 2 3 E2 3Y2 2 8E BE 2 z 1 z _ +1 r 3¢ Fig. 2.1.1. A TE-polarized plane wave illuminates a vertical receiving probe located near a long sheathed conducting cylinder. Now assuming Ez(r,¢) = R(r)¢(¢) to obtain a separation of variables solution, equation (2.1.6) gives, 2 2 2 dzo +kr “7176?! (2.1.7) '1 mm a. :0 at r *‘Rr a'n. :0 Since the left hand side of equation (2.1.7) is only r-dependent, both should be equal to the same constant. Furthermore, the field is single valued, i.e., Ez(rs¢) = E2(r’¢ + 2“) Therefore, the above mentioned constant should be an integer. Now since the incident field, expressed by equation (2.1.5) is even in o, the scattered field E5 is expected to be even in a. Hence, keeping in mindthe properties of Bessel functions, the scattered field in three regions may be written as, an Jn(k]r) cos r2 (2.1.8) Where an, bn’ cn and dn are constants and usual notations for Bessel and Hankel functions are employed. Hence the total electric field Ez(r,¢) in three regions are, n20 an Jn(k]r) c05(n¢) r < r1 E (r a) = T [b H(])(k r) + c H(2)(k r)] c05(n¢ r < r < r z ’ ”£0 n n 2 n n 2 ) l 2 _. °° (2) E02 exp( jkor cos o) + n20 dan (kor)COS(n¢) r > r2 (2.1.9) For evaluation of constants, boundary conditions, the continuity of tangential fields, EZ and H¢, at r1 and r2 are used. For that H¢ is evaluated from equation (2.1.2) as k1 n20 an Jn(k]r) C05(n¢) . r < r1 = 1 °° (1)' (2)' H¢(r,¢) jwuo k2 n20 [ann (k2r) + ann (kzr)]cos(n¢) r1 < r < r2 -jkO cos ¢ EOz exp(-jkor cos a) + °° (2)' k0 n20 dan (kor) c05(n¢) r > r2 (2.1.10) Now, in order to satisfy boundary conditions, the following four equations must be satisfied. { [aan(k1r]) - an£])(k2r]) - an£2)(k2r])]c05(n¢)= 0 (2.1.11) n=0 {0 [ané1)(k2r2) + an£2)(k2r2) - dnH£2)(k0r2)]c05(n¢) n: = E0Z exp (-jk0r2 cos¢) (2.1.12) 8 °° . "2 (0' (2r ' X [aan(k]r]) - R;'{ann (kzrl) + ann (k2r1)}]cos(n@ = 0 n=0 (2.1.13) and w k (2)' "20 [dan (k 2 0r2) - R; {an£1)'(k2r2) + CnHéz)'(k2r2)}]cos(n& = j cos ¢ EOz exp(-jkor2 cos ¢) (2.1.14) Equations (2.1.11) - (2.1.14) can be solved for an, bn’ cn and dn‘ From equation (2.1.11), _ (1) (2) ~ aan(k1r]) — ann (k2rl) + ann (k2r1) (2.1.15) while from equation (2.1.13), a J'(k r ) = Eg-Ib H(‘)'(k r ) + c H(2)'(k r )] (2 1 16) n n 1 1 k1 n n 2 1 n n 2 l ' ' From equations (2.1.15) and (2.1.16), bn = -chn (2.1.17) where 1 (2)' Jn(k]r1) - E§_Hn (k2r1) Jn1k1”15 k1 H£2)(k2r1) H(2)(k r]) X = 11) 2 (2 1 18) n . . Hn (k2r1) I 9 Now, using equation (2.1.17), equation (2.1.12) may be written as, oo n20 {E-XnHA1)(k2r2) + HA2)(k2F2)]n C ' dnH£2)(k0r2)} cos(n& = EOZ exp(-jkor2 cos o) (2.1.19) Multiplying both the sides of equation (2.1.19) by cos(m¢) and then integrating over 0 to Zn, one gets, (1) (2) (2) [‘mem (kzrz) + Hm (k2‘”2)J cm ' dem (korz) em = 2m m1m(kor2) (2.1.20) - where I m(k0r2)= an m0 m(korz) (2.1.21) and = Neumann number The orthogonality property of cosine functions is utilized in equation (2.1.20). From equations (2.1.14) and (2.1.17), m k ' . . Z {‘R%{'anA1) (kzrz) + H42) (k2F213Cn ' danz) (k0r2)}cos(n¢) = —j cos ¢ EOz exp(-jkor2 cos ¢) As before, multiplying by cos m , integrating them over 0 to Zn, and provoking the orthogonality property of cosine functions, the above equation reduces to, 10 k .2. - (1)' (2)' (2)' I k0 L X mHm (k2r2)+ Hm (k2r2)]cm - dem (korz) _f_m ‘ 2n EOzIm(kOr2) (2‘]°22) where, Im(k0r2)= an mJ' m(korz) (2.1.23) and 6m = Neumann number cm can be expressed in terms of dm using equations (2.1.20) and (2.1.21) as follows: (2) c = Hm (korz) d + m Hrg21(k2r2)-xm H(1)(k2r2) m Jm( kOrZ) -m ' E (2 1.24) ”Ez)(k2’2)'meA1)(k252) 6m 02 Now, substituting for C from equation (2.1.24) into equation (2.1.22) m and then solving for dm’ one gets, .-m Ffl$( korz) - y 1 am - E026 3 Jm(korz) Jm(10527 ' m (2.1.25) Hé2)(k0r2) H(21 (kor 2) ' H(2)(k org) 11 where ”Az)'(kzrz) ' XmHA])'(k2r2) y =-—— (2.1.26) m k0 Hé2)(k2r2) ' XmHé1)(k2r2) Thus, the electric field outside cylinder is given by, dnH£2)(k0r)cos no (2.1.27) 2 Ez(r,¢) = EOZ exp(-Jkor cos a) + n 0 Where dn is given by equation (2.1.25) with m replaced by 2.1.2 Equivalent voltage induced in a receiving probe The EM fields in three different regions have been determined in the previous subsection. Now, consider that there is a small cylindrical receiving antennaata distance of R (R > r2) from the axis of the cylinder and aligned along z-axis, as shown in Figure 2.1.1. Then the boundary condition to be satisfied at the antenna surface is 2 . E = vO 5(2) = 2 I0 5(2) (2.2.1) Where V0 is the voltage across the load ZL due to current 0 at z = 0 of the receiving antenna, and + _ +i a a Ep _ Et + Eself + Eimage (2'2'2) E; is the total E field given by equation (2.1.27), Egelf is the electric field maintained by the induced current on the receiving 12 b a? pro e an image created by the presence of the cylindrical body. is the electric field maintained by its image The induced current in the antenna is a function of z and can be expressed as Where f(z) is the current distribution function. I(z=0) = I f(0) = 1. 0’ Therefore, from equation (2.2.1), h . + J f(z)z-E dz = Z I -h P - L O or _ h A +i h ~ +a ZLI0 I- f(z)z-Etdz + )_hf(z)Z°Eself dz + h . + I f(z)2.E9 dz -h image Therefore, if and, Since, (2.2.3) (2.2.4) (2.2.5) (2.2.6) (2.2.7) 13 Here the induced EMF method [4] is used to get equation (2.2.6). The effect of probe-body coupling is included via image theory, except that the strenth of the image is approximated by weighting it with appropriate reflection coefficient [5,6,7]. Zm is the mutual impedance of the antenna and its image fOr the perfect conducting body case. Hence from equations (2.2.4) - (2.2.7), v I - eq 0 ZL + Zin + FzZm For a small probe, Zin is very large. For example, for a probe of 2h = 1.3 cm, Zin at 2.45 GHz is found to be about 2-j1137 Ohm [8]. The load impedance, ZL’ for a lOkLOhm in parallel with 6pF capacitor which is a typical value for the probe, is approximately -j10.8 Ohm, If two of these probes are placedin parallel 2.54 cm apart, which re- present the probe and its image, the mutual impedance, Zm, can be com- puted [9] as 2.06 - j2.07 Ohm. Since lrz| 5 l, |ZL + Zinl >>|FZZm|. Therefore, for practical purposes, V I0 :_799;:7——- (2.2.8) L in Veq is determined as follows: h co _ . (2) _ )_hf(z)[E02 exP('Jk0R cos ¢) + n20 dan (kOR)cos(ndfldz OY‘ 14 w h _ - 2 Veq - [E02 exp(-jkoR cos ¢) + n20 dng )(kOR)cos(n@] J-hf(z)dz (2.2.9) Assuming a triangular distribution of current over the probe which is a short dipole as, f(z) = 1 - 151- 0 3 [2| 5 h The equation (2.2.9) reduces to C!) E n 0 dan2)(k0R)cos(ndfl (2.2.10) Veq = h[EOz exp(-jkOR cos 6) + Hence, the load current I0 can be determined for a given probe with known input-impedance Zin and load impedance ZL. 2.2 Human body exposed to a TM-polarized EM wave When the human body is exposed to a TM-polarized EM wave, the electric field will be coupled to both azimuthally as well as radially aligned probes. Again, the human-body is modeled as two layered infinite cylinder of complex permittivities. The expressions for the scattered field distributions are obtained in the following sub-section. The induced voltages in the two probes are then obtained from the total E-field. 2.2.1 Determination of the scattered EM-field The geometry and the coordinate system for the analysis are depicted in Figure 2.2.1. The magnetic field components Hr and H¢ are zero. The electric field component EZ is also zero. The relations 15 *8 a N as :3) m :@ ..__..._——._.—.Y _ X _ i, 1 l (a) | I / I 1 ' I I x | ' )0 i 8* Fig. 2.2.1. A TM-polarized plane wave illuminates a horizontal receiving probe located near a long sheathed conducting cylinder for (a) the probe oriented azimuthally and (b) the probe oriented radially. 16 among other three field components are obtained via Maxwell's equation, assuming that the partial derivative with respect to z is zero, as follows: pr 3H _ _.0 .1. __2 Er - - k2—- r 3¢ (2.2.1) qu OH = O z a H 3H 8 H z 1 z 1 z 2 + —-———— + ——- + k H = 0 (2.2.3) 3r,2 r r r2 a¢2 2 Now using the method of separation of variables and following the procedure similar to the TE-wave case, the scattered magnetic field H:(r,¢) in the three regions is found as, andn(k1r) cos(no) r < r1 5 = °° (1) (2) Hz(r,¢) n20 [ann (kzr) + ann (kzr)]cos(n6) r1 < r < r2 (2) dan (kor) cos(n¢) r > r2 (2.2.4) Where an’bn’cn and dn are constants. Hence the total magnetic field Hz(r,¢) in the three regions can be expressed as n20 aan(k]r) cos(n¢) r < r] H (r ¢) = E [b H(1)(k r) + c H(2)(k r)]cos(n@ r < r < r z ’ ":0 n n 2 n n 2 1 2 HOz exp(-jkor cos a) + Z dnH£2)(k0r)cos(nd) r > r2 n 0 (2.2.5) 17 For evaluating the constants, the continuity of the tangential fields, Hz and E , at r1 and r2 is imposed. E is evaluated ¢ ¢ using equation (2.2.2) as follows: M0 1 J (k ) ( ) . a ' r cos no r < r R1 ":0 nn 1 1 jwll °° I 1 = o (1) (2) E¢(r,o) k2 n20 [ann (kzr) + ann (kzr)]cos(no) r1 < r < r2 qu0 . . k0 [-3 cos o HOz exp(-jkor cos o) + + E d H(2)'(k r)cos(no) r > r _ n n 0 2 n—O (2.2.6) Now enforcing the boundary conditions at r1 and re, the following equations are obtained: 00 ) [aan(k1r1) - b H1 l 2 _ "£0 n n )(k2r1) - an( )(k2r])]cos(no)— 0 (2.2.7) 11 oo 2 [an£1)(k2r2) + an£2)(k2r2) -dnH£2)(k0r2)]cos(no n=0 = HOZ exp(-jkor2 cos o) (2.2.8) m k (1)' (2)' _ 2 . n20 [ann (kzrl) + ann (k2r1) RY'aan(klr1)] - cos(no) = 0 (2.2.9) and, w k _11 (1)' (2)' (2)' z [ {b H (k 2r2) + cn Hn (k2r2)}- dan (k0r2)] . n-O 2 - cos(n@ = -j cos o HOz exp(-jkor2 cos o) (2.2.10) Thus an, Nb" n and dn can be evaluated from equations (2.2.7) - (2.2.10). Equations (2.2.7) and (2.2.9) can be solved to get bn = -XnCn (2.2.11) where J' n(k1r1) k1 Héz)'(k2r]) H(2)(k r ) Jn1k1r11 k2 H32)(k2r1) x = . (2.2.12) n HE1)(k2r1) J' "(k]r]) k1 H51) (k2r1) Jn1k1r17 - E2— HET)(k2r1) Now substituting for bn from equation (2.2.11) into equation (2.2.8) and then multiplying the resulting equation by cos mo, and in- tegrating over 0 to Zn, one gets, (1) (2) _ (2) ['XmHm (“2(2) + Hm (k252)]°m dem (“0’11 6m = 2m021m(k0r2) (2.2.13) where I m(k znj'mam(k0r2) (2.2.14) 052) And by a similar process, equations (2.2.10) and (2.2.11) lead to, 19 k n | I .Eg'E'meél) (kzrz) + “#2) (k2r213cm ' deéz) (korz) 6m ' = EE-H021m(k0r2) (2.2.15) where I'(k r ) = an'md$(k m 0 2 (2.2.16) orz) and, Em in equations (2.2.13) and (2.2.15) is Neumann number. Now equations (2.2.13) and (2.2.l5) can be solved for dm to get fh r2 is given by Et(r,¢) = fiar>|r for a short dipole, as Z ¢ m¢l illustrated in TE-wave case, the expression for I0 may be approximated as vTM 9¢ e (2 2 28) I z . . 0 L + Zin TM,¢, Evaluation of veq As the probe is very small, a triangular distribution of current over it can be assumed. Hence ¢’¢0 ¢0+¢h (1-———)=(-————-:?—) ¢<¢< (¢+¢) ¢h ¢h oh 0 h 0 f(¢) = ¢0-¢ ¢h'¢0 ]-_______= +L - ( ¢h ) ( ¢h ¢h ) ¢0 >¢> (¢0 ¢h) (2.2.29) Therefore, from equations (2.2.21), (2.2.27) and (2.2.29) TM V ’¢ for r = R may be found as eq 23 ¢ '¢ ¢ VTM’¢ = c R Ell—11 ‘(c) [H cos ¢ exp(-jkOR cos ¢) + eq 0 ¢h ¢0'¢h 02 + j 2 danz) (kOR)cos(ndfld¢ + n=O ¢h+¢0 ¢O+¢h . + g R [ ] ( [HO cos ¢ exp(-JkOR cos ¢) + O ¢h $0 2 + ° w d H(2)'(k R)cos(n‘pd + 3 X n n 0 ¢ ¢ n=0 ¢ c R 0 + —9—- [HOZ cos ¢ exp(-jkOR cos o) + ¢h ¢0_¢h +' 00 d H(2)'(k R)cos(n )an d) + 3 Z n n 0 ¢ n=0 R ¢o+¢h c - _9_. [H cos ¢ exp(-jkOR COS 1) + ¢h ¢0 Oz 2 I + j n20 <1"ng ) (kor)cos(n¢)]¢ dcp (2.2.30) Thus, the integrals involved in equation (2.2.30) are of the form H II ¢2 AI cos ¢ exp(-ja cos ¢)d¢ ¢1 ¢2 I = Bf cos no d¢ ¢1 ¢2 I3 = C] ¢ cos a exp(-ja cos ¢)d¢ i1 24 and 4’2 I4 = D] o cos no do 4’1 Clearly, the evaluation of 12 and I4 is straight forward, B (¢2 ‘ ¢]) n = 0 I2 = B... . fi-Ls1n(noé)- s1n(nop] n 3 l and D 2 2 _ I4 = ozsin(n¢2)-¢1 sin(n¢1) D [ + n cos(no2)- cos(no]) + 2 J n 3 l n However, evaluation of I1 and I3 is a bit tricky. The integrals can be evaluated in form of series, using Jacobi-Anger ex- pansion [10]. Alternatively, the numerical techniques can be employed for this purpose. For the present case, however, integration interval is small because of the very short probe. Therefore, the exponential term exp(-ja cos o) can be pulled out of the integrals I1 and 13. Hence I1 2 AEsin o2 - sin o1] exp(-ja cos oa) 25 and I3 z C[o2 sin oz-o1 sin o1 + cos o2 - cos o13exp(-ja cos oa) where oa = (o1 + ¢Z)/2 Further, using the trignometric relations ¢0 sin(n¢0)-(¢0-¢h)sin n(¢0-¢h)-(¢O + oh)sin n(¢0 + oh) + o0 sin(n¢0) = Zoo sin(no0)[l-cos nohJ-Zoh cos(no0)sin (noh) (¢h-¢0)sin n(¢0-¢h)-(¢h + o0)sin n(¢h + ¢0) = -2oh cos(no0)sin (noh)-2o0 sin(no0)cos(noh) and, noting that oh is very small, therefore . ¢h Sln (if) z oh/2 the expression for V::,¢ is found from equation (2.2.30) as, H ¢ R ¢ ¢ TM.o ~ Co 02 h _ h _. _ h Veq ~ 2 [cos(o0 4 ) exp{ JkoR cos (o0 2} + ¢h . ¢h + cos(o0 + 7?) exp{-JkOR cos(o0 + 7f1}] + + jcodoohR Héz) (koR) + d + Eg-{l-cos(noh)}cos(no0)H£2)'(kOR) jZCOR 3° ¢h nél (2.2.31) 26 2.2.3 Equivalent voltage induced in a radially aligned receiving probe When the probe is radially aligned and its center is at r = R, the boundary condition that must be satisfied at its surface is r-E(r,o) = V06(r-R) = ZLIod(r-R) (2.2.32) where .+ + Ear image(r’¢) + —> + E(r,¢) = Et> |rrZ still holds for a small probe. There- mrI fore, I0 can be approximated as TM,r I v9 2 (2.2.37) 0 ZL + Z. 1n TM,r, Evaluat1on of Veq For a short probe, current distribution function, f(r), can be assumed as triangular. Hence, [B%£-%] R r > (R - h) 28 Therefore, from equations (2.2.20), (2.2.36) and (2.2.38), an TM,r eq can be found as follows: expression for V R ‘———] CO (R-h [H0251n o exp(-akor cos o) + +-J—- E ndn sin (no) H(2)(k0 r)]dr + Wk n=l R+h [H0z 51n o exp(-akor cos o) + + 41— Z] ndn sin(no)H£2)(kor)]dr + COR + Tr-J [r HOz Sln ¢ EXP('Jk0r COS ¢) 1 +.—:L - (2) 0 n ndn s1n (no)Hn (kor)]dr + 11MB 1 0 R+h . . "'7? (R [rHOZs1n o exp(-akor cos o) + + 4%b "2] ndn sin(no)H£2)(kor)]dr (2.2.39) Thus, equation (2.2.39) involves the integrals of the form, r2 A1 J exp(-jar)dr I] = r 1 r2 H(2)(k r) 1 = A .JL___£L_. dr 2 2 r r 1 r 2 I3 = A3 (r r exp(-Jar)dr 1 and 29 Integrals I1 and I3 are simple and can be evaluated as, 3“] . . I1 — —E—-[exp(-Jar2) - exp(-Jar])] and I = jA E r2exp(-Jar2)-r1 exp(-Jarl) + 3 3 a . exp(-flare) - exp(-iar1) ' J 2 :1 a While I2 and I4 should be evaluated numerically. However, under the assumption that probe is small, the interval of integration is very small, and these can be approximated as, (r +r ) I2 z A2H£2){k0 —-l§—g-} £n(r2/r]) and, - _ (2) 5.12.). I4 ~ A4(r2 r])Hn {kO 2 } TM,r eq is found from equation Hence, an approximate expression for V (2.2.39) as, 30 4; k hCOS¢ TM,r 0 . 2 0 Veq R! ? H02 tan (1) SEC (1) $171 ( 2 )- 0 - exp(-jkOR cos o) + + ndn sin(n¢)[(h-R)H£2){kO(R- £1} :1 In~48 h n l .gn(—R§—fi—) + R+h _) +H H(2){k0 (R+ w2)}2n( + +J——:° of ndn sin(n¢)[H(2){ko (R- g}) k0 n= 1 - Héz){k0(R + 9)}] (2.2.40) Thus, the approximate expressions of V (and hence load current, eq IO) for individual probes are now known. In practice, the three probes are orthogonally connected with diode detectors across the load terminals. In that case the square of the current amplitudes of each is added up, assuming the detectors are behaving as square-law. In the following chapter, the theory presented here is verified experimentally and some of the theoretically computed results are also given. CHAPTER 3 RESPONSE OF E-FIELD PROBE IN THE PROXIMITY OF HUMAN BODY-EXPERIMENTAL VERIFICATION The simplified theory for the response of E-field probes is presented in the preceding chapter. Here in this chapter an attempt is made to verify that theory experimentally. For that purpose a cylindrical dielectric shell filled with saline water was used to simulate the human body. The experimental results thus obtained, are compared with computed ones, for both, including the effect of the wall thickness of the shell as well as by ignoring it. Also, the probe response near the empty shell is compared with theoretical results. Finally, some computed results of the probe-response near the body are given. 3.l Set-up of the experimental system The experimental set-up used for verification of the theory is shown in Figure 3.l.l.A GR type l360-B signal generator was used as source. Since it had a built-in calibrated frequency dial and a variable attenuator, its output was used directly through a 10 dB pad, to excite - the pyramidal horn antenna. A plexiglass cylindrical dielectric shell (inner and outer radii 0.l46 m‘ and 0.l524 m, respectively, and 0.83 m high) was filled with saline water (salt/water = l/75 by weight) to simulate the human body 31 32 Anechoic Chamber [::::::}<:::: Horn antenna ;?‘-+f ‘ / :L ) v“ _ ’ Pad Source Antenna Pattern Recorder 10 dB GR type 1360-8 ___ microwave osciiiator Fig. 3.1.1 Experimental set-up for recording the response of E-fieid probe near the cyiindricai body. 33 [ll,l2]. A short probe with diode detector [22] was fixed at a suitable distance on the surface of the shell and the detector output was coupled to antenna pattern recorder (Scientific Atlanta) through the resistive leads of the probe [l3]. The probe was oriented axially, azimuthally and radially with respect to the cylinder to measure the three components of the electric field on the surface of the cylinder. The polarization of the incident field was varied by changing the orientation of the transmitting horn antenna. The experiment was carried out at three different frequencies, viz, ZGHz, 2.4SGHz and BGHz for all the three, axial, azimuthal and radial field components near the body. After the responses of the axial, the azimuthal and the radial probe are experimentally confirmed, the response of an orthogonal probe can be easily predicted by combining the responses of the former three single probes. 3.2 Results and inference The experimental results obtained by the method described in the preceding section are illustrated in Figures 3.2.l-3.2.27 along with the corresponding computed results. Figure 3.2.l shows the response of an axially aligned probe as function of azimuthal angle, ¢, when a TE-polarized plane wave of BGHz is incident on the saline water filled shell from a = l80° direction. In this case, the response shows a maximum on the front side (i.e., ¢ = l80°) and a very small output on the backside (i.e., ¢ = 0°). This type of probe response is understandable via shadow region formation behind a conducting body 61-60(7337-J25i €,-€o(l.r‘-J'G.~‘ll) III-0.146911. V. I /~\ I~—q§ Fig.3.2.l. Response of an uinlly align-d E-probe nut a shuthod conducting cylinder illuminated by a T! pol-rind plane wave at LOOGHz. ' —o- .0- + :hoory , up: rincn t + .4... #- probcltuponsc in than“ of the body (theoretical) "~_—'—..-~' " . 13” M rz- 0.1523m. . \ R - 0.15631. . “’1 ’L. a L '~ \ ’ a” - ‘ it)":~ \b’ ‘1 : )I’Q \‘ l), I,» .4 l f 61-50(73.57-jzs) 52'60 r1-0.146.n. r2. 0.152£n. , I / . ,. - V>< 0.. 0.15m. / ‘ , - \ F15.3.2.2. Reeponee of an axially aligned E-probe near a conducting cylinder illmineted by a It polarized plane wave at 3.00612. —o—o—o— "um-y , . experinent + -I- + probe response in abeence of the body (theoreti cal) '9 36 illuminated by EM wave. In this figure, the thickness of the shell was taken into account in theoretical results. These results are in good agreement with the experimentally recorded response of the probe. The theoretically computed response of the probe in the absence of the body is also shown in the same figure, which is in the form of a circle with a radius little smaller than the maximum of the response in the presence of the body. When the thickness of the shell is ignored (i.e., £2 = so) in the computation, the results depicted in Figure 3.2.2 are still in good agreement. However, the response of the probe in the absence of the body is lower in this case in comparison with the previous case. In Figure53.2.3 and 3.2.4, the experimentally recorded response of the probe at 2.456Hz is compared with the computed results, in the former the thickness of the shell is included while in the latter it is ignored. Again, in both figures the experimentally recorded results are in close agreement with theoretically predicted values, and the level of the probe response in the absence of the body is higher in the former case. A comparison of the experimentally observed response of the probe at ZGHz in Figures 3.2.5 and 3.2.6 also shows a good agreement with the theory, and the probe response in absence of the body is lower when the effect of the shell is ignored in Figure 3.2.6. When a TM polarized plane wave of BGHz is illuminating the sheathed conducting cylinder, the azimuthally as well as the axially aligned probe both respond. The response of an azimuthally aligned probe is illustrated in Figures 3.2.7 and 3.2.8, while that of a radially aligned probe is shown in Figures 3.2.13 and 3.2.14. The response of an azimuthally aligned probe shows a maximum on front side (¢ = 180°) l L—sb “3.3.2.3. Reeponu of an axially aligned E-probe see: a eheatbed conducting cylinder illuminated by a TE polarized plane wave at 2.6632. theory, probe teeponee in ebeence of the body (theoretical) 61-50014. 3-j25.-’.) 52-50(2.6-j0.02) t1-0.1-’.6:n. r '0.152.’.m. 2 I‘.‘ '0.156m. ft \ 13;." n experiment r -o.152;a. . 1» | . \ I~—- ¢ ‘ Fig. 3.2.6. Reeponse of an axially aligned E-probe near a conducting cylinder illuminated by a 1'5 polarized plane wave at 2.55632. experiment .9—0-3— theory . -I- -i- -It- probe. teeponee in absence of the body (theoretical) experiment -qr— -§— -*- r use in absence of the body (theoretical) .31 axially aligned E-probe n olariz P cylinder illunin ated by a TE p of an ed plane wave .__—____- experiment El'éo(.73.57-j25) €2-€O(Z.6-j0.0i) r1-0.146m. t2'0.1524m. R '0.156m. - Fig. 3.2.7. Response of an azimuthally aligned E-probe near a sheathed conducting cylinder illuminated by a- m polarized plane wave at 3.00682. w—o—o— theory. experiant + 4.. + probe response in absence of the body (theoretical) \ 4 I" I I -| _\ / I a \. ”I! 0 IO' 20' _ m- wr _ Mr I _ . “—1.“, I}. 61-6-00; 37-:23) ‘32-:0 rl'OJéfim. rz-OJSZLJ. R'OJS'EL l '. '. - I /\ . . t. \ |~ ._ " ‘~‘-‘:-- \ . . Fig.3.2.8. Response of an szinuthslly aligned E-probe near a conducting cylinder illuminated by s m polarized plane wave at 3.006112. , —°.—o—°— theory . experinent —e- —e- —)I— probe response in absence of the body (theoretical) ,' . .. .-. -.J‘J.. .-'\-3o.02) Fig.3.2.9. Response of an azinuthally aligned E-probe near a sheathed conducting cylinder illuminated by a m polarized plane wave at 2.6568:. axperinent —o—e—o— theory, + q. + probe response in absence of. the body (theoretical) .L) |,!H|.-.:"[ll!|fl'! \ n: 3.1 )31'1 J‘J I ' . \. Fig.3.2.10. Response of an azinuthally aligned E-probe near a conductina cylinder illnineted by a “D! polarized plane wave at 2.456112. ' -—-o-—o-—o— theory , experiment _ __ _. probe response in absence of the body (theoretical) ' /\ .1 ‘Ix ,- / . - __.._—-—r= ‘ ’ ‘. /\ ‘ / l ’ x \. ,/ i - \ . I" 1 \ ' \ ~ ' . '- " '- / \ ' 1 x 1’ ‘\."I‘ l ' .1. ‘. . l/ \‘L l I -.T_._~_——I : -" \_ / / ' I '~ - —-_._-.. M m H" "" "i " m )Ir' J” rl-OJLr‘vm. r2 R '9. I 34.1. Fig.3.2.ll. Response 0 conducting wave at 2. _o_H—— _gp .qp— .45.. 5,-t0(2.6-;n.02) ‘:-- .. '0..4_.... . \.\\\ 1 an azimuthally aligned E-probe near a sheathed cylinder illuminated by a In polarized plane 00632. ...,_..;“"_1_-"” \ _ \ theory, experiment probe response in absence of the body (theoretical) as ’ \ / I. \ ”)f \‘\ >< . ' ’ .\. l . |. ‘/-./ .‘\ ,‘ ./ - 51g.3.;.ll. Response of an azimuthally aligned E-probe near a conducting cylinder illuminated by a m polarized plane wave at 2.006Hz. / M thCOry ' experiment 4.. q— ...- probe response in absence of the body (theoretical) I ' II I . . . ’ . I . _ _. \ . . j. . ._. _.. J30" 'f - '- .’- Ha" . s--- \- \ 61-E0(73.57-525) 52-50(2.6-j0.01) rl-0.l-’.6n. r2-0.1524n. ‘ n I0.156m. ‘ . u ‘1}, ~'\_ I . \' . t~ -; ‘ “3.3.2.13. Response of a radially aligned E-probe near a sheathed conducting cylinder illuminated by e TH polarized plane wave at 3.00GHz., 4—0—0— theory , experiment I l 5 ’ + + -I- probe response in absence of the body (theoretical) I ~' ’ .5 ' ‘ -7.-,- ‘ ‘ 4 ‘ . ' w " “ . ' 1;, I {m m 1““ ‘ ' "' lap-1.1.1..“ 48 and a very small output on the backside (a = 0°) in the presence of the body. Theoretically determined response of the azimuthally aligned probe in which the effect of the shell is included, is compared with the experimental results in Figure 3.2.7, while in Figure 3.2.8 only the saline water column is considered in theoretical computation. In both cases, the theoretical response is very close to experimental values. The probe response in the absence of the body is also depicted in Figures 3.2.7 and 3.2.8 for respective cases over 90° 5 ¢ 5 270° range. For 2700 5 ¢ 5 360° and 0° 5 ¢ 5 90°, this is same as for 90° 5 ¢ 5 270°, hence omitted for brevity. The shadow on the back side of the body and the higher response level in the absense of the body in Figure 3.2.7. in comparison with Figure 3.2.8 are noted. The computed response of a radially aligned E-probe depicted in Figure 3.2.13 for 3GHz in which the effect of the shell is included, is in relatively better agreement with experimental result in comparison with that of Figure 3.2.l4, where only the saline water column is con- sidered for the theoretical calculations (i.e., £2 = so). The calculated probe response in the absence of the body is a little smaller in the case of the sheathed conducting cylinder illustrated in Figure 3.2.13 with respect to the corresponding results in Figure 3.2.14 where sheath is ignored. Figures 3.2.9 and 3.2.ll illustrate the response of an azimuthally aligned E-probe near a sheathed conducting cylinder illuminated by a TM polarized plane wave at 2.4SGHZ and ZGHz, respectively. The re- sponses of a radially aligned probe for these cases are shown in Figures 3.2.15 and 3.2.l7. The corresponding results when the effect :hmlusallz!!'!,l..!9. .__.L_.. )3” 30‘ ‘ . \ \ Pig.3.2.IL. Response of a radially aligned E-probe near a conducting cylinder illuminated by a in polarized plane wave at 3.006Hz. experinent —¢.—°—°— theory. -— —I's- + probe response in absence of the body (theoretical) 61-50(73.57-j25) f 62-60 ' ' ' rl-O.Ih6m._ y r2-0.1524m. ' ' - ‘5 ($3 R-0.156m. “ : \' §. ' F 96 I N!— ' . o’L 1 L 1d” 350' 0 If 20' 10’ b" . ___ I(r Mn" 50" no lutnl 2| -.—._- 'r T——"‘ ' u \- 5 \ [N ’ p ' 61-60(74.3-125.4) .‘ ' .f -‘ ‘\. '.' -= " I "\ \\ . , 62-60(2.6 ,o.oz) \1 ' \K \.\. t‘1'0.146m. " '1 \‘4 \\ ' , r2'0.lSZ-’.m. ' ~. ‘- ‘- ' R -o.156m “x .\ .’ \\ ‘ \ \ 4 \ \ .l . \ \~ V \. ' . I“ “ .- , -\ ' \ A .. / , \ "/ \‘ \- L¢A A , >1 “3.3.2.15. Response of a radially aligned E-probe near a sheathed conducting cylinder illulinated by a n1 polarized plane 98V. It 2.656Hz. r —o-o—e— theory. experisent -I- -e- -I- probe response in absence of the body (theoretical) I I ' ' \ 1w Jdlvl' 1 0 "—10" “ "' :‘i: ‘—' '13-— .‘9 , 2" 'm' w- as- =14 Hula: ’ Manse _" ' . ‘~. \ J I \ -. ' - - r2-0.1524m. \_‘. \5 R '0.156m .\_ _‘ ,\. V A: x-.. L o A “8.3.2.16. Response of a radially aligned E-probe near a conducting cylinder illuminated by a ll! polarized plane wave at 2.4563z. —°—°—°— Chm” v experiment -e- -e- -e- probe response in absence of the body (theoretical) Inn‘r—-———‘:'I_- . ._ .537.“ I. -v‘..._.’v— . 20‘ 10‘ YT .'- m W! H! _ -3” 61-60(74.8-126.9) 62-60(2.6-jo.02) rI-0.146m. r2-0. 15241:. R-O . 156m. Fig.3.2.17. Response of a radially aligned E—probe near a sheathed conducting cylinder illuminated by a TM polarized plane wave at 2.0068z. “ tr? —°—¢-o- theory . experiment .g. * .g. probe reaponse in absence of the body (theoretical) Jju- 140' .W 8' 0 to- aa- sat w- m 340' so ___.'.'_;f'__,_ " "" ' " ' ' ' 77!". ETTT'I'TTTI'T'II—I " 1Wl'F1Tmi {WWW-— 53 of the sheath is ignored in the computation are compared with the re- spective experimental responses in Figures 3.2.l0, 3.2.12, 3.2.l6 and 3.2.l8. The theoretically predicted results shown in these figures, are in fairly close agreement with the corresponding experimentally recorded responses at both frequencies, viz, 2.4SGHz and ZGHz. General behaviour of these results is similar to that of corresponding 3GHz cases diSCussed earlier and therefore omitted here for brevity. When a TE polarized plane wave of BGHz frequency illuminates a cylindrical dielectric shell (i.e., e] = so) from ¢ = 1800 directtion, the response of the axially aligned E-probe in its proximity shows a large peak at ¢ = 0° as depicted in Figure 3.2.l9 alongwith I a circular response computed when shell is not there. The experimentally observed response of the probe is still in close agreement with theoretically predicted results. Figures 3.2.20 and 3.2.21 illustrate these results for 2.4SGHz and 2GHz, respectively. These responses are quite different from the one, shown in Figure 3.2.l9 for BGHz. However, these unusual probe responses can be accurately predicted theoretically. The response of an azimuthally aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 3GHz is illustrated in Figure 3.2.22 alongwith the computed results of response in absence of the shell. Relatively higher response in ¢ = 00 direction with respect to o = l80°, and some depressions in the peaks when the shell is present are the main features to be noted. Figures 3.2.23 and 3.2.24 depict the response of the azimuthally aligned probe near the cylindrical dielectric shell for the illuminating TM polarized 61-60(7b.8-326.9) 62'60 21.0.146‘11. r2-0.1524a. _ R-0.156m. no - 7 50‘ , Fig. 3. 2.18. Response of a radially aligned E-probe near a conduscti 4? )2. ng cylinder illuminated by a n4 polarized plane were at 2.00632. 53" ‘0' +9—9— :hgory, experiment -e- -e- -e- probe response in absence of the body (theoretical) .. \L ' " ' I 'M \ 110' 10" 15W If 10' 30' I? 20 In J” W ”P "4" ' """ " ‘ -'r-r'i"' ' 3 ‘71 / . g .; .e! . 62=€0(2.6-j0.01) rl=0.146m. 1’2' 0.152413. I‘. I 0.156m. Fig.3.2.l9. Response of an axially aligned E-probe near a cylindrical dielectric shell illuminated by a TI: polarized plane wave at 3.006112. . . experiment —°.—°—o— theory. IO' 35!" -\ 5 , I -. . - 25..-; l- M ' if," 0 ,2}; probe response in absence of the body (theoretical) \ J 3 ' '17 170’ .' 70' .‘ .' 7)? W m s‘. 1.. C at ~1 *0 _ 52:50r2.6-ao.o:i , rl=0.146m. / r '0.1524m. IJ" 2 a 2m R '0.156m. I?" in nn' 4 250 Im 2H" no 170 so 70 2m a - ‘ / 1r- \ \ \ / -~ ;. Fig.3-2.20. Response 0! an axially aligned E—probe near a cylindrical 5‘ - . dielectric shell illuminated by a TE polarized plane wave 3|- i at 2.1.501“. _ l E —°—o—°— theory, experiment .l —e- -e- -e- probe response in absence of the body (theoretical) ‘ , . . _- x \ 4 \\’ ‘7‘ -\' :’ :' ’1 ' / "‘\ X ”‘54-“- -—- l / "\FL I! i i ‘l. ”5.!" Jul 150 ‘) nr 20‘ .m‘ w .- \ pi .21 < . /(\ “ ".4’” " I-' :5. ' ,-'/ .\ _, \ 61-60 / \\\ g / _ - 57-50(2.6-j0.02) \ ,/ L; 5 ' "\ / r1-0.146m. . _ ./)\ r2=0.152§m. R-0.156m. on my “5.3.2.21. Response of an axially aligned E—probe, near a cylindrical dielectric shell illuminated by a TB polarized plane wave at LOGGEL —°—°—°— theory. experiment —e\- -e- -a-— probe response in absence of the body (theoretical) l/-_'_J-” i \2: “337'" ‘ .m,‘ 350 0 w‘ 20- iv 3" I“ I0“ ”Ir )Ji‘ u. a1) e o the body (theoretic laud: ' i 250‘ . IIG' 2w |l)(1' . . 2&7 -' 8"‘.'. 23.. . , 240' 120' ‘ 279‘ ‘M' be N't )"T ' u" 3‘ ti .. .; /‘\’ 6 ‘0 ‘ E =€O(Z.6-j0.02) 1 ‘. I \ "\ 2 /\ . _,—'\" ‘ Il'O.l-':6ra. . ,"’ \ a ' ”Q... \// ,5 \ r2 0-.S- I“ P13.3.2.23. Response of an azimuthally aligned E—probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.65632. I —O—-°—-O— theory, . — experinmnt -e- -e- -s— probe response in absence of the body (theoretical) \' ’1 ‘71...\i f ’ g /\< \ I I,“ /; / '-~.....'_ / \\/ .' --.-._- ‘ . 5,. ,-., / /rI/-' "\“ )lO' . ' / ~ . . I K . "' Pig.3.2.24. Response of an azimuthally aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 2.00GHz. _.g__._o— theory, _ experiment v- c.- -ss- un- probe response in absence of the body (theoretical) 60 _ . 3‘ 5‘ "" '\\ : 5/“4 \\ \. 61":0 ,. / ~ ‘/" e '5 (Ls-30.02) 4‘ u . \ \ /’ 2 O 1: ~. \ ,v'» . a I \ \\ y. .\ r1 0.1-.6m. -, ‘. ~\ / ‘\ ~ - . la . \‘l' . \ ‘ y 2 2 1‘ , ~_ -. r; \ 61 plane wave of 2.456Hz and ZGHZ, respectively. A good agreement between experimentally recorded and computed results 'is found in all these figures. Figures 3.2.25 - 3.2.27 illustrate the response of the radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 3GHz, 2.456Hz and ZGHz, respectively, alongwith the corresponding computed results with and without the dielectric shell. When a 3GHz TM wave is illuminating the shell, peaks in the probe response are observed at ¢ = 65°, 90°, 2700 and 295° while null for ¢ = 0° and l80°. The computed results are still very close to the experimentally observed response.’ Similar agreements. are noted for 2.456Hz and 2GHz in Figues 3.2.26 and 3.2.27, respect- ively. A l0 k Ohm resistor in parallel with a 6 pF capacitor is taken as load to the probe for the computations. The other related data are given in respective figures. The computer program developed for theoretically predicting the response of the probe is given in appendix A while the computer print-outs are included in appendix B. 3.3 Some theoretically computed results for the cylindrical biological body Figures 3.3.l to 3.3.3 illustrate the response of an orthogonal- probe-system as well as its individual components when the body is ex- posed to an incident plane wave field of BGHz, 2.4SGHz and l.SGH , respectively. The permittivities of the body at these frequencies are also given there [ll]. Polarization angle of the incident plane wave r,=0.1524;. I! '0.ISC::. 310‘ SN lend... Fig. 3. 2. 25. Response of a radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane wave at 3 006B: . _°—°__°_ *-m——.—— theory , experiment probe response in absence of the body (theoretical) AL 5" JR" 4'." ”(1' ‘fl!!!l..'1'£5l!!s‘! \ 63 I . i \ \ ”V \ ‘ - If I "j “ 7\/ t. \v' ‘ ‘ -—-.—- ----- ' ' " - ' -. \ ’ "1 ".\ \\I / /"r— ' T\ / i N7 ‘y" . . \ ii 51' ,4 ' \ . \ , '\ / -. '~ 214,- ,/‘». \ ~\I \x/ 61.60 4’ / I... / - . \ \\ .I ‘ €2'€O(2.6-j0.02) .3 \\ tl'OJLI‘m. \ >_ \ r2'0.152-’.m. 20' ° \ g R'0.156m. ” I: .2..- . \ :1 \\ l . ~® I lla't % I f" ‘ ’6 n: l\ 4; \ 15‘- Ir’\e ; N W a A ‘ a 7% w. I \ ”5 1 ‘ I. \/ / // i, I -’ |‘ \ \ \\ \ ’ . , .- / I/ \- I I l \ \ ‘ . . n4.3.2.26. Response of a radially aligned E-probe near a cylindrical dielectric shell illuminated by a TM polarized plane move at Jlu -' 5“. 2.1.5682. I: _°_.o-—o-— theory . experiment (\I -e— u— —-e— probe response in absence of the body (theoretical) i 'l ‘ I. I-\ ‘ g I ‘ I I‘ ’"II ‘ L | , \ ./ . ‘~_~-- e_1__._..-"/ ’\ . }\ \. / . / .'. \_ I - ' - \ ,x \ ‘ \ b; l I, I" ~ I ' I .I ‘I . ,1 ' . .5 r/ 4 I / \\1 l . -. ". / I l . ' [I I l I I . IL '/|__/‘\ I 0- , _.I“ - ‘-" ' - - _.-._— __ . ’3‘; 32f: .7. l I I", .2." £0 7- o . 0 ..J . . . m .0 3 4 _u. . 6 5. 6 2 '4 5 5 . /\ 1.. I 1 0 O . . . ,C .: 0 A; o = a = = s . l «.3 ya 5 R . § \W/Myim“ “w Fry fl---thWVW\\\.\ofinflna i Xe é .‘C near a ylindrical . .- ~ - ro e llunina ed by a m poleriz d plane wave at flaw. , f- .1 o o a dielectri c shell . z. e e at e oy t eoretical) 65 is taken as 45°. Hence TE as well as TM waves are equally in- cident. From these results, it seems that axial alongwith azimuthal component contributes dominantly at 3GHz and 2.4SGHz. The response of orthogonally connected probe in the absence of the body is also shown in Figures 3.3.l and 3.3.2, which indicates a little increase in the probe output for ¢ = 1800 and a shadow region formation for ¢ = 0° in the presence of the body. At l.SGHz as shown in Figure 3.3.3, the radial component dominates over the other two taken together. Figures 3.3.4 to 3.3.6 depict the probe responses with polariza- tion angle of 0°, 30°, 60° and 900 at aforementioned three frequencies. For 3GHz, the maximum occurs when polarization angle is e = 0° in Figure 3.3.4, while at the other two frequencies, viz, 2.456Hz and ZGHz, it is for e = 90°. Finally, Figure 3.3.7 shows the probe response as a function of spacing between the probe and the body at the azimuthal angles of l80°, 135° and 90°, when the incident field is polarized at 45°. As expected, this gives a standing wave pattern with decreasing amplitude as probe moves away from the body for each azimuthal angle. This is computed only at 2.456Hz. f\ IIIIJIHH'HIIIHII'HHIIIIIIIIHIHIII”MINNIHHIII'IIH~hw|1mlnw l I u ’12’. - -<. . ' '3 . .a-ke-e- Axial / ..-...... Azimuthal ”pm,” Radial rl-o.146m. *"“'*° Total R '0-156m. . 61-60(46-113'5) ;‘ Fig. 3.3.1. Response of an orthogonally connected E-probe systen and its individual components near a biological body illuminated by a plane wave of polarization angle 945° at 3.006112. ‘———‘a————J5———;F 3:. 3... I... o 1.2: 32‘. .39; A ES IHIIIIIIIJJIJIIIIIIIJIIIIIIII'!Illllllllllllllll"IIIlllHlllHl'Illl'llllllll|I"I"': f" I) Fig.- 3.3.2. Response of an orthogonally connected E-probe system and its individual components near a biological body illuminated by a plane wave of polarization angle 8- 65° at 2. 1.5GHz. \/ ‘ -a-a.A-A~ Axill / \p '- .e-e-e-e- Azimuthal /\ \ a—m-v- Radial 21.0.1463. . . ~ un-o-O-O-Tocal R '0.156m. ‘ ., z .5 («7-116-2) -' " \g/ ‘1 o \ . .//.\y I . ‘ . / \L x _______.__—.——— (r 4 3w IO' zo- .m- 1:? 3 0- ur 0 no- no A lllH'l’n|!|l|!|llll‘li|!'f||||llllllll||I'-'iiu l? "E -a-e-O-A- Axiél ---o--- Azimumal -0 146 r1 . n. R '0.156::. 4.-."... Radial -I-.-..D. IO tal Fig. 3.3.3. Response of an orthogonally connected E-probe system and individual components near a biological body illuminated by a plane wave of polarization angle 9-45 at 1.5632. b ‘11'605‘9-121.» ‘ its A EIIJJIIHIIJHHILIH'IIHIHJIIiI1IIHHIIIIIIIIHllmlIIIIIIIHIIIIIIIIHMI- n :1: u 25-: \ U H 3.9. E ,...'\;-7 ' _<\- 3 \ _..,..__ . ' ,- ......... 6' / “nae-e- 30c -A-s-a-e-e- -.—..y-§ 9- , Fig. 3. 3. 4. Response of an orthogonally connected E—probe system near biological body illuminated by plane wave of different polari- zation angles, 9 , at z. 3. .- P - .; _ 2' "' i',‘ Y- - 2:5 3: 75 _...._ 3"". lamlmzllwu 3231' " | : 'IIH IHI .-- -old|l|l¢r l _l -xu-y-r- 6- 30a ' Judd-e. 60 P '0 156m -.-t-r~> 6" 90 ‘ ' ' 5.-€O(L7-116.Z) 1:13. 3.3.5. Response of an orthogonally connected E-probe system near e 510103131 body illuminated by plane wave of different polari- s zation angles, 6 . at 2.4 2- ‘ 71 a. 32: .. . . f. .....\\.v./ .. m I “1 n. D um. . m L at - 62 u - 5.... an lu9 e... 4 as. w( y: .o .a -. R,» e . 1 a...“ z: r . W .. 3.. - .n u - .6 I3] e e u v... .. on mp - a cw.” .M R out e t. I ”I I p.11 “.1 l I cut I 6 o s - . O O O 0 an a . . I. om mo ¢ :1 .. 0.. 9 eye r.‘ l: c u a — “M8: .4....... .H 9666 x be i - o o I. d “11 .‘..- I «H.» r a“ .... .. Q o a . u .C‘ . l a u... a ”do w . " ... q 4 ”mm .. an a o t .1. R.b a .3.3.6 a. Fig 3 ._:_._.:_:::_:_::.1_.__..._:: m. . .M 72 Relative probe response—aa- 2’ 1'2 1'6 20 l... s(in cm.) 4.. H E Ill- Relative probe response—u- l‘.) ® ' j’Eki\ 16 20 O .3) col- .4 N s(in cm.)-——-p- 6 = 45° r ._ +. +. T J H1 'i :E‘ a) d. 2 4 900 O a l. . @- (D '8 2._ —.{s}.. ‘5. a; 1.. :3 (U n "c3 0 d i i 4. 2 cr 0 4 8 12 16 20 s(in cm.)__,b Fig. 3.3.7. Relative probe response as a function of spacing between the probe and the body at 2.45 GHz. CHAPTER 4 SCATTERING 0F EM WAVES BY SIMPLE MODELS OF HUMAN BODY In this chapter, the scattering of EM waves by a human body will be studied. The purpose of this study is to provide a theoretical basis for the development of a distant life detection system. When a human subject is illuminated by an incident EM wave, the scattered wave from the human body is modulated by the body movements due to breathing and heart beat. If the backscattered wave is received and detected properly, the breathing and heart signals which modulate the backscattered wave can be measured. In our study,the microwave with a frequency in the X-band or the L-band will be employed and the human subject is located at a distance of 100 feet or farther from the antenna. To analyse the nature of the backscattered field from the body, two simple models of human body, an infinite cylinder of complex per- mittivity with a time-varying radius and a sphere of complex permit- tivity with a time-varying radius, are considered. We aim to find the perturbance of the phase and the magnitude of the backscattered field due to the variation of the radius of the body model which simulates the breathing and heart beat. 4.1 Scattering of a TE-polarized EM wave by a circular cylinder of complex permittivity. The EM wave scattered by an infinite cylinder of complex 73 74 permittivity when it is illuminated by a TE-polarized wave can be deter- mined following the procedure presented in Chapter 2. Here in this section, equations (2.1.18) and (2.1.25) to (2.1.27) are specialized for the case when k1 = k2 = k and r2 = a, as follows: For k] = k2 = k, equation (2.1.18) can be simplified using the wronskian formulas for Bessel function as x = -1 (4.1.1) and from (2.1.26) and (4.1.1), H£2)'(ka) + H£])'(ka) — L y" k2 = k1 = k ko [ H£Z)(ka) + Hél)(ka) r2 = 3 Since, H32)'(ka) + Hé])lka) = 2 06(ka) and Héz)(ka) + H£1)(ka) = 2 Jn(ka) Therefore, J'(ka) _ k n ,n .2 = k. =.. ‘(k—o‘) W ‘4“) r2 = 3 Hence, for the present case equation (2.1.25) may be written as k Ja(ka) , J$(koa) d E j-n "a n(koa) (Eb) 3;(E§T" JETEEET = _ e . " OZ " H22 )(koa) k 06(ka) H52) (koa) o Jn(ka) - H£Z)(k0a) (4.1.3) Whereas the scattered electric field outside cylinder is given by s = °° (2) Ez(r,¢) n20 dn Hn (kor) cos(n¢) (4.1.4) Thus, the backscattered field,when kor is very large and the series is nicely converging such that the infinite series can be term- inated at n = N with |k0r| >> N, is given by, Es(r = ) 2 ex {-‘(k r - 1111" (-°)"d (415) z 2¢ “ 2- nkor p 3 o 4 "20 3 n ' ' Hence 5 2 2 2 IEZM - .11 .———.,..0,.ITI where N k a A . A . T = 201-3)"dn = 1—3—1 (0 + 3") (4.1.6) n: A computer program was prepared for computing |E:(r,¢ = n)|2, phase (in degrees) of E:(r,¢ = n), 0 and P. The computed results for a highly conducting cylinder (0 = 99.995/m and (r = 1.0) as well as for a cylinder with a conductivity of 0.6685/m and a zero relative permittivity (hypothetical case) are compared in Figure 4.1.1 76 1! 1r (r = 0, G = 0.668 S/m 0 . . g i ‘i k a -—————4F- 0 2 6 8. i0 0 . ‘r l ‘ ' (r = O, O 3 0.668 S/m #——p-——% e = 1.0, o = 99.99 S/m .______— Computed a x x I After Van De HUlSt [l4] Fig. 4.1.1. Coefficients Q and P as a function 0f koa (f = 3-0 6H2)- 77 ’1500 '1200 2x10' l. -900 1x163» 3600 N a3; 0 - : i 5 00 2 4 6 8 10 12 koa ——-—-3— Fig. 4.1.2. Phase and square of the magnitude of the back scattered field ES from a cylinder as a function of koa at 3 GHz at a diétance of 30.48m. Phase of E: (in deg.) 78 6v=39.9 _3 cr =1o.3 S/m 2x10 .[ f =10 GHZ. .,2000 h 1 (a 2;) 1» a”' I .. 11:51 2 .,...---"‘" XX 4 1500 a/ ," coo-0“" “ lb “‘9' I]! l- ’7 l -3 . / '5: 1x10 4. {/r Phase «-1000 '° I C x, "- J1- ,‘I‘ ‘l V g" m N ”I 500 w .. 4p- 3"... l I"; 14- ea . o ,‘l 4) OJ I (I) f E 0’ t 4 : . 4f 0 26 31 36 41 k a : o Fig.4.1.3. Phase and square of the magnitude of the back- scattered field E: from a cylinder as a function of koa at 10 GHz at a distance of 30.48m. 79 with known results [14] which are in excellent agreement. Figures 4.1.2 and 4.1.3 depict IE:(r = 30.48m, 4 = n)|2 and phase of E:(r = 30.48m, ¢ = n) as functions of koa for a cylinder of complex permittivity at 3GHz and lOGHz, respectively. At 3GHz, both the magnitude and phase of the backscattered field vary linearly with koa. However, at lOGHz, the magnitude of the backscattered field does not vary linearly with koa even though the phase still does. For this reason it is desirable to measure the phase of the backscattered field if the variation of 'a' is to be detected. The computer program and tabulated results print-outs are given in Appendix C. 4.2. Scattering of plane EM wave by a sphere of complex permittivity In this section, the scattering of plane electromagnetic wave by a sphere of complex permittivity and radius a is considered. As shown in Figure 4.2.1, the x-polarized incident wave is propagating in positive z-direction. The time variation of exp(jwt) is assumed and suppressed throughout. This scattering problem is treated as a boundary value problem. The partial differential equation being, of course, the vector Helmholtz equation, 3 = 0 (4.2.1) Where k = Zn/l, and 6 may be either the electric E or the magnetic field H. Solutions of (4.2.1) are obtained in the form of infinite series containing unknown constants. To complete the 80 incident wave Fig. 4.2.1. Coordinate system for the sphere. 81 solution of the problem, these constants are determined by matching the + + boundary conditions for E and H on the surface of the sphere. 4.2.1 Solution to the vector Helmholtz equation in the spherical co- ordinate system It can be proved that the solutions of the vector Helmholtz equation (4.2.1) in the spherical coordinate system are the spherical vector wave functions [15], E(r,e,¢) = vf(r,e,¢) (4.2.2) M(r,e,¢) = vx[rf(r,e,¢)] (4.2.3)‘ N(r,e,¢) = %-vx M(r,e,¢) (4.2.4) Where F is the radial vector in spherical coordinates and f(r,e.¢) is the solution to the scalar Helmholtz equation, v2f(r,e,¢) + k2 f(r,e,¢) = 0 (4.2.5) + In the region surrounding the scatterer, V-E = v-H = 0. Since v-E(r,e,¢) f 0, only the M(r,e.¢) and N(r,e,¢) solutions can be used to represent E and M. It is well known that the solutions to equation (4.2.5) in spherical coordinate system are of the form, airmen...) = zn(kr)P':(cos e) {:32 :33} (4.2.6) 82 Where m and n can be any integer, e denotes "even" for the use of cos(m¢) and 0 denotes "odd" for the use of sin(m¢). P:(cos e) is the associated Legendre polynomial, and zn(kr) represents the spherical Bessel functions of the first kind, jn(kr), of the second kind, nn(kr), spherical Hankel function of the first kind, hél)(kr), or of the second kind, hé2)(kr), respectively. The desired solutions to the vector Helmholtz equation are then the spherical vector wave functions obtained from equations (4.2.3), (4.2.4) and (4.2.6), Mgmn = ; $1: a zn(kr)P:(cos e) {:;:E::;} 6 + a . - zn(kr)[%- p':(eos e): {23:3} 4 (4.2.7) and + _ +1 .. Nam" Pinwl zn(kr)P:l(cos 9) {3%} r + 1 a a m COS(m¢) ‘ ---—- [r z (kr)]D—— P (cos 0)] } e + kr 3r n 39 n Sin(m¢) +l m a m sin(m¢) . n ————.———- ——-[rz (kr)]P (cos a) } 4 (4.2.0) kr 510 9 3r n n cos(m¢) 4.2.2 Transformation of the plane wave into spherical coordinate system The x-polarized plane EM wave propagating in +mz direction can be represented as, 83 +1 . . .. . E = xE0 exp(-Jkoz) = XEO exp(-Jkor cos 6) (4.2.9) and +1 AE0 AE H = y E—-exp(-jkoz) = y Ef-exp(-jk0r cos 6) (4.2.10) 0 0 Where to = 110/6 intrinsic impedance of free space. 0 Since x =(sin 9 cos 4)? +(cos 6 cos ¢)é-sin a 8, equation (4.2.9) can be written as, +0 E1 ={(sin 9 cos ¢)r +(cos 6 cos ¢)5-sin a $}E0 exp(-jkor cos 6) (4.2.11) Now, after comparing equation (4.2.11) with (4.2.7) and (4.2.8), it can be concluded that + M01n + bnNeln] (4.2.12) +1 ' °° E = E E [a 0 ":0 n and, since the incident field is finite at r = 0, only first kind of .+ Bessel functions are allowed for fi01n and The coefficient eln' bn is determined by comparing r components of both the sides as follows: n(n+1) . l kr Jn(kor)Pn(cos 6) cos a sin 6 cos 4 exp(-jkor cos a) = 2 bn n=0 (4.2.13) Now, noting that fi%{exp(-jk0r cos e)}= jkor sin e exp(-jkor cos 6) . _ . n . and, exp(-akor cos a) — n20 (-J) (2n + l)Jn(k0r). Pn(cos 9), bn can be evaluated from eqaution (4.1.13) as, 84 _ . n-l (2n+1g bn _ (-J) h n+ (4.2.14) x +‘ To determine an, r component of H1 field is compared. Since 9 =(sin a sin a)? +(cos a sin ¢)é + cos 4 6. equation (4.2.10) can be written as, . E '+ . . A . A A o 1 ={(51n e Sln ¢)r +(cos e Sln ¢)e + cos ¢ ¢ }EQ-exp(-Jk0r cos e) 0 (4.2.15) Now from Maxwells's equations and equation (4.2.12), Hi is found to be, _.;i_ T ' wu ) [an vXM01n + bn VXNeln] (4.1.16) 0 n= -0 . + _ k + + _ + . S1nce VXMOln - ONOln and VXNeln - kOMeln’ equation (4.2.16) reduces to +1.1” 2 H CO n20 [a "N01” + bnMeln] (4.2.17) Now, comparing F components of equations (4.2.15) and (4.1.17), and after some mathematical manipulations, an is found as, _ . n (2n+l; +1 Thus E and H] can be written as =nZ ( -j)" %%%$}}-[Mélg + jN(h ) (4.2.19) and 85 +1 ._-_1_ °° _-n 2n+1 W1) 111-.1“) H Cl nZ]( J) n n+ [Me1n W01” (4°2°20) 0 Where superscript (1) on M and N denotes the first kind of the spherical Bessel function. 4.2.3 Construction of solution and computed results When the incident EM wave represented by equations (4.2.19) and (4.2.20), illuminates the sphere, there should be a similar series of functions representing the fields scattered by as well as the fields transmitted into the spherical medium. Since the fields are finite at the origin and bounded at infinity, the appropriate expressions may be written as, 55 = a. 272-45 22:5 .. .422 + .442. 2...... 115 = --:(:n:( - 3')" $1114 [ean-jd dn Ngfli (4.2.22) 25-42245 5.52:5 4412-4412 4.2.-- and At = - —g— n: ( -J')" $1;— [gnNgn- jf "Nélgj (4.2.24) -> + Where superscript (4) on M and N in equation (4.2.21) and (4.2.22) represents the use of spherical Hankel function of second kind and C. in equation (4.2.24) is intrinsic impedance of the medium. The superscripts s and t used in equations (4.2.21) - (4.2.24) 86 represent scattered and transmitted fields, respectively. Since the tangential fields must be continuous across the boundary at r = a, therefore, (El)e + (ES)e = (E )e at r = a (4.2.25) (El) MES) -(E) t - (4226) ¢ ¢ ¢ a r a . . (11")e + (115)6 = (11")6 at r = a (4.2.27) and, (ill),10 + (is), - (A ) at r = a (4.2.28) From equations (4.2.7), (4.2.8) and (4.2.19) - (4.2.28) one can get, m n 2n+l (2) Pl(cos e) nZT(-J) n n+1 [Jn(k0a) + dnhn (kOa)'fnjn(ka)] -—s1n_6——' m . n-l 2n+1 gn en “Zi(-J n n+1 ka aar {rjn (kr)} ' Rae ° _3_ (2) _1___a_ . a 1 3r {rhn (kor)} - koa 3r {rJn(k0r)}]L. SEan(cos 6)} =3 (4.2.29) E](‘j)" "22:1 [jn(k0a) + dnh32)(k0a)-fnjn(ka)] 5%{Pn(cos 9)} n: . e = ”Z ( -.1')n 1 (.4ng [F33 —{rin (krll - {la 3;{ rh£2)(k0r)} 0a P‘( ‘12—’37 {rJn(kor)}l ms," 9 - - 0a r=a 87 m P (cos a) . + . 11H)" "22,1 [Jn(k0a)+ e nhézhko al- —— 0,,9 3’ "(ka)] 15717;— w f _ . n-l 2n+1 ’50 n a . 1 - nZ]('J) n n+ [73°k5°57°{r3n(kr}} ' k—a°° - 0 a . dn 3 (2) a 1 5}- {Y‘Jn(kor‘)} - l-(B-a 31:th (kor)}] 5‘6’ {Pn(cos 9)} r=a (4.2.31) and, 2 +1 . 2 C . 1 (-1)",,;‘,.,1 11,210.) + enhf, ’(koa) - Tognan(ka)] 53—6—1133“). e1} _ m . n-l 2n+1§0fn a 1 - "2105.11 6171—1114:? r‘gfil‘jnfil‘fl - E03 ' a dn 3 (2) P;(cos e) ' 571151,,(kom ' E6” aéfi r‘hn “0”” ”sin e (4.2.32) r=a Noting that ——{rz n(kor)} = koaz$(koa) + zn(k0a), and r=a P:(cos e) 2 a 1 2 -—-§gfi-§- # [SB-{Pn(cos e)}] for arbitrary n, equations (4.2.29) - (4.2.32) are always true if and only if, jn(k0a) + dnh£2)(k0a) - fnjn(ka) = 0 (4.2.33) :1 (ka) . h(2)(k a) .1 (k 6)) 9n{5$(ka) + nka } ' en{h62° (kOa) + n koao } ‘jfilkoa) - nkog = 0 (4.2.34) 3 (k a) + e h(2)(k a) - EQ-g j (ka) = 0 (4 2 35) n 0 n n 0 c n n ' ' and, 88 - (2) C0 .' J (ka) 2). h (koa) ? fn{.]n(ka) + "ka 1 - dn{hr(' (koa) + _"_k_o.a__} _ J n(kOa) - 1;,(koa) - i136;— = 0 (4.2.36) Thus, equations (4.2.33) - (4.2.36) can be solved for the un- C . 0 _ known constants dn’ en, fn and 9". Since 7§-—1/6r and k = k0'(‘r’ the constants dn and en which are needed for the present problem, are found as, _f1, =.,/3§5-z 2n..(xx> Where Zn+%(Ax) are usua1 cy1indrica1 Besse1 functions. . _ .1.‘ zn(Ax) — Ax Zn(Ax) A150, 26(Ax) = 26::X) - -—l—2-2n(Ax) (AX) and z (Ax) 2'(Ax) "I n _ n zn(Ax) + Ax - Ax Therefore, equation (4.2.38) may be written as, .3 lno(k a)5"1(ka) fin J (k oa)3n(ka) " fiHEZ) (koa)5n(ka) - nH£2)(k0a)3"‘(ka) e Further, using the re1ation, 26(A1x)2n(A2x) Zn (A x)Zn (A2 x) Zn(*1X)zn(*ZX) = (A1x)-(x2x) (A X>2 (12x) equation (4.2.37) may be written as, f?" J (ka)3n (k0 a) - 3 Ino(k a)Jn (ka) d" Hm (k0 .305In (ka) WK" 3 0(ka)H(2)(k0 a) (4.2.43) Then, (4.2.44) (4.2.45) (4.2.46) (4.2.47) (4.2.48) (4.2.49) 91 The backscattered fie1d, EBS’ may be written in terms of Zn(k0r) as, -E w = 0 on “(2) - “(2)' E35 ZESF-nZTJ (2n+1)[-dnHn (kor) + Jean (kor)] (4.2.50) As a specia1 case, when conductivity is very high, terms having 1(‘r as a mu1tip1ying coefficient in equations (4.2.47) and (4.2.49) dominate and hence en and dn reduce to 1im en = -56(k0a)/H£2)'(koa) (4.2.51) O—XD and 1im an = -3n(k0a)/Hé2)(koa) (4.2.52) o—)oo Here, it is to be noted that, ' A - pl. 1 = ' 9."..- 11:1” Jn(ka) - cos(ka - 2 2) sm( 2 ka) (4.2.53) Therefore, this term is never zero even for the infinite con- ducitivity. Hence the expressions for en and dn’ as given by equations (4.2.47) and (4.2.49), approach re1ative1y sTowTy to the perfect1y conducting case in comparison to the fie1ds scattered by an infinite cylinder. It is a normaT practice to determine the backscattering cross- section (aTSo known as echo area) of the sphere, which is defined as, 2 2 IE I E Ae = 11m (41m2 —§§§—. = 1im (4nr2'-%§+ ) (4.2.54) r->oo I E I Y‘-*°° 0 92 NormaTized backscattering cross-section can be defined as —- _ 2 Ae - Ae/na (4.2.55) where a is the radius of the sphere. A computer program is prepared for ca1cu1ating the EBS as we11 as A; from equations (4.2.50) and (4.2.55). The program is tested for its correctness with known data [14]. These data are plotted in Figure 4.2.2 for the case with a conductivity of 99.995/m and a re1ative permittivity of 1 as we11 as for the case with a conductivity of 2.215/m and a re1ative permittivity of 7.8 at 3GHz; our computed resu1ts and the existing resu1ts are in exce11ent agreement. Figures 4.2.3 and 4.2.4 i11ustrate the change in |EBS|2 and phase angTe of EBS (in degrees) as a function of koa for the case with a conductivity of 2.285/m and a re1ative permittivity of 46 at 3GHz, and for the case with a conductivity of 10.3S/m and a re1ative permittivity of 39.9 at 1OGHz. These conductivity and re1ative permittivity represent the properties of the bioTogicaT media at the specified frequencies [11]. The computer program and printout resu1ts are given in Appendix D. From Figures 4.1.2, 4.1.3, 4.2.3 and 4.2.4, it may be observed that the phase of the backscattered fie1d varies 1inear1y with the change in koa whi1e its magnitude does not have this Tinear re1ation. There- fore, for the detection of sma11 change of a, which varies s1ow1y with time, it is easier to detect the phase change in the backscattered fie1d. Phase of EBS (in deg.) 93 *- 3.. ‘r = 1'0 o = 99.99 S/m ‘ (a) 2.. 6 =7.8 cu 1 Y' o=2.2] S/m .( / 0 1 2 3 4 ’ k a ——-> 1 0 -—--- Computed x x x 8 After Van De Hu1st[l4l 300 ” 200 100 n 0 4.2.2. Norma1ized backscattering cross section (a), and phase of backscattered fie1d EB<(b) from a sphere as a function of koa at 3 GHz. Fig. 4.2.3. 94 - 1200 » 1000 . 800 :3» Q) 'U - 600 c U) m M q... C --400 a TD .2 Q. 4-200 1 0 mall)- 8 10 12 koa a Phase and square of the magnitude of the backscattered fie1d E from a sphere as a function of koa at 3 GHz at a diééance of 30.48m. 95 ‘r= 39 9 0= 10 3 S/m ‘F f=10 GHz x/[3600 / ‘1 -5 1.2x10 J- ’ ..2400 H xf' Phase »~ .4- ,A 3} ’{I ”I '[' 'U -5 0’: V 0.6x10 4 / I 41200”, 4' a: N. 5' ol/IE I 2 m g f ‘0‘ BS ‘_ “a u. w" ,z m — I; .o’,‘ m 13"" 2 0 E 3 1k § 0 o. 0 5 1O 15 20 25 30 k a 9: Fig.4.2.4. Phase and square of the magnitude of the back- scattered fier EBS from a sphere as a function of koa at 10GHz at a distance of 30.48m. CHAPTER 5 THE DISTANT LIFE DETECTION SYSTEM DESIGN AND TESTING In the preceding chapter, it has been observed that when the radius of a circu1ar cy1inder or a sphere changes, it affects the amp1itude as we11 as phase of the return signa1. However, in genera1, if the radius is changing in time as r0u(t), the magnitude changes as Aou](t), whi1e the phase behaves as ¢0u2(t), i.e., they are not 1inear1y re1ated. Simi1ar1y, when a human being is exposed to an e1ectromagnetic- wave, the return signa1 is expected to vary in magnitude and phase with breathing as we11 as with heart beat. A1th0ugh these variations may be re1ated in a very comp1icated way, these give definite signa1$ of Tife. In this chapter, two different systems, viz, the one based on a magic tee and the other, based on a circu1ator, are ana1yzed and tested for detecting the breathing as we11 as heart signaTS from 1ong distances (~ 100 feet or over). The effects of body orientation, c10thing and poTarization of EM wave are a1$o studied experimenta11y. 5.1 Ana1ysis of the magic tee system A simp1ified b1ock diagram for detecting the breathing and heart signaTS using a magic tee is shown in Figure 5.1.1. The microwave signa1 is connected to the port 3 (H-arm) of the magic tee whi1e a detector 96 97 REFLEX KLYSTRON OSCILLATOR \g PAD FREQUENCY METER POWER ’20 05 COUPLER MONITOR H ’3 MOVABLE , k / SHORT ' T cmcun' ’ 2 \ VAR. ATT. 4 HORN ANTENNA oETEcTOR RECORDER Fig. 5.1.1. Circuit diagram of an interferometer using a magic tee 98 (so far, it may be magnitude or phase detector) is connected to port 4 (E-arm). A variab1e attenuator and an adjustab1e short is connected at port 1, and an antenna at the port 2. When the EM wave is radiated by the antenna, it hits the different objects and the backscattered fie1d is intercepted by the antenna and this signa1 works as an input to port 2. Hence, the effective impedance connected to port 2 may be con- sidered as the antenna impedance and the impedance offered by different objects connected in para11e1, through a transmission Tine of 1ength A. Now, if some parts of an object are vibrating, then the 1ength 2 and the impedance for that region is a1so changing, which, in turn, affects the ref1ection coefficient (both, magnitude and phase) at port 2. Hence, it can be assumed that an effective impedance Z(t) is con- nected at port 2 [17, 18], which gives rise to a ref1ection coefficient rR(t) at this port. A150, it can be assumed for genera1ity, that the detector gives rise to a ref1ection coefficient of PD at port 4, attenuator and the short offers a ref1ection coefficient FA at port 1. The source is a1so mismatched with a ref1ection coefficient of PG at port 3. Hence, it can be described in terms of scattering parameters as f0110ws [19], ‘ " 1 b1] ‘ S11 S12 S13 514-1 [31 52 = 521 $22 $23 $24 a2 (5.1.1) b3 S31 S32 S33 S34 a3 6’44 1:41 342 S43 S44J La4 .. 99 Where ai and bi are the incoming signa1 to and the outgoing signa1 from the ith port of the magic tee junction, respective1y. Furthermore, ai and bi are re1ated as a] = FA b1 (5-1-2) a2 = rR(t) b2 (5.1.3) a3 = bG + PG b3 (5.1.4) a4 = PD b4 (5.1.5) If the four port magic tee junction is perfect, the equation (5.1.1) may be written as '51] [0 o 1 1'1 rA b1 1 b = — o o -1 1 r (t) b (5.1.5) 2 (‘2 R 2 b 1 1 0 0 F b 4 0 4 L J L . - Equation (5.1.6) represents 4 equations in 4 unknowns, viz, b1, b2, b3 and b4 which can be so1ved for known excitation bG' However, the behaviour of b4/bG on1y need to be studied for the present pr0b1em. Fronlequation (5.1.6), J2b b -F b = b (5.1.7) 1 'P03 04 G b (5.1.8) II I U' /2b2 + r b -r 100 -FA b1 + FR(t)b2 + /2b3 = 0 (5.1 and, -rAb]-1‘R(t)b2 + /2'b3 = 0 (5.1 Thus, from equations (5.1.7) to (5.1.10), 04 FA - rR(t) bG Z-rGrR(t) - rDrR(t) - FGPA - FDPA + ZrerDrArR(t) (5.1 Now, if source and detector are matched, PG = FD = 0, and equation (5.1.11) reduces to, __. (5.1. G 2 Thus, equation (5.1.12) represents the idea1 case. It is to be noted that if the source and/0r detector is not matched, equation (5.1.11) shou1d be used, whi1e the imperfections of the magic tee can be incorporated by inc1uding appropriate coefficitents of [S] in equation (5.1.1) at the first p1ace. If PA = 0A exp(-jeA) and PR(t) = [pR + Apu1(t) exp{-jAeu2(t)}] - exp(-JeR) Where u1(t) and u2(t) are arbitrary time function repre- senting the effect due to the vibration of the body and OR exp(-jeR) represents the c1utter, then, .9) .10) .11) 12) 101 b 4 . . . —E-= %[0A exp(-JeA)-oR exp(-16R)-Apu](t) exp{-JteR + A8u2(t)]}] (5.1.13) Therefore, 2 2 lb4/bGl = hoA + 0% + {Aou](t)}2 - ZOROA cos(eR-eA) - ZpAApu](t) cos{eR-eA + A0u2(t)} + ZpRApu](t) cos{Aeu2(t)}] (5.1.14) If the attenuator and variable short is adjusted in such a way that 0A = pR and 9A = 0R, so that the clutter is cancelled, then equation (5.1.14) reduces to, |b4/bG|2 = {%§-u](t)12 (5.1.15) The phase angle 04 of b4/bG can be found from equation (5.1.13) as, -pA sin 6A + pR sin 6R + Apu1(t)sin{oR + Aeuz(t)} pA cos 8A - pR cos 6R -Apu1(t)C0S{6R + Aeu2(t)} (5.1.16) 04 = arc tan [ For pA = OR and 0A = 0R, it reduces to, 04 = -eR -Aeu2(t) (5.1.17) Thus from equations (5.1.15) and (5.1.17), it may be noted that the magnitude detectors, which behave as square-law, will respond to 102 the square of the half of the variations, while the phase detectors will respond linearly. Since these variations are assumed very small, the phase detectors may be preferred over the magnitude detectors for re- 1ative1y large sensitivity. 5.2 Analysis of the circulator system Figure 5.2.1 illustrates a simplified circuit using a three port circulator which can be used for detecting the breathing and heart signals. As discussed in the preceding section, the antenna is replaced by a load which offers a reflection coefficient rR(t). In general, any three port network can be described by, P q - 1 r . b1 S11 S12 S13 I 31 52 = $2, $22 523 a2 (5.2.1) P3, ‘(531 S32 533] _as. Where a's and b's are as defined in the preceding section, and for the present system (tuner connected at port 2 in Figure 5.2.1 is ignored for time being), a1 = bG + PG b1 (5.2.2) a2 = PR(t) b2 (5.2.3) and a3 = FD b3 (5.2.4) 103 .MOumasuuHo m wcflm: uwumEoummumucH cm mo Empwmwv ufisuuwu .H.N. «$950.3 cOhUMhmo auznh Ewauw moeéw J \ meQDOuM moom M 043 L q.wa 1m mmhwE >uzm30ucu :OCZOZ mmBOa a0h<4.:umo zoahw>4x quuwm 104 Thus, equations (5.2.1) - (5.2.4) give three algebraic equations in three unknowns, viz, b1, b2 and b3, which can be solved easily. However, for the present problem, only b3/bG is of interest. Further, assuming that the three port circulator is an ideal circulator, its scattering matrix may be found as [20], o o 1 [s] = 1 o 0 (5.2.5) o 1 0 Hence, from equations (5.2.1) - (5.2.5), b3/bG is found as, E§__ rR(t) b _ (5.2.6) G l - FDFGPRIt) It can be simplified further assuming that the source and the detector are matched such that PG = FD = 0. Therefore, b3/bG = rR(t) (5.2.7) If rR(t) = [pR + Aou](t)exp{-JAeu2(t)}]exp(-JeR) Where pR exp(-jeR) is due t01clutter and Apu](t)exp{-jeR-jAeuz(t)} is due to the vibration of the body, then the phase, 93, and the square of the magnitude of bB/bG is found as, -pRsin 6R -Apu](t)sln{0R + A0u2(t)} = arc tan[ ] (5.2.8) pR cos 9R + Apu](t)COS{0R + Aeu2(t)} e3 105 and |b3/bG|2 = p: + {Apu](t)}2 + ZoRApu](t)COS{Aeuz(t)} (5.2.9) Now, if the tuner connected at port 2 of the circulator is ad- justed such that OR = 0, or the clutter is cancelled, equations (5.2.8) and (5.2.9) reduce to, 03 = -eR-Aeu2(t) ' (5.2.10) and Ib3/b0'2 = [Apu](t)]2 (5.2.11) Comparing equations (5.2.10) and (5.2.11) with (5.1.17) and (5.1.15), respectively, it may be noted that both systems have similar response. However, the circulator system has an advantage of having a 6 dB higher magnitude of the return signal in comparison to magic tee system. 5.3 The magic tee system for life detection The schematic diagram of the X-band life detection system uSing a magic tee is shown in Figure 5.3.1. A klystron microwave generator generates a C.ML microwave at 9.350Hz with a power of about 10 mW. This wave is passed through an isolator, a frequency meter, a fixed attenuator, another isolator and a tuner before entering arm 1 of the hybrid T. This incoming wave is divided into arms 2 and 3 of the hybrid T. One wave E1 = A1 cos wt coming out of arm 2 of the hybrid T passes .Emummm comuomumc meF vcma-x mg“ mo accomwu ovumsmgomfi.m.m.mwa .u.n + Ae+fluvsemrocuws Lm_o:ou wooum A Louoopov .uumc?t mm mm 106 107 through another tuner and then radiates out through the antenna. In the beginning, the two tuners are adjusted in such a way that hybrid T behaves as a magic tee [21]. The wave radiated through the antenna illuminates the subject and the surrounding, and the reflected wave E2 coming back to the antenna may consist of a scattered wave modulated by the subject's body motion caused by heart beat and breathing and a clutter wave reflected by the stationary surrounding. The modulated signal can be expressed as A2 cos (mt + A¢u(t)), where A¢u(t) re- presents the phase perturbation caused by the heart beat and the breathing. The c1utter wave can be expressed as A3 coshnt + ¢c). Another wave E1 coming through arm 3 of the hybrid T gives a reflected wave, E3 = -A3 cos(wt + ¢c)’ which is the negative of the clutter wave, when the variable attenuator and the variable phase shifter (variab1e short) are properly adjusted. When E2 and E are combined in the hybrid 3 T, the clutter wave is cancelled and the resultant wave E4 coming out of arm 4 of the hybrid T contains only the modulated wave, A2 coshmt + A¢U(t)). It is now aimed to measure the phase perturbation A¢u(t) by mixing E4 with a reference wave E5 = A5 cos(mt + ¢) in the second hybrid T ( it is also tuned to behave like a magic tee). E4 is fed into an arm of the second hybrid T after passing through an isolator and a tuner. The reference wave E5 is obtained from the main wave- guide through a 10 dB directional coupler and its amplitude and phase are adjusted by a variable attenuator and a variable phase shifter before it is fed into another arm of the second hybrid T. The phase ¢ of E5 is adjusted in such a way to maximize the sensitivity in the detection of A¢u(t). As E4 and E5 are fed into two arms of the 108 second hybrid T, two outputs from two other arms of the second hybrid T take the forms of E4-E5 and E4+E5. When these two waves are de- tected, the resultant outputs are E6 and E7. The wave E6 consists of -A2A5 cos(A¢u(t) + o) and a d.c. component and, similarly, E7 includes A2A5 cos(A¢u(t) + ¢) and a d.c. component. When E6 and E7 are fed into a differential amplifier, it gives an output of 2 A2A5 cos(A¢u(t) + o). This output signal is of extremely low frequency (heart beat or breathing frequency) and can be measured by a scope, a chart recorder or an acoustic indicator. The typical measured heart and breathing signals by this X- band life detection system are shown in Figure 5.3.2. Figure 5.3.2(a) shows the recorded heart signals when the human subject was sitting at a distance of 17 feet facing the antenna which radiated a power of 4.5 mW at 9.350Hz. The heart signal was recorded when the subject was holding the breath. In this figure, the heart beat is clearly observed at an interval of about 0.87 second. The large signals at both ends of the recording are due to the breathing. As the distance between the human subject and the antenna was increased beyond 20 feet, the heart signal became obscure. However, the breathing signal was detected at a distance of upto about 90 feet. Figure 5.3.2(b) shows the recorded breathing signal of the human subject who sat at a distance of 80 feet facing the antenna. The subject was breathing at an interval of 2 to 3 seconds. A significant improvement in the performance of the system was found when a phase-locked oscillator was used in place of klystron I. breathing heart beat breathing (a) Recorded heart signal; the human subject holding the breath at the distance of 17 feet. The heart beat is clearly seen at an interval of about 0.87 second. The large signals at both ends of the recording are due to breathing. The antenna radiated power is 4.5 mW. breathing (b) Recorded breathing signal; the human subject at the ditance of 80 feet was breathing at an interval of 2-3 seconds. At this long distance only the breathing pattern can be clearly observed. The heart signal is immersed in the noise. The gain of the amplifier system was increased from case (a) for this recording. Fig.5.3.2Heart and breathing signals measured by the x-band life detection system. 1 \UL. . _ .q 1.- "wart (holding the breath 5 mN ; . ‘ radiated 5 ’-g power 1 1 1 l -L_ ly‘ng on the groqnd 41th fa<+ or (bad; awrpe'11LU1ar to the beam) uackground noise breathincl heart (holding the breath) _u. i. ; ; rr:* , 1’ 1 ’1 r“““ . 1- 4 1 L- 1..-; -.- -3- I ;_ I 1 . | 1 - '1 r— »: - ‘ --1—- 4— ”AMI—«.4 1 3 . 1 2.5 mW radiated power 1 1 .' 1 1_ .1__.;1--1 lying or tn; ground with face up (body serpen01Cular to the beam) background noise HDV\Ah~enL’TP\H’Vxn,/“r\"‘fw+'quu‘" 1 Fig5.3.3. Recorded heart and breathing signals 0‘ 0 human subject lying on the ground at a distance of 100 ft. The life detection system uses a magic T and the radiated power is 5 mH or 2.5 mW at 10 GHz. 110 111 smumxm cowuumumc mm?F acu314.q;m.m.mwu “Auvzec + mevmoum 82.6 me E e rs . a a, Lmfigzou \ aw ..uuocmn ‘ me o -1 me i 11111.1 1.! .5 m :5 OON ~me 9 % 1.411 1? 11111 mpnmwwm>w1 111 5:295. L 38.27250 .11 _1111r111L mm1mmmm m>mzoLo_E nmxuop1mmmgn .68 4r.\ , accmucm .uumeo Loam~suc_o 115 a circulator. The horn antenna radiates a microwave beam of about 10° beamwidth aiming at the human subject lying on the ground. The re- ceived signal by the antenna consists of a large clutter and a weak return signal scattered from the body. The large clutter signal is cancelled by a reference signal, the amplitude and phase of which are adjusted by a variable attenuator and a phaseshifter, in a 10 dB direct- ional coupler. After this clutter cancellation, the output of the 10 dB directional coupler contains only the weak scattered signal from the body. This body-scattered signal is a lOGHz cw microwave modulated by the breathing and the heart beat. This signal is then amplified by a low-noise microwave preamplifier of 30 dB gain. The amplified, body—. scattered signal is then mixed with another reference signal in a double- balanced mixer. In between the microwave preamplifier and the double- balanced mixer, a 10 dB directional coupler is inserted to take out a small portion of the amplified signal for monitoring its intensity. This monitoring is mainly for checking how well the clutter is cancelled. The mixing of the amplified, body-scattered signal and a reference signal (7 ~ 10 mW) in the double-balanced mixer produces a low frequency breathing and heart signals which modulate the scattered microwave from the body. This output from the mixer is amplified by an operational amplifier and then it passes through a low-pass filter (4 Hz cut-off) before reaching a recorder. The typical measured breathing and heart signals are shown in Figures 5.4.2 - 5.4.4. For the results shown in Figure 5.4.2, the antenna radiated with a power of 45 mw at lOGHz and the microwave 116 lying on the ground with face up (body perpendicular to the beam) _ IbreathingI .. I __ I heart (holding breath) ' ‘ - . '1' ‘ é ‘.::“*'-' F779¥:§5* -. . = i . . 2 _~ | lying on the ground with face down (body perpendicular to the beam) breathing heart (holding breath) I l lying on the ground with face down (body parallel to the beam) breathing aghgg g Egg? “Egmfieas Fig.5.4.2Heart and breathing signals of a human subject lying on the ground measured at a distance of lOO ft. with a power of 45 mw at l0 GHz. 117 on the ground with f (bogy_perpendicular ‘ ‘ ' ’ , ~d%;te4_eheart~( . l r-.._ i 1' 'L . , ,L, -1 —l , .. lying on the ground with face down (body Fig.5.4.3.Heart and breathing signals of a human subject lying on the ground measured at a distance of lOO ft. with a power of ll.25 mw at l0 GHz. (Amplifier gain increased). 118 breathing si with f up ( heart signal (holding the breath) lying on the ground with face up (body perpendicular to the beam) Fig.5.4.4.Heart and breathing signals of a human subject lying on the ground at a distance of 100 ft. measured with a microwave beam with a power of 4.5 mw at 10 GHz. (Amplifier gain further increased). 119 beam was aimed at a human subject lying on the ground at a distance of 100 feet. The top figure shows the results when the subject's body with face-up was perpendicular to the direction of the microwave beam. The left portion of this figure shows the breathing signals (superim- posed with the heart signals) and the right portion of the figure in- dicates only the heart signal when the subject held the breathing. In this figure, both the breathing and heart signals are clearly recorded. The second figure from the top of Figure 5.4.2 shows the recorded breathing and heart signals when the same subject lay face-down on the ground at the same location. It is interesting to observe that with the face-down position, the breathing and heart signals unexpectedly became stronger than the face-up case. The third figure from the top of Figure 5.4.2 shows the recorded breathing and heart signals when the position of the human subject was rotated to the direction parallel to the microwave beam. For this case, the breathing signal was clearly measured but the heart signal became rather obscure. It was found that when the body position was slightly adjusted, the heart signal could be enhanced. The bottom figure of Figure 5.4.2 shows the recorded back- ground noise. It is noted that the background noise varied from day to day depending on the movement of the machines, air conditioners and elevators in the building. On some occasions when the background noise was lower, it was easier to measure heart signals of human subjects lying in various positions at a distance of 100 feet or farther. Figure 5.4.3 shows the measured breathing and heart signals of the same human subject when the antenna radiated power was reduced to ll mw and the gain of the operational amplifier was increased. The brwif MM. heart (holding breath) 5 mw radiated power 'tmzlyvlvvuxvn‘,;-.zfgn_h; Y..' 3:1; rlfII-JII; I! . I I I i“ I. lyinc or the grOund with face up (body perpendicular to the beam) bac ground Oise 7' tuirxx 1 -: l:st.ls ‘ : $31.;V; - . artyitzrzi.‘ ....'.;: 5' "g; .; I .; I”! . 4.....a_.s. " ”-—ri. . . .1 i ' 7‘7 _L i Me i T . . 2.x. breathint ' heart (holding breath) 1 ' ‘ ! ‘ ‘ 2.5 mw radiated power FigSo4-5- Recorded heart and breathing signals of a human subject lying on the ground at a distance of TOO ft. The life detection system uses a circulator and the radiated power is 5 mw or 2.5 mw at l0 GHz. 120 121 human subject lay at a distance of lOO feet with face-up or face-down position and with the body perpendicular to the direction of the micro- wave beam. It is observed in this figure that the breathing and heart signals were clearly recorded and the background noise was also reduced. Figure 5.4.4 shows the measured breathing and heart signals of the same human subject lying at the same location when the antenna radiated power was further reduced to 4.5 mW and the gain of the operational amplifier was increased further. Surprisingly, with a lower radiated power the recorded heart signal seemed to be even clearer than the previous cases of higher radiated power. This phenomenon may be ex- plained as follows. As the radiated power is increased, the clutter and the body scattered signals are both increased and when they exceed a certain level the microwave preamplifier may start to saturate. Therefore, the increase in the antenna radiated power may not enhance the amplitude and quality of the measured breathing and heart signals. Figure 5.4.5 illustrates the breathing and hearth signals of a human subject lying on the ground at a distance of 100 feet with radiated power of 5 mW or 2.5 mW only. 5.5 Effects of clutter cancellation, polarization, and the clothing of the human subject on the system performance When the life detection system operates at different backgrounds, the nature of the clutter also varies. With the present system, it is easy to cancel or minimize different clutters with amplitude and phase adjustment in the cancellation circuit. When the clutter is not can- celled, the sum of the clutter and the body scattered signal can easily 122 saturate the microwave preamplifier, and consequently, leading to the failure of heart signal detection. To study this effect a series of experiments were performed and the results are shown in Figures 5.5.l - 5.5.2. In this series of experiments, the antenna radiated power was kept constant while the level of uncancelled clutter was varied by detuning the clutter cancellation circuit. The top figure of Figure 5.5.l shows the recorded breathing and heart signals when the power level after the microwave preamplifier was 3 mW. This condition represents a good cancellation of the clutter and a significant portion of the input signal to the microwave preamplifier may consist of the body- scattered wave modulated by the heart beat. Because of this condition, the breathing and heart signals were clearly detected. The second figure from the top of Figure 5.5.1 indicates the recorded breathing and heart signals when the clutter was not very well cancelled, by purposely detuning the clutter cancellation circuit slightly, and the power level after the microwave preamplifier was increased to 5 mW. This increase in the output power of the microwave preamplifier was entirely due to an increased level of the uncancelled clutter because the antenna radiated power and the position of the human subject were unchanged from the previous case. Under this condition, the breathing and heart signals were still clearly recorded, implying that the micro- wave preamplifier was still working in the linear range. When the un- cancelled clutter was further increased to a level that the microwave preamplifier output reached 60 mW, the recorded breathing and heart signals start to deteriorate as shown in the third figure from the top in Figure 5.5.l. This phenomenon clearly indicates the start of the saturation of the microwave preamplifier. 123 breathing heart (holding breath) . ' ' , ‘ ' E z ' zf‘i‘l"-" t? 3 mW after preamplifier 5 mW after preamplifier 60 mW after preamplifier Fig.5.5.1.Performance of the system as a function of signal power level (heart signal plus clutter) input to the mixer. breathing 'TIT - : 80 mW after ' . preamplifier (without an attenuator) with 3 dB attenuator connected after preamplifier with 3 dB attenuator connected before preamplifier background noise "%.w ._ - , 1-- . - 1. __cs :rflia-‘lsr'ti- lid-£1: i-.;1_1i__; ..: without attenuator with 3 dB attenuator FWQLSoS-Zéffect of microwave preamplifier saturation on the syStem performance. The output of the preamplifier was 80 mW and the preamplifier was saturated due to a large un- cancelled clutter. Under this condition, the heart signal was obscure even though the breathing signal was detect- able. A 3 dB attenuator connected after the preamplifier can not recover the heart signal. The attenuator connected before the preamplifier can neither recover the heart signal because it reduced both the clutter and the body-scattered signal input to the preamplifier. 125 When the uncancelled clutter was increased to a level that the output of the microwave preamplifier became more than 80 mW, the saturation of the preamplifier caused the recorded heart signal to be quite obscure even though the breathing was still very clearly recorded. This phenomenon is shown in the first figure at the top of Figure 5.5.2. To further study this effect, a 3dB attenuator was inserted after and before the microwave preamplifier in an attempt to undo the saturation of the preamplifier. In either case, a clear heart signal could not be recovered due to the following probable reasons. When the 3dB attenuator was inserted after the microwave preamplifier (the second figure from the top in Figure 5.5.2), the saturated and distorted heart signals after the preamplifier were reduced in amplitude but its quality was not improved. Also from this experiment, it is observed that the deterioration of the heart signal was not due to the saturation of the double-balanced mixer, but rather was due to the saturation of the microwave preamplifier. When the 3dB attenuator was inserted before the preamplifier to undo the saturation of the preamplifier (the third figure from the top in Figure 5.5.2), a clear heart signal was not recorded either. The reason for this result was probably due to the fact that the 3dB attenuator while reduced the clutter it also reduced the body-scattered wave. Thus, the heart signal became too weak to be detected. The bottom figures in Figure 5.5.2 show the background noise levels in the experiment. The results of Figures 5.5.l - 5.5.2 indicate the importance of the clutter cancellation and the operating range of the microwave preamplifier. It is essential to operate the microwave preamplifier 126 breathi Iheart beat“ circular polarization _ _. __....'..'.I__. background noise, . . . H , . . ....,.. . , _ __ I I l sec breathin a”tii ‘ _ ,_-b§art.be,a.t:_, linear- vertical polarization I 1 . r 1‘1; ; I ~1"3-::';:-x- I. II .JIJ. ., ;. IIII .L. i < i: background : si~gi _ is ~L§ noise 1 - "I '1 tt'I .3 . 3:2. "I; ' 1 5 .I '7' I- ':: 1 ‘ 1 1 101 1 a heart beat ‘ W '2 '1111' ‘3; 1 -1'; linear- horizontal polarization é ’ '57 ": m' 1‘ 1'311';i' background ., .' '1;:' . L...‘.. '1'. . 'i.. .. .. 5. noise 'IL;-J>"t;31;-: (9551; Tig.5,5,3,Measured breathing and heart signals from a human subject lying on the ground at a distance of lOO ft. with a microwave beam of 20 mW at l0 GHz with different polarizations; (l) circular polarization, (2) linear-vertical polarization and (3) linear- horizontal polarization. 127 in its linear range and to avoid the preamplifier saturation by a proper control of the clutter cancellation. The second factor which may affect the system performance is the polarization of the microwave illuminating the human body. It was suspected that a certain type of polarization may lead to a best heart signal detection. To test this conjecture the circular polarization, the linear-vertical polarization, and the linear-horizontal polarization were employed. The circularly polarized wave was produced with a cir- cularly polarized horn antenna commonly used in the car radar system. The linear-vertical and horizontal polarizations were produced by a home made pyramidal horn antenna. The results of the measured breathing and heart signals of a human subject lying on the ground at a distance of lOO feet with these three polarizations are shown in Figure 5.5.3. It is observed that the different polarizations did not cause a signi- ficant difference in the detection of breathing and heart signals when the human subject was lying on the ground at a distance of lOO feet. However, for shorter distances (20 ~ 40 feet) and the human subject lying on a metallic ground plane, the polarization effect on system performance is found to be more significant. As one of the requirements, it is highly desirable to design a distant life detection system which performance is not significantly affected by the clothing of the human subject to be illuminated by the microwaves. Ideally, a microwave of particular frequency should be selected which can easily penetrate the clothing. It has been found that the X-band microwave at lOGHz can penetrate the clothing quite well as evidenced by the results shown in Figure 5.5.4. The top figure 128 its» breathing heart M . . l T L I . a... ...- ha ....... r 'r“ I I ..-.J-.._.'-..- . , ..A--. l . . . . .1 I. I ,- a... . . . .g. 0 ' ‘ ‘ 1 ~ -. >-~o‘ t-e Or.‘ -5 - --. ...' (a) recorded breathing and heart signal of a human subject with one layer of clothing lying on the ground at a distance of 100 ft breathing heart o>~ w.-. ...... """"""""" .I.i 3. .. . . ..J . '91:." '1";" . r i Q I I l 1 1 l n ' ’.I.‘. .w~hl I 10 . . 1! '1'1, '91. 511.. - .1 i .. 5 H (b) recorded breathing and heart signals of the same human subject covered with four layers of clothing lying on the ground at a distance of 100 ft. 1:11;?! 1 1 1 1";111 :‘i W11éhi'h 1.. .‘ Fig.5.5.4. Effect of the clothing of the human subject on the performance of the distant life detection system. 129 of Figure 5.5.4 shows the measured breathing and heart signals of a human subject with one layer of clothing lying on the ground at a distance of 100 feet. The antenna radiated a linear-vertically polarized wave with a power of lo mW. It is observed that both breathing and heart signals were clearly detected. The bottom figure in Figure 5.5.4 shows the recorded breathing and heart signals of the same human subject covered with four layers of clothing, three of them were heavy, lying at the same location. This result shows a slight reduction in the amplitude of the measured heart signal but the quality of the measured heart signal remains good. After many more experiments it is concluded that the effect of clothing on the heart signal detection is not signi- ficant at the X-band around l0 GHz. 5.6 Detection of breathing and heart signals through a concrete wall For the completeness, the performance of the life detection system was also studied through a concrete wall. It may be interesting to test whether the system can detect the breathing and heart signals of human subjects located behind a concrete wall. Surprisingly enough, the system was able to detect the breathing and heart signals of a human subject sitting at a distance of l0 feet behind a concrete wall with an antenna radiated power of only 20 mW. With a higher radiated power, the detectable distance is expected to increase further. The results of this experiment are shown in Figure 5.6.l where the measured breathing and heart signals of a human subject sitting behind a 6 inch concrete wall at a distance of 2, 7 or l0 feet are given. The antenna breathing heart beat 1 . subject at 2 ft. from the wall ._.,,. . $00.0-“ a... background noise IF:— _.....—-c 1 : I-‘II, 1 7" ... I III ‘ ‘ I ' . . 1m4sct.i.:f?1 .kfitu-si e 1 l sec breathing ”-- heart beat III N -y... i .0 7 ft. from the wall I‘I-*:"I:{ _ ; ;-.- 4': .. background ;¢.aIw2::?;ua?tui'.u1 "°ise r _;; - -,-_ 1 I . . .- -. ~ >4 ..9. .. ng‘ \ .4. ... - . c o , | , . ~ _ ,...-..- > breathing_ eart_be§t 7 ‘ T:' TC’TITT'" " ' ,L l", '1 . . L . .' ..,.. , _-.. .. ' .. . . ... .Q.. . ' -. - . ., c -. .. --6. ,-§-... 1 . i. 0‘ '1 '1‘ I ._.,. ... ...‘ 1" . . "‘, .. 10 f . . . 2 1. L»h ... .. e .. ' . . .. ..-4 . .5...| .. . _... .I -, .. T -. . ' .An .1 w from the ‘ 1 ' ' ' 1 " ‘ ‘ W W31] .1 ' i; . . , -3' ',”,.fi;. ... 1 ' "3' 4' 1 g . . 1‘5’TJ'4"1 rg—:-a+-I '1 " "; background 1 . ....i‘ t ‘1 - --¢:~. ‘-*1 noise Fig.5.6.1.Measured breathing and heart si nals from a human subject sitting behind a concrete wall (6" thick) at various dis- tances. The antenna of the life detection system was located at the other side of the wall and radiated with a power of 20 mW at 10 GHz. 130 131 was located close to the wall and radiated with a power of 20 mW. In this experiment, it was necessary to use a matching (tuning) circuit between the antenna and the circulator to match the antenna through the wall, or to reduce a large reflection of microwave from the wall. In Figure 5.6.l, the breathing and heart signals are clearly recorded for all the three distances. CHAPTER 6 SUMMARY This thesis presents a study of the scattering of electromagnetic waves by the human body and also demonstrates some of its possible appli- cations. The aim and scope of this study is presented in Chapter l. In Chapter 2, the EM field near a cylindrical biological body illuminated by a plane wave is analysed and the responses of the single and orthogonal E-field probes located near the body-surface are determined. These results were experimentally verified in Chapter 3 using a cylindrical dielectric shell filled with saline solution at the fre- quencies of ZGHz, 2.45GHz and BGHz. The theoretically computed results for the empty shell are also compared with the experimentally recorded probe responses. An excellent agreement is found between the theory and the experiments. Some additional theoretically computed results of the probe response near the biological body are also presented in this chapter. The shadowing effect due to the body and the difference in the probe response in the presence and in the absence of the body are noticed. In Chapter 4, an expression for the backscattered electric field from a cylindrical body illuminated by a plane wave is obtained. The variations in the magnitude and phase of this backscattered field is then studied assuming the body-radius changes with time. In the latter part of this chapter, an expression for the backscattered electric field from a spherical body exposed to the plane EM waves is obtained and the 132 133 effect of the change in the radius of the sphere with time on the magnitude and phase of the field is studied. It is noted that the change in the phase of the backscattered field is linear with the change in the radius of the cylindrical or spherical body. However, the magnitude of the return signal is not linearly affected by the change in the radius in both cases. Two different techniques are presented in Chapter 5 for detecting the breathing and heart beats of humans from large distances. In one, a magic tee is used while in the other, a circulator is employed. The breathing and heart signals from the distance of upto lOO feet and also through a concrete wall are reported in this chapter. The ap- plication of these techniques for remotely detecting the physiological status of humans at distances or trapped living beings behind the barriers is noted. [l] [2] [3] [4] [5] [6] [7] [8] [9] REFERENCES K.M. Chen, "Interaction of electromagnetic fields with biological bodies", Research Topices in Electromagnetic Wave Theory, J.A. Kong, Ed., Ch. l3, Wiley-Interscience, NY, 198l. J.C. Lin, J. Kiernicki, M. Kiernicki and P.B. Wollschlaeger, "Microwave apexcardiography", IEEE Trans. Microwave Theory Tech., vol. MTT-27, No. 6, pp. 6l8-620, June l979. D.W. Griffin, "MW interferometers for biological studies", Micro- wave J., vol. 2l, No. 5, pp. 69-72, May l978. E.C. Jordan and K.G. Balmain, "Electromagnetic Waves and Radiating Systems", Prentice-Hall, N.J., l968; p. 535. W.L. Stutzman and G.A. Thiele, "Antenna Theory and Design", Wiley, N.Y., l98l; pp. 229-235. E.K. Miller, A.J. Poggio, G.J. Burke and E.S. Selden, "Analysis of wire antennas in the presence of a conducting half space. Part I. The vertical antenna in free space", Canadian J. Physics, vol. 50, pp. 879-888, l972. , "Analysis of wire antennas in the presence of a conducting half space. Part II. The horizontal antenna in free space", Canadian J. Physics, vol. 50, pp. 26l4-2627, l972. R.W.P. King, "The Theory of Linear Antennas", Harvard University Press, Cambridge, Mass., l956; pp. lQl-l92. R.S. Elliot, "Antenna Theory and Design", Prentice Hall, N.J., l98l; pp. 332-333. [l0] G. Arfken, "Mathematical Methods for Physicists", Academic Press, N.Y., 1970; p. 488. [ll] C.C. Johnson and A.W. Guy, "Nonionizing electromagnetic wave ef- fects in biological materials and systems", Proc. IEEE, vol. 60, No. 6, pp. 692-7l8, June l972. [l2] J.A. Saxton and J.A. Lane, "Electrical properties of sea water", Wireless Engineer, vol. 29, pp. 269-275, Oct. l952. 134 [13] [14] [15] [l6] [17] [18] [19] [20] [21] [22] [23] 135 G.S. Smith, "Analysis of miniature electric field probes with resistive transmission lines", IEEE Trans. Microwave Theory Tech, vol. MTT-29, No. ll, pp. l213-l224, Nov. l98l. H.C. Van De Hulst, "Light Scattering by Small Particles", Wiley, N.Y., l957; PP. 285-286 and 313-320. J.A. Stratton, “Electromagnetic Theory", McGraw Hill, N.Y., l94l; pp. 563-573. S.A. Schelkunoff, "Electromagnetic Waves", D. Van Nostrand, N.J., l943; PP. 5l-52. A. Thansandote, S.S. Stuchly and J.S. Wright, "Microwave inter- ferometer for measurements of small displacements", IEEE Trans. Instrum. Meas., vol IM-3l, No. 4, pp. 227-232, Dec. l982. - P.C. Pedersen, C.C. Johnson, C.H. Durney and 0.6. Bragg, "An investigation of the use of microwave radiation for pulmonary diagnostics", IEEE Trans. Biomed. Eng., vol. BME-23, No. 5, pp. 4l0-4l2, Sept. 1976. D.M. Kerns and R.W. Beatty, "Basic Theory of Waveguide Junctions and Introductory Microwave Network Analysis", Pergamon Press, N.Y., l967; pp. ll6-123. B. Lax and K.J. Button, "Microwave Ferrites and Ferrimagnetics", McGraw Hill, N.Y., l962; pp. 5l8-522. T. Tamaru, "A note on bolometer mount efficiency measurement technique by impedance method in Japan", IEEE Trans. Micro- wave Theory Tech., vol. MTT-l4, No. 9, p. 437, Sept. 1966. K.M. Chen, S. Rukspollmuang, and D.P. Nyquist, "Measurement of induced electric fields in a phantom model of man", Radio Science, vol. l7, No. SS, pp. 49S-59S, Sept.-Oct. l982. M. Goldstein, "Bessel Functions, for complex argument and order", AEC Computing and Applied Mathematics Center, Courant Institute of Mathematical Sciences, New York University. Nov. l965.‘ APPENDIX A Com uter program for determining the response of an . gr; ogonally connected E-probe system near the cylindrical o y. 136 nonnnnnnnnnnnnnn 137 PROGRAM SHELL (INPUT,OUTPUT,TAPE l0 - INPUT,TAPE 20 - OUTPUT) DIMENSION BJRE(75). BJIM(75),YRE(hl), YiM(hl) COMPLEx BODYl,BODY2,WKl,WK2,WKlRl,WKZRl,WK2R2,ZLOAD,ZINPUT,FACTRZ *,FACTRl,VEQPH|,CURENT.VEQRAD,DHARA,VEQTE,TELOAD COMMON WKl,WK2,WKlRl,WKZRl,WK2R2.CKO.CKOR.CKOR2 9mm!Swami:”Mimic”!kahuna":thud:************************************* THIS PROGRAM COMPUTES THE LOAD CURRENT DETECTED BY E-FIELD PROBE NEAR Two CONCENTRIC CYLINDRICAL MEDIA OF COMPLEx PERMITTIVITIES. SIGMAl AND SIGMAz ARE CONDUCTIVITIES OF INNER ANO OUTER MEDIA, RESPECTIVELY,WHILE DIELCl AND DIELCZ ARE RELATIVE PERMITTIVITIES. IT READS THESE DATA AND FREQ FROM FORMATTED DATA CARDS.FIELD IS MAGNITUDE OF INCIDENT E-FIELD,ANGLE IS ITS POLARIZATION ANGLE MEASURED FROM THE PLANE PASSING THRO. THE PROPAGATION AXIS AND AXIS OF THE CYLINDER.RI AND R2 ARE THE RADII OF INNER AND OUTER CYLINDERS. HEIGHT IS HALF OF THE LENGTH OF PROBE LOCATED AT R FROM THE CYLINDER AXIS. A l0 KOHM RESISTOR IN PARALLEL WITH 6 PF CAPACITOR IS ASSUMED LOAD FOR THE PROBE AND SQURE-LAW DETECTOR IS ASSUMED. IN THE 0UTPUT,IT PRINTS THE CURRENTS FOR THREE INDIVIDUAL PROBES AS WELL As THE TOTAL CURRENT FOR THE THREE ORTHOGONALLY CONNECTED PROBE SYSTEM AROUND CYLINDER AT 5 DEGREE INTERVAL. *a’ddn’t*************9:*********************************************** FIELD-2.0 ANGLE-A5.O HEIGHT-0.0065 Rl - O.iA6 R2 - 0.152A R-0.l56 Pl - A.O A ATAN (1.0) DO 99 M - 1.3 READ(l0,l)S|GMAl,SIGMA2,DIELCl.DIELC2,FREQ FORMAT(2F6.A,2F5.2.EIT.h) FREEMU - h.0E-O7*PI VACCUM - 8.85hE-l2 PHlo-ATAN(HEIGHT/R) VELITE - 3.0E+08 OMEGA - 2.0 A Pl * FREQ CKO - OMEGA / VELITE DIERl - DIELCl * VACCUM DIER2 - DIELCZ * VACCUM BODYl - CMPLx(DIERi.-(SIGMAi/OMEGA)) BODYz - CMPLx (DIER2.-(SIGMA2/OMEGA)) SQROMG - OMEGA **2 WKl - CSQRT(SQROMG*FREEMU*BODYl) WKZ - CSQRT(SQROMG*FREEMU*BODY2) wKiRi - WKl*Rl wszi - WK2*Rl wK2R2 - WK2*R2 CKORZ - CKO*R2 CKOR - CKO*R RLOAD-i.OE+OA XLOAD-l.0E+lZ/(6.0*0MEGA) 75 750 200 hhh Ill 99 133 ZLOAD-RLOAD*CMPLX(0.0.-XLOAD)/CHPLX(RLOAD,-XLOAD) BETAHsCKO*HEIGHT RINPUT-l8.3*(BETAH**2)*(I.O+0.086*(BETAH**2)) ' X1NPUT--396.0*(1.0-0.383*(BETAH**2))/BETAH ZINPUT-CMPLx(RINPUT.XINPUT) FACTRI-ZINPUT+2LOAD FACTR2=2INPUT+ZLOAD ANGLRD-ANGLE*Pl/180. wRITE(20,2)FREQ,FIELD,ANGLE FORMAT(IHI,5x,IIHFREQUENCY -,EII.A,5x,7HFIELD -,F5.2,5x, *7HANGLE -,F6.2./) NRITE(20,75) FORMAT(2x,6HPHI IN.3x,15HL0AD CURRENT SQ.3x.15HLOAD CURRENT SQ, *3X,15HLOAD CURRENT SQ,3x,15HLOAD CURRENT SQ) NRITE(20.750) FORMAT(2x,3HDEG,6x,7HFOR PHI,IIx,5HFOR R,13x,6HFOR TE,12x, *5HTOTAL.//) PHI . 0.0 00 A I . 1,15 00 AAA J - 1,5 PHIR - PHI * Pl / 180.0 CALL TMPHI (PHIR,VEQPHI,PHI0) CURENT-FIELD*VEQPHI*SIN(ANGLRD)/FACTR1 CALL TMRAD (PHI,VEQRAD,HEIGHT) DHARA-FIELD*VEQRAD*SIN(ANGLRD)/FACTR2 CALL TEHAVE (PHIR,VEQTE.HEIGHT) TELOAD-FIELD*VEQTE*COS(ANGLRD)/FACTRI AA-CABS(CURENT) BA-CABS(DHARA) CA-CABS(TELOAD) AASQ-AA**2 BASQ=BA**2 CASQ-CA**2 DA-AASO+BASO+CASQ wRITE(20,2OO)PHI,AASQ,BASQ,CASQ,DA FORMAT(2x,F6.2,3x,EI1.A,7x,EII.A.7x,EII.A,7x,E1I.A) PHI - PHI+5.0 |F(PHI .GE.365.O) GO TO 99 CONTINUE HRITE (20.111) FORMAT (IHO) CONTINUE CONTINUE STOP END SUBROUTINE THPHI ( PHIR,VEQTMF,PHIO) COMMON wKI,HK2,NKIR1,HK2R1,HK2R2,CKO.CKOR,CK0R2 DIMENSION BJRE(75),BJIM(75),YRE(AI),YIM(AI) COMPLEX HKI,wK2,HKIR1,HK2R2,BSRS,DM.UP,HANKLR,UPI,HNKLRI,DERHKL, *COFCNT,BSERIS,X,Y,XANDY,VEQTHF ,HK2RI PI - A.O * ATAN (1.) R - CKOR/CKO BSRS - CMPLx (0.0.0.0) 00 AA N-I,2O q-FLOAT(N) - 1.0 CALL DMPART (N,PI,DM,O.O) IF (ABS(CKOR) .LE. 50.0) GO TO I FRONT- SQRT(2.0/(PI*CKOR) ) UP-CMPLx(O.0.-CKOR+PI*(2.0*FLOAT(N)+I.O)/A.O) HANKLR- FRONT * CEXP (UP) UPI - CHPLX(0.0,-CKOR+PI*(2.0*FLOAT(N+I)+I.O)/h.0) 139 HNKLRl-FRONT*CEXP(UP1) GO TO 2 CALL COMBES(CKOR,O.O,O.O,O.O.N.BJRE,BJIM,YRE,YIM) HANKLR=CMPLX(BJRE(N),-YRE(N)) HNKLRI-CMPLX(BJRE(N+I).-YRE(N+I)) DERHKL=(Q*HANKLR/CKOR)-HNKLR1 IF (N-])50596 COFCNT-DM*PHIO*DERHKL GO TO 9 CX - -2.0/(Q*PHIO) QTETAR-Q*PHIR REMAIN-(1.0/Q)*(l.O-COS(Q*PHIO))*COS(QTETAR) COFCNT--CX*DH*DERHKL*REMAIN BSRS-BSRS+COFCNT CONTINUE BSERIS=BSRS*CMPLX(0.0,1.0) X1-CKOR* COS(PHIR-(PHIO/2.O)) YI=CKOR*COS(PH|R+(PHIO/2.0)) DOMEI-COS(PHIR-(PHIO/A.O)) DOMEZ-COS(PHIR+(PHIO/A.O)) X-CMPLX(DOMEI.0.0)*CHPLX(COS(X1),-SIN(X1)) Y-DOME2*CMPLX(COS(YI),-SIN(YI)) XANDY-(X+Y)*PHIO/2.0 VEQTMF-R*(BSERIS+XANDY) RETURN END SUBROUTINE TMRAD (PHI,VEQTMR,HEIGHT) DIMENSION BJRE(75).BJIM(75),YRE(AI),YIM(AI) COMMON VKI,HK2,HKIRI,HK2RI.HK2R2,CXO,CKOR,CKOR2 COMPLEX NXI,NK2,HKIRI,HK2R2.SERIES,DM,UPI,HNI.TERMI,UP2,HN2, *TERM2,TOTAL,CI,C2,C3,E1,E2.E3,BODYNO,VEQTHR ,wK2RI Pl-h.0*ATAN(1.0) PH!R-PHI*Pl/180.0 R-CKOR/CKO SERIES=CMPLX(O.O,O.O) 00 AA N-I,2O q-FLOATIN)-1.O CALL DMPART (N,PI,DM,O.O) RMINUS=R-HEIGHT/2.O RPLUS-R+HEIGHT/2.O ARGUl-CKO*RMINUS ARGUZ-CKO*RPLUS IF(ABS(ARGU1) .LE.50.0) GO TO 1 X1 - SQRT(2.0/(PI*ARGUI)) UPI-EMPLX(0.0,-ARGU1+PI*(2.0*FLOAT(N)+1.0)/A.O) HNl-XI*CEXP(UP1) GO TO 2 CALL COMBES(ARGUI,O.O,O.O,O.O,N.BJRE,BJIM,YRE,YIM) HNI-CMPLX(BJRE(N).-YRE(N)) TERMl-(l.O+(I.O-R/HEIGHT)*ALOG(R/(R-HEIGHT)))*HN1 IF (ABS(ARGU2) .LE. 50.0) GO TO 3 X2-SQRT(2.0/(PI*ARGU2)) UPz-CMPLX(O.O,-ARGU2+PI*(2.O*FLOAT(N)+I.O)/A.O) HNZ-X2* CEXP(UP2) GO TO A CALL COMBES(ARGU2,O.O,O.O.O.O,N,BJRE,BJIM,YRE,YIM) HNz-CHPLX(BJRE(N),-YRE(N)) _ TERMZ-((l.O+R/HEIGHT)*ALOG((R+HEIGHT)/R)-l.O)*HN2 TOTAL-(Q/CKO)*DM*(TERH1+TERH2)*SIN(Q*PHIR)*CMPLX(0.0,I.0) SERIES-SERIES+TOTAL CONTINUE 1] Ah IF(PHI.EQ.90.0) GO To 6 140 IF ( PHI .EQ. 270.0) GO TO 6 C1-CMPLX(0.0.-CKO*R*COS(PHIR)) C2-CHPLX(C.C.-CKO*(R-HEIGHT)*COS(PHIR)) C3-CHPLX(0.0,-CKO*(R+HEIGHT)*COS(PHIR)) EI-CEXP(CI) E2- CEXP(c2) E3-CEXP(C3) DINOM-HEIGHT*(CKO**2) TRIG=(SIN(PHIR))/((COS(PHIR))**2) BODYNO=(2.0*El-E2-E3)*TRIG/DINOM GO TO 66 BODYNO - HEIGHT*SIN(PHIR) VEQTHR-BODYNO+SERIES RETURN END SUBROUTINE TEHAVE (PHIR,EZRPHI,HEIGHT) COMMON HKI,NK2,NKIRI,HX2RI,HK2R2,CKO,CKOR,CKOR2 DIMENSION BJRE(75).BJIM(75),YRE(AI),YIM(AI) COMPLEX HXI.HK2,HXIRI,HX2R2,HX2RI,VSERIS,DM,HANXEL,SUM,C6,C7, *EZRPHI PIaA.O*ATAN(I.O) VSERIS=CMPLX(0.0,0.0) DO AA N-I,20 Q=FLOAT(N)-I.O CALL DMPART (N,PI,DM,I.O) IF (ABS(CKOR) .LE. 50.0) GO TO II C5=SQRT(2.0/PI*CKOR) TN2-CKOR-(2.O*Q+I.O)*PI/A.O BEScC5*COS(TN2) BESZ=C5*SIN(TN2) HANKEL-CMPLX(BEs.-BE52) GO TO 8 CALL COMBES (CKOR,O.O,O.O,O.O,N,BJRE.BJIM,YRE,YIM) HANKEL-CMPLx(BJRE(N).-YRE(N)) PHICOS-COS( Q*PH|R) SUM-DM*HANKEL*PHICOS VSERISsVSERIS+SUM CONTINUE C6-CMPLX(0.0.-CKOR*COS(PHIR)) C7-CEXP(C6) EZRPHI=(C7+VSERIS)*HEIGHT RETURN END SUBROUTINE DMPART (N,PI,DM,TE) DIMENSION BJRE(75).BJIM(75),YRE(AI),YIM(AI) COMPLEX NKIRI,HX2R1.XN,HK2,NKI,NK2R2,B2,B3,HNKL,DHNKL,BA,C3,CA, *C3H.COMPXJ.DECOH.DM COMMON HXI,NX2,HKIRI,HK2R1,HK2R2,CXO.CKOR,CKOR2 CALL ABC (HXIRI,HK2RI,N,PI,XN,HN2,NXI,TE) CALL BCD (HK2R2.NK2.CKO.N.PI,XN,Bz,TE) 83 - 32 Q - N-I IF(ABS(CKOR2) .LE.5O.0) GO TO 1000 ARGUOI - CKORZ-(Q*PI/2.0)'(3.0*Pl/h.0) ARGu02 - ARGUOI+(PI/2.O) CI - SQRT(2.0/(P|*CKOR2)) Bl-CI*COS(ARGUOI) B- COS(ARGuoz) * C1 TNI - CKORZ - (2.0*Q+l.0)*Pl/h.0 BESELz - CI*SIN(TNI) 141 HNKL - CMPLX(B.-BESEL2) GO TO 10 I000 CALL COMBES(CKOR2.O.0.0.0.0.0.N.BJRE,BJIM.YRE.YIM) B = BJRE(N) BI . BJRE(N+]) HNKL = CHPLX(BJRE(N).-YRE(N)) 10 PART = QAB/CKORz DERBEs-PART-BI BI = DERBES/B 02 - 2.0/(PIACKOR2AB) DHNKL - B1 A HNKL - C2 A CMPLX ( 0.0.1.0) BA - DHNKL/HNKL £3 - (81-83)/(B3-Bh) CA - B/HNKL C3A . C3ACA IF(N-I) 20.20.16 20 EPCLON = 1.0 60 T0 7 16 EPCLON 3 2.0 7 COMPXJ = CMPLX (0.0.1.0) DECOM - COMPXJAA(N-I) DM - EPCLON A C3A/DECOM RETURN END SUBROUTINE ABC (HKIRI.HK2RI.N.PI.XN.HK2.HKI.TE) DIMENSION BJRE(75). BJIM(75). YRE(A1). YIM(AI) COMPLEX NKI.HX2.HXIRI.NX2RI.XN.DEBESI.BI.BIII.PARTII.AI.DEBESH. ABH.COEFFI.BESEL2.PART21.BH2I.DBES.HNL221.HNL121.NR0N.DHL22I. ADHLIzI. A2. AA. A3.CBI RENKII - REAL (NKIRI) AMNKII - AIMAG (HKIRI) RENK21 - REAL (HK2RI) AMwK21 - AIMAG (HK2RI) O - N - I IF (CABS(HXIRI) .LE. 50.0) GO TO I ARGUII - REHKII - ( Q A PI / 2.0) - (3.0 A PI / A.0) ARGUIz - ARGDII+ ( PI / 2.0 ) CBI-CSQRT(2.0/(PIAHKIRI)) BIII- CBIACMPLX(COS(ARGUII).-SIN(ARGUII)ATANH(AMNKII)) B1 = CMPLX (COS (ARGU12). - SIN (ARGUIz) ATANH (AMwKII)) ACBI GO TO 10 I CALL COMBES (REHKII.AMHKII.O.O.0.O.N.BJRE.BJIM.YRE.YIM) BI - CMPLX (BJRE (N). BJIM (N) ) BIII - CMPLX (BJRE (N+I), BJIM (N+I) ) I0 PARTII - Q A BI / HKIRI DEBESI - PARTII - BIII AI - DEBESI / BI IF (CABS (HK2RI) .LE. 50.0) GO TO 2 ARGuzI - REHK21 - ( OAPI/2.O) - (3.0 API / A.O) ARGU22 - ARGU21 + (PI / 2.0) COEFFI - CSQRT ( 2.0 / ( PI A HK2R1) ) BH21-COEFFIACMPLX(COS(ARGU21).-SIN(ARGuzI)ATANH(AMHK21)) BH = CMPLX (COS (ARGU22),-S|N(ARGU22)*TANH (AMHK21) )ACOEFFI COSINE - ( EXP ( AwazI) + EXP (-AMHK21) ) / 2.0 TN - REHK21 - ( 2.0AQ+I.O)API/A.O BESEL2 - COEFFIACOSINEA(SIN(TN)+TANH(AMHK21)ACOS(TN)A CCMPLX(0.O.I.0)) GO TO 3 2 CALL COMBES (REHK21.AMHX21.O.O,O.O.N.BJRE.BJIM.YRE.YIM) BH - CMPLX ( BJRE (N). BJIM (N) ) BHzI - CMPLX (BJRE(N+I). BJIM (N+I) ) “7 10 142 BESEL2 . CMPLX (YRE(N). YIM (N) ) PART21 . QABH / HK2R1 DEBESH . PART21 - BH21 DBES - DEBESH /BH HNL221 = BH + BESEL2 A CMPLX (O.0.-1.0) HNL121 - BH + BESEL2 A CMPLX (0.0. 1.0) HRON = 2.0 / (PI A HK2RI A BH) DHL221 . DBES A HNL221 - HRONACMPLX (0.0.1.0) DHL121 - DBES A HNL121 + HRON A CMPLX (0.0.1.0) IF(TE-I.0)5.6.6 A2=(wKIADHL221)/(HK2AHNL221) AA=(HKIADHL12I)/(NX2AHNL121) GO TO A7 A2 - (wK2 A DHL221) / ( HKI A HNL221) AA - (HK2 A DHL121) / ( HKI A HNL121) A3 = HNL221 / HNL121 XN . A3 A (AI-A2)/(A1-AA) RETURN END SUBROUTINE BCD (HK2R2.NK2.GK0.N.PI.XN.Bz.TE) DIMENSION BJRE(75). BJIM(75).YRE(AI). YIM(AI) COMPLEX DEBEsz.B.BESEL2.COEFF2.PART22.BI22.HNL222.HNL122.DBE52. *WRONZ,DHL222,DHL122.UNUM,DINOH,82,NK2R2,WK2,XN REwK22 = REAL (HK2R2) AMwK22 - AIMAG (HK2R2) Q - N - 1 IF(CABS(HK2R2) .LE. 50.0) 00 TO I ARG21 - REHK22 - (QAPI/2.O) — (3.0API/A.O) ARG22 - AR021 + (P1 /2.0) COEFF2 - CSQRT (2.0/(PIAHK2R2) ) BI22-COEFF2ACMPLX(COS(AR021).-SIN(AR021)ATANH(AMHK22)) B - CMPLX (COS (AR022).-SIN(AR022)ATANH(AMHK22) )ACOEFF2 COSINE - (EXP(AMNK22)+EXP(-AMHX22) )/2.0 TN - REHK22 -(2.OAQ+I.0)API/A.O BESEL2-COEFF2ACOSINEA(SIN(TN)+COS(TN)ATANH(AMNK22)A CCMPLX(0.O.I.0) ) GO T0 10 CALL COMBES(REHK22.AMNK22.0.0.0.0.N.BJRE,BJIM.YRE.YIH) B - CMPLX (BJRE(N).BJIM(N) ) BESEL2 - CMPLX (YRE(N).YIM(N) ) B122 - CMPLX (BJRE(N+I).BJIM(N+I) ) PART22 - OAB/HK2R2 HNL122 = B+BESEL2 A CMPLX (0.0.1.0) HNL222 - B+BESEL2ACMPLX(O.0.-I.O) DEBEsz - PART22 - B122 DBEsz - DEBEsz / B HRONz - 2.0/(PIAHK2R2AB) DHL222 . DBEsz A HNL222 - HRON2 A CMPLX (0.0.1.0) DHL122 - DBEsz A HNL122+HRON2 A CMPLX (0.0.1.0) UNUM - DHL222-XNADHL122 DINOM - HNL222 - XN A HNL122 IF (TE-1.0)5.6.6 B2-(CKOAUNDM)/(HX2ADINOM) GO TO A7 02 - (NK2 AUNUM) / ( CKO A DINOM ) RETURN END 143 2'::‘n’n‘n’dnh'::‘n'n‘ddckidn‘n'dtfl*kin'n'n'tfla'dn'n‘t*2':2':2':*kid:*a'du'd:********************fd¢ SUBROUTINE “ COMBES “[23] *in'cfddn‘tkin‘du‘ckfdt*a'n‘n‘nh‘nY'n':2‘C************ :ka‘nk*iu‘dn‘n'ca'tf:****2‘:2‘<***2‘C*2‘::‘::\2‘C**2‘:3’C SUBROUTINE COMBES (X.Y .ALPHA. BETA. N. BJRE BJIM. YRE .YIM) DIMENSION BJRE(75). BJIM(75). YRE(A1). YIM(AI I) CALL BEGIN(X Y K. R CALL JRECUR(X.Y.ALPHA. BETA. K.R.BJRE. BJIM) CALL JSUM(ALPHA.BETA,K .BJRE.BJIM.SUMRA.SUMIA) CALL FACTOR(X.Y.ALPHA,BETA.Q.R) CALL JNORM K.$.R.SUMRA.SUMIA.BJRE,BJ|M) 5 CALL YSUM X. .ALPHA.BETA.K,BJRE.BJIM,ASUMR.ASUMI) CALL YGNU X.Y.ALPHA, A.Q.R.ASUMR.ASUMI.BJRE.BJIM.YRE.YIM) 9 CALL HRONSK (X.Y.BJRE.BJIM.YRE.YIM) BJSE=BJRE(l)**2+BJ|M(1)**2 IF( JS -.00000008) 1A.IA.15 IA CALL Ys MPEX.Y.AL HA.BETA.K.BJRE. BR IM. ASUMR. ASUMI) CALL YGNUP X,Y,ALPHA.BETA.Q.R.ASUM R.ASUMI. BJRE. BJIM.YRE.YIM) 15 IF (N-1)10,12,II 10 IF N)lé.12.12 I3 ESLLONEZN (X.Y.ALPHA,BETA.N.BJRE.BJIM.YRE,YIM) 11 CALL YRECUR(X.Y.N.BJRE.BJIM.YRE.YIM) 12 REEgRN CBESA02 BEGIN SUBROUTINE PART 2 OF 16 CBESLOéUBJRECUR SUBRO END CBEShOh JSUH SUBR 80 2] I 15 SUBROUTINE BEGIN(X. Y. N.K,R) SS “X A2+YAA2 KT N= :SQRT(SSQ)+20. .0 NTEN= IABS N)+IO M=MAX0(KTEN. NTEN) /2 K=2AM+I R = K + 1 REEURN U E PART 3 OF 16 ROUTINE JRECU BETA, K. R. BJRE, BJIM) DIMENSION BJRE(I ) RALPHA=R+ALPHA S SQ=X2"'CAC2+Y2':2:2 BJRE K+2 =0 BJIM K+2 =0 BJRE K+1 =1.0E-37 BJIM K+I 20.0 DOA1-1.K Ll=K+l-l RALPHA=RALPHA- 1.0 A= 2.0AXARALPHA) B= -2.0AYARALPHA BJRESng=EAABJREE BJIM L1 - BABJRE RETURN 021—1 .0*BETA*Y) 2.0*BETA*X lgg- 8*BJ I + A*BJ gg-BJREELI+23 -BJ|M L1+2 I T h 0F 16 PAR .BJRE, BJIM, SUMRA,SUMIA) T AAHIIIIBH 0U SUBROUTINE JSU DIMENSION BJRE SUMRA= BJRE(g) SUMIA= BETAA J GRE=I.O GIM=O 1TH (l 2':( RE GREN=E(GRE*(ALPHA+S- I. .0; '(BETA*GI Hflg) /S G|M=( G|M*(ALPHA+S- I .0) (BE TA*GRE ) /S GRE=GREN ALPTS=ALPHA+2.0*S GJR=GRE*BJRE I; GJ|=G|M*BJIM l GJRl-GRE*BJIMEI; GJ|R=G|M*BJRE I SUMRB=ALPTSAAéGJR- GJI) BETA*(GJ|R+GJRI3+SUMRA SUM|B=ALPTS* GJ|R+GJR|) BETA*(GJ| -GJR +SUMIA IF SUMRA))1§2 1% IF ABS((SU RB/éU RA)-l.0)-.00000005)2],21.10 IF SUMIA)20, I], 20 144‘ 20 IF (ABS((SUMIB/SUMIA)-I.0)-.00000005)11.11.10 10 SU MRAsSUMRB SUMIA-SUMIB II RETBRN CBEShog FACTOR SUBROUTINE PART 5 OF 16 UBROUTINE FACTOR(X. Y.ALPH A.BETA. Q, R) CALL LOGGAM ALPHA+I. 0.BETA .U. V) CALL COMLOG X.Y.A1.BI) A2-ALPHAAA1-BETAABI 82=BETAAAI+ALPHAAB1 A2=-A2 BZ=~BZ CALL COMEXP A2. 82, A3. B3) AA=. 6931 W; 06AALPHA BA=. 6931 06ABETA CALL COMEXP(AA. BA, A5. B5) A6= A3AA5- B3AB 5 86=B3AA5+AA CALL COMEX (U. V.A7.B7) g: -A6au A;- 86*8; =86AA +A6AB REEBRN CBESA06 COMLOG SUBROUTINE PART 6 OF 16 C COMPLEX LOGARITHM - BRANCH CUT ON NEGATIVE REAL AXIS SUBROUTINE COMLOG(LY Flag. 1A159265A A= AALOG(XAX+YAY) IF(X)5 1 B=. 5A API IF(Y)2.3.8 2 B=-B GO TO 8 3 B=0. GO TO 8 B=ATAN Y/X) B=ATAN(Y/X) IF(Y)6.7.7 6 B=B-Pl GO TO 8 g B=B+Pl RETURN CBEShogE NCOMEXP SUBROUTINE PART 7 OF 16 UBROUTINE COMEXP(X. Y. A. B) C= EXP (X) A=CACOS(Y ) B=CASIN Y RETURN END CBESA08 JNDRM SUBROU 101 12 13 100 102 B 10?“ BJRER' "NngJREN I E ART 8 OF 16 Q.R.SUMRA.SUMIA.BJRE.BJ1M) .BJIM(IOO) )-((SUMIA+BJIM1))AR) + SUMRA+BJRE 1 AR .IOI.IOI ) I ATS /Ts éEAI) “A W) TgS SQ T SUBROUTINE JNORM( DIMENSION BJRE 10 S- (SUMRA+BJREI T- SUMIA+BJIM IF ABS(S) -ABS(T) TS =T/S 33S§=:A(I. .0+(TSAA2 BJR N- (BJRE(I)+BJI BJIM I;-(BJIM(I)- B BJRE -BJREN GO TO 1A ST=S/T 331 =TA((STAA2)+I. 0) BJREAN =(BJRE(|)*ST+BJIM(I)){STS$ JI (BJIM(I)AST- BJRE(| ) SQ N K 0 1 1 5 A A 0 ) M J END CBESA02UBYSUM SUBROUTINE PART OF 16 ROUTINE YSUM (XY DIMENSION BJRE(IOO$. BJIM A1=ALPHA- 1.0 A2= AI-I A2=Al+ALPHA A=BETAAA2 A522. 0AAA MR? BETA,K,BJRE,BJIM,ASUM ,ASUMI) 145 ABSQ=(-A1)AA2+AA GAMRE=E(2.0+ALPHA)*(‘A1)-AA)/ABSQ GAMIMA BETA*g.O)/ABS ASUMR=GAMRE* JREé3g- AMIM*BJIME3; ASUMéscAMIMABJRE 3 +OAMREABJIM 3 DO 500 I-5,K,2 T=T+1.O B1=2.0*T F1-B1+ALPHA ,, n; will >~4>a> k)l—&N +1>++~ aH—-+4 -ru 3: >1 1*F2-A5 F2+2.0*F1)*BETA 1*F -G2*BETA 2*F +G]*BETA AF +AA 5-F6)*BETA p =p1AA2+P2AA2 C E=E§H1*P1+H2*P2 /P3 /T CIM= H2*P1-H1*P2 /P3 /T TEHP=-(CRE*GAMRE-CIM*GAMIM) GAMIM=-(CIM*GAMRE+CRE*GAMIM) GAMRE=TEMP gig-GAMIH*BJIM BSUMR=GAMRE*BJRE BSUMI=GAM|M*BJRE I +GAMRE*BJ|M "1 IF IF ASUMR=BSUMR ASUMl-BSUMI RETURN END CBESAIO YGNU SUBROUTI SUBROUTINE YGNU DIMENSION BJRE( Pl=3.1hlg9265h TP1=2.0/ I RE:TP|*(Q**2-R**2) IM=TPIA2.OA AR RE=QREAASUM - IMAASUMI M=QIMAASUMR+ REAASUMI ALPHA)1,2,1 BETA)1,3,1 L YZESO(X,Y,ALPRE,ALPIM) deN-dm 1313200717171 v N u 11 ASUMI) 20,511,520 NE X .Y. 100). AL BJ EX * EXY+EXY1 * EXY-EXY1 X*CDSH)**2+(CDX*SINH)**2 X*CDX)/DEN OSH*S|NH)/DEN .O* ALPHA**2+BETA**2) RE- {3RE*ALPHA+BETA*§ C lM*ALPHA-BETA* ALPRE BJRE 1;-ALP|M* ALP|M*BJRE +ALPRE*B X I Y,ALPRE,ALPIM) 5A .B) 315157+A1 IN; RE 720 JIM JIM w<<>>>mmcmnmmmnvmn——UDOIO f: 11 INE E CBESA12 WRONSK SUBROUTINE SUBROUTINE WRONSK(X,Y,B DIMENSION BJRE(100),BJ1 ssq=XAA2+YAA2 TPI=2.0/3.1A1 9265A AZRE=TP|*X/SS AZIM=-TP1*Y/S 2 ZRE‘BJRE(2)*YR (1)‘BJ|M(2)*YIM(1) JRE M(1O +ASUMR +ASUMI ABS((BSUMR/ASUHR)-1.0)-.00000005)521,521,510 ABS((B UMI/ASUMl)-1.0)-.00000005)511,511,510 T 10 OF R 16 I,BJRE,BJIM,YRE,YIM) PART 11 OF 16 PART 12 OF 16 146 ZIM-BJIM(2)AYRE(1)+BJRE(2)AYIM(1) BZRE-ZRE- BZIMsZIM-A A21M BJs=BJRE1gAA2+BJln(1)AA2 CZR =BJRE /BJs CZIM=(-BJIM(1))/ /JSQ YREézg-BZRE*CZRE- BZIMACZIM YIM2 =BZIMACZRE+BZREACZIM RgggRN CBESAIE NEGN SUBROUTINE PART 1 OF 16 UBROUTINE NEGN(X, Y, ALPHA,BETA,N,BJRE,BJIM.YRE,YI ) DIMENSION BJRE(IOO ), BJIM(IOO),YRE(5O).YIM(5O) L-IABS(N)+1 ssq=xAA2+YAA2 Tx-z. OAX TY-z. OAY RALPHAAALPHA A:ETXARALPHA+TY*BETA){SSS B= -TYARALPHA+TXABETA /S 1 BJREEZ§=A*BJREElg-B*BJIME g-BJREézg BJIM 2 =BABJRE +AABJIM 1 -BJIM 2 YRE 23-AAYREé1g-BAYIME1g-YRE£2) YIM 2 =BAYRE 1 +AAYIM 1 -YIM 2 IF(L- 3) ,2,2 2 Do 1 1-3,L RALPHA- ALPHA- 1. O AsETX*RALPHA+TYABETA) SSE B= -TYARALPHA+TXABETA /S a BJREElg-A*BJREéI-1;-B*BJI EI-1g-BJREEI-2; BJIM I -BABJRE 1-1 +AABJIM 1-1 -BJIM 1-2 YREélg-A*YRE I-I) -BAYIMEI-1)-YREEI-2) 1 YIM I =BAYRE 1-1 +AAYIM 1-1 -Y1M 1-2 3 CONTINUE REEERN CBESAIA YRECUR SUBROUTINE PART 1A OF 16 SUBROUTINE YRECUR(X.Y fiBJRE,BJIM,YRE,YIM) DIMENSION BJRE(IOO),M(IOO),YRE(5O),Y1M(5O) SSQ:X**2+Y*::2 TP|=2.0/3.1A159265A A2RE=TPIAX/ss AZIM=-TPIAY/S Q L=N +1 IF (L’?) D 2,2 2 DO 1 ,L ZREABJR EIgAYg 1t 1g-BJIMEIg*YIMél-lg ZIM=BJIM I AYR +BJRE 1 AYIM I-1 BZRE= ZRE-AZRE B21M=21M~A21M BJs =BJREEl-1;**2+BJIM(l-1)**2 CZR =BJRE 1-1 /BJS CZIM=(-BJIM(I-1))/ Jsg YREElg-BZRE*CZRE-BZIH CZIM 1 YIM 1 =BZIMAC2RE+BZREAC2IM 3 CONTINUE CBESAIg YGNUP SUBROUTINEY PART 15 0F 16 UBROUTINE YGNUP(XY fiPHA,BETA,2,R,ASUMR,ASUMI,BJRE,BJ|M,YRE,YIM) DIMENSION BJRE(IOO),B JIM(IOO),YR (5O),YIM(5O) PI-3. 1A1 265A TPI =2 0/ RE=TPIA(QAA2- RAA2) IM= TPIA2. OA AR RE: REAASUM- IMAASUMI DIM= IMAASUMR+ REAASUMI IFEALPHA)1,2 2 IF BETA)1 1 3 CALL YZERO X, Y, ALPRE, ALPIM) GO TO 720 I PALPHA=PI*ALPHA cox-COS PALPHA; SIX=SIN PALPHA EXYaEXP PIABETA) EXY1-1. O/EXY COSHI. EXY+EXY1 SINH=. *EXY-EX Y1 DEN= S|X*COSH)**2+(COX*SINH)**2 EREB SIX*CDX)/DEN E|M= 'CDSH*SINH)/DEN 720 CBESA] \nUmn —nun: OCLa -HO -HO L G HI 0 ruwrufirufiruw t n-io HERE X IS T 147 ABSSE=2.0* ALPHA**2+BETA**2) ALP =ERE- RE*ALPHA+BETA* ALPlM-EIM- lM*ALPHA-BETA* TREBALPRE*BJREEZ;-ALPIM*BJ1 T1M=ALP|M*BJRE +ALPRE*BJ|M LPREB-E *X+R*Y;/ /X**2+Y**2 *R- *Y / X**2+Y**2 E2g=ALPRE BJRE 1g-ALP|M*BJ| 2 =ALP|M*BJRE 1 +ALPRE*BJ| NNI‘HZ Mm- 1 UM MP SUBROUTINE PART 16 OF 16 UT INE YSUMP(X, Y, ALP HA 6BETA,K,BJRE,BJIM,ASUMR,ASUMI) SI ION BJRE(100). BJIM W( O) PHA- 1.0 -1. O +ALPHA T Q.0 (A E M g+TRE +TIM 33 S O N L 1 1 E As‘n'cz *Ah ]')*:<2+AL Q=20. .O+ALPHA )A(-AI)-AA)/ABSQ = BETAA3. 0)/ /ABSQ ROLDRE/2.o -RDLDIM/2.O *EALPHA*X+BETA*Y;/ X**2+Y**2g .A XABETA- ALPHAAY / XAA2+YAA2 ZOLDREASTORE- -ROLDIMASTOIM VM52=1ROLDREASTOIM+ROLDINASTORE ASUMR= RESIABJRE(2) -VMS1ABJIM(2) ASUMR=ASUMR+RE32ABJRE(3) -VM52ABJIM(3) ASUMI=VMS1ABJRE(2)+RES1ABJIM M(2) ASDM6=ASUMI+VM52ABJRE(3)+RE52ABJIM(3) DO 500 |=3,K,2 T=T+I.O B1=2.0*T F1=B1+ALPHA A A Y Y R 6 S D A A A A A A R R RM SM 5 R nznwun-—wu 1AF2-A F2+2.OAF1)ABETA 1AF3-C2ABETA 2AF +CIABETA gAF +AA -F6)ABETA 1*2':2+P2:'::':2 E H1*P1+H2AP2g/P3;/T H2AP1 H1AP2 /P /T TEMP=-(CRE*ROLDRE- CI ARDLDIM) RNENI M=-(C1MAROLDRE+CREARDLDIM) RNENRE=TEMP RESI= ROLDRE-RNEWREg/2.0 = ROLDIM-RNEWIM /2.0 = RNENREASTORE-RNENIMASTDI VM52= RNENREASTOIM+RNENIMASTOR BSUMR=RESIABJRE 1+1 -VMSIABJIM BSUMI=VMSIABJRE 1+1 +RESIABJIM BSUMR=RE52ABJRE I+2 -VMszABJIM BSUMIeVMszABJRE I+2 +RE52ABJIM n'U'O‘OIIODTiTI WNdN—‘Nd r"Illllllllflllll I ‘Ur-x'" 00"“ C1 3 11 M £1 1+1 1+1 I+2 +BSUMR I+2 +BSUMI FgABSHBSUMR/ASUMR0 -1. O)-. 00000005)521, 521, 510 I IF ASUMI) 20 511 5 IF ABS((B UMl/ASUM|)-1. 0)-. OOOOOOOS)S11, 511, 510 ASUMR=BSUMR ASUM1=BSUMI ROLDIM=RNEW|M ROLDRE=RNEWRE RETURN END SUBROUTINE LOGGAM(X,Y UV) G M LOG OF THE GAMMA FUNCTION OF COMPLEX ARGUMENTS FORTRAN ll SUBROUTINE COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR M LEX ARGUMENTS. THE ROUTINE IS ENTERED BY THE STATEMENT CALL LOGGAM(X,Y,U,V) REAL PART OF THE ARGUMENT IMAGINARY PART OF THE ARGUMENT REAL PART OF THE RESULT IMAGINARY PART OF THE RESULT tflIIIEIZZ 148 6.0.1X2HY8F6.0) ) - E 2 F 3 a 3 x 5 H 8 2 3 9 F 8 ) 0 . 2 M 9 .R A * G + G Y 0 x L + — E 2 K CY x 0. v 0 VAT ) (3” G 9 D 22 7 VI 0 8 E . — B an" L) 1' T . -3399 .I. You 2 .II 5 / ) M 08014333 T606 5 + 3 9 ( 12 T “6923325 ) 0L 9 ( . %+0 2 9 * 9 9T 606533936 3X +LA7 0 7 Xr2| .l .| La N )0 A 39322 i/ o. +- 9 T +VI 92 .|. EA] 7.558 2 7260333 Y Fawn-[6] x 1+ + QJB] Q .T IIE XH Ark/08337:) 2( 20 )BTO 6( .IT * x. 9 B] nus o OA+O 9 71.63330] . 50 B /1.~T2 9. 1 EE . .(+ .2T 11:52 . .ZO NZcflT .++.| nun VI =)T cu“ .5 . 3 O ++6ql6 9 II 50256385] .0 X]A**R02 u” . l*(* T)3 ) . . ‘2 .0 E 1:05 1(X . . . . . .0 . T.” A .12.? “Y6 7|.(T '41.” .ITZZ 2 0 E5250 .Oh5l+ OE.“ E 1152-. 813 O =)A VIP I XBB .BXIB .TT. . Tx3 2N322N .)- E 0 EE )M T 8 = I s a 2 x x x10 H = J: TTXRTTXROV- 0 O: 8 .xx BOTA )\I\I\.I\.I\l== .— (= __L (:3 Tax: :8 =3....( 8( U U (eTzT : a. Iu\l.\ TINML 2314.27 .l. :2 a A] = .— 5 = 3 a = 3T 2 8 3T: I“ 6 6: 5 IRLD E2882 F6 7E F12 032.“. 1|0 b5132FT2F E E FIDO/DOESELBE FFEOROAN HHHHHHEE BJXIBTBRTIIBBVAJGTTTITTDTTTTTTII TIUVXRUVXRTIBGBG EIEEIX|| GPFCE O :43 5 6 8 .l .l .I APPENDIX 8 The probe response near the cylindrical body - computer print outs. . 149 150 TABLE B-l : Prope near a sheathed conducting cylinder. Ingadent field - (2,h§ de?.) V/m,f-3.0GH2. (ans. 3.2.1,3.2.7,3. .13 PIIOUIICV I .20000010 FIILO I 2.00 AISLE I 00.00 PM] ll LOAO CURRENT 00 LOAO 00000”? 00 LOAO 00.2207 00 LOAO CUIIINY 00 020 POI PM] '02 I POI 7! TOTAL O 00 .20270'12 0. .00000'1‘ .20020'12 0.00 .12220'12 .10000-10 .22000-10 .10000-10 10 00 .00200‘12 .22000'10 .27702-10 .2200I*10 10.00 .20070'12 00020-11 .10070°12 .00020'11 20.00 .20720-12 .10210'10 .10070'12 .10020'10 20.00 .11000'12 .21000-10 .22020-12 .22000'10 20 00 00020.12 .10000-10 .02000'12 .10002-10 20.00 .00000'12 .10000-10 .72010'12 .20010-10 ‘0 00 .20020-12 .00200-10 .1210l°12 .00700°10 00.00 .0207l°12 .02200-10 .2122I°12 .00100'10 00 00 .10100-11 .20220-10 .20110-12 .0070l°10 00.00 .00200°12 .07200'10 .00002'12 .00012'10 00 00 .11220-11 .70000-10 .00000'12 .01070'10 00 00 .17070-11 .70220-10 .10100-11 .70000'10 70 00 .20000'11 .00000'10 .22002'11 .10000-00 70.00 .20410-11 .12200-00 .2000I°11 .12072’00 00 00 .20120-11 .12200'00 .02000'11 .12000'00 00.00 .07000‘11 .12022'00 .7000!°11 .10700-00 00 00 .00000-11 .10000-00 .1100I°10 .17000'00 00 00 .00700-11 .10000'00 .10000-10 .1021l°00 100.00 .11110-10 .10700-00 .20120-10 .1002I°00 100.00 .10220°10 .10700-00 .20100'10 .20700°00 110.00 .10000-10 .10000'00 .22220-10 .21720'00 110 00 .22000‘10 .10000-00 .01110-10 .21012'00 120 00 .20000'10 .10020'00 .00020'10 .2202I°00 120 00 .27000-10 .12210'00 .00010'10 .22000'00 120 00 .00770-10 .11000'00 .07000-10 .22770'00 120 00 .00000°10 .02000-10 .70222'10 .22002'00 100.00 .00070'10 .77070'10 .00000-10 .2200I°00 100 00 .70000‘10 .02000-10 .02200°10 .22100-00 100 00 .00000-10 .07700-10 .00200'10 .22270-00 100 00 .00000'10 .22000-10 .10000-00 .22270'00 100 00 .10000-00 .20002°10 .11002'00 .22010-00 100 00 .11100-00 .12020-10 .11002'00 .22000'00 170 00 .11710-00 .00070-11 .11700-00 .20000-00 170.00 .12002-00 .10700-11 .11000°00 .20100‘00 100 00 .12100-00 2020I°20 .12000-00 .20100'00 100.00 .12000-00 .10722°11 .1100l°00 .20100-00 100.00 .11710°00 .00072'11 .11700°00 .20000‘00 100.00 .11100'00 .12020°10 .11002'00 .22000'00 200.00 .10000'00 .2000!°10 .11000’00 .22010'00 200 00 .00002'10 .22000'10 .10000°00 .22270-00 210.00 .20000'10 .077II°10 .00200-10 .22272-00 210.00 .70002°10 .02000'10 .02200'10 .22102’02 220.00 .00070-10 .77070-10 .00000-10 .22000'00 220.00 .00002'10 .02000-10 .70220-10 .22002'00 220 00 .00770-10 .11002-00 .07000-10 .22772'00 220.00 .27002'10 .12210-00 .00010°10 .22002‘00 200.00 .20000-10 .10020'00 .0002I°10 .22020-00 240.00 .22000'10 .10000-00 .01110-10 .21010'00 200.00 .1000!°10 .10000'00 .22220-10 .21722'00 200.00 .10222'10 .10700-00 .20100'10 .20700'00 200.00 .11110'10 .10700'00 .2012!°10 .10020'00 200.00 .00702‘11 .10000-00 .10000-10 .10210°00 270.00 .00002'11 .10000'00 .1100!°10 .17000'00 270.00 .070OI°11 .12022'00 .70000-11 .14702°00 200.00 .20120-11 .12202'00 .02000-11 .12000-00 200.00 .20010-11 .12202°00 .20000-11 .12070'00 200.00 .20000-11 .000OI°10 .22000'11 .10002‘00 200.00 .17072-11 .70220-10 .10100-11 .70000'10 200.00 .1122I°11 .70000°10 .00000'12 .01072010 200.00 .00200'12 .07200°10 .00000’12 .0001I°10 210.00 .10102°11 .20220‘10 .20112-12 .00700-10 210.00 .0207I°12 .02202'10 .2122I°12 .00100-10 220.00 .2002I°12 .002OI°10 .12102°12 .00702'10 220.00 .00002'12 .10000‘10 .72210'12 .20012010 220 00 .00022‘12 .10000'10 .02000'12 .10000-10 220.00 .11002°12 .21000-10 .22020'12 .22002'10 200.00 .20722'12 .10210-10 .10272'12 .10020'10 200.00 .20072°12 .00020'11 .10070'12 .00022-11 200.00 .00200-12 .22200-10 .27702'10 .22002'10 200.00 .12220‘12 .10000-10 .22000-10 .10002'10 200.00 .20272’12 .20000'20 .00000'10 .20020‘12 151 TABLE B-Z : Prohe near.,conductin cylinder. lngndent fueld - 62 h de .) V/m.f-3.OGH2. (ths. 3.2.2.3.2. ,3. .1h? FIIOUOICV 0 .20000610 PHI II LOAO 0000007 00 LOAO COIIIIY 00 LOAO 0000007 00 LOAO 0000007 00 000 F00 PH! '00 '00 7! VOYAL 0.00 .22000*12 0. .00170-10 .22000'12 0 00 .01010-12 .00020'11 .20020-10 .00000-11 10 00 .21000-12 .00200'11 .20200°10 .00010'11 10 00 .22000~12 .20200’11 .12200-12 .27000'11 20.00 .20000°12 .20010-11 .10170'12 .27200‘11 20 00 .10020'12 .00200-11 .27000'12 .10010'10 20.00 .20700-12 .00000-11 .00020'12 .10200'10 20 00 .00210-12 .00210-11 .00100-12 .00170'11 00.00 .07000-12 .10700°10 .10000-12 .17010'10 00.00 .00000'12 .20100-10 .27000'12 .20020'10 00 00 .00020'12 .20000-10 .07000'12 .27200-10 00 00 .10120'11 .20210-10 .77070'12 .20000-10 00 00 .10000-11 .00000-10 .12700-11 .0120l°10 00 00 .12200-11 .00020’10 .20270*11 .02100'10 70 00 .12270-11 .00170'10 .21000-11 .72700'10 70 00 .11000-11 .07710'10 .00000-11 .02700'10 00 00 .02000-12 .10010-00 .72000'11 .11202-00 00 00 .02710-12 .11070-00 .10720'10 .12010°00 00.00 .22200-12 .12000-00 .10100-10 .10000-00 00 00 .12070'12 .10070-00 .20020-10 .10000'00 100.00 .20000-12 .10070-00 .20020-10 .17000-00 100.00 .12020-11 .10120-00 .20000-10 10010‘00 110 00 .20170-11 .10020'00 .00000-10 .2000I°00 110 00 .00000'11 .10020-00 .07020'10 .20072'00 120.00 .10000-10 .12170'00 .00000-10 .21002'00 120 00 .22200-10 .11070-00 .01000-10 .22100'00 120.00 .20000-10 .10120-00 .0022l°10 .22020’00 120.00 .00010-10 .00000-10 .10000'00 .22000'00 100.00 .00000-10 .07000-10 .11010'00 .20010'00 100.00 .01000'10 .01010'10 .12070-00 .20210°00 100.00 .0001ls10 .27000-10 12020-00 .27070'00 100 00 .11000°00 .20210'10 .10000'00 .20000°00 100.00 .12200°00 .10020'10 .1020I°00 .20200'00 100.00 .10000'00 .01070-11 .10000°00 .21200'00 170 00 .10000-00 .00000'11 .10200-00 .2227I°00 170 00 .10220'00 .00020-12 .1002I°O0 .22000'00 100 00 .10000-00 .1100!°20 .10000'00 .2200I°00 100 00 .10220-00 .00020-12 .10020'00 .22000'00 100.00 .10000-00 .0000!°11 .10200'00 .22270-00 100.00 .10000'00 .01070-11 .10000’00 .21200'00 200.00 .12200-00 .10020°10 .10200'00 .20200'00 200.00 .11000-00 .20210-10 .10000'00 .20000'00 210 00 .00010-10 .27000'10 .12020'00 .27070'00 210.00 .01000'10 .01010-10 .12070'00 .20210°00 220.00 .00000‘10 .07000-10 .11010-00 .20010-00 220.00 .00010'10 .00000'10 .10000'00 .22000'00 220.00 .20000°10 .10120-00 .00220-10 .22020'00 220.00 .22200°10 .11070000 .01000-10 .22100-00 200.00 .10000-10 .12170'00 .00000'10 .21000-00 200.00 .00000-11 .10020°00 .0702I°10 .20070-00 200 00 .20170-11 .10020-00 .0000l°10 .20000‘00 200 00 .12020-11 .10120°00 .20000'10 .1001l°00 200.00 .20000-12 .10070°00 .20020-10 .17000-00 200.00 .1207I°12 .10070-00 .20020°10 .10000'00 270.00 .22200‘12 .12000°00 .10100'10 .10000-00 270.00 .02710’12 .11070-00 .10720°10 .12010'00 200.00 .02000-12 .10010'00 .72000°11 .11200'00 200.00 .1100!*11 .07710-10 .00000°11 .02700'10 200 00 .12270°11 .0017I°10 .21000-11 .72700-10 200.00 .12200°11 .00020-10 .20270'11 .02100°10 200.00 .10000-11 .00000'10 .12700'11 .0120I°10 200.00 .10120-11 .20210°10 .77070-12 .20000-10 210.00 .0002I°12 .20000-10 .07000'12 27200.10 210.00 .00000-12 .20100-10 .27000-12 .2002I°10 220.00 .07000'12 .10700‘10 .1000I°12 .17010'10 220.00 .00210-12 .00210'11 .00100'12 .00170'11 220 00 .20700'12 .00000-11 .00020-12 .10202°10 220.00 .10020~12 .00200'11 .27000'12 .1001I°10 200.00 .20000-12 .20010-11 .10170-12 .27200-11 200.00 .22000'12 .20200'11 .12200'12 .27000‘11 200.00 .21000°12 .00200‘11 .2020I°10 .00010'11 200.00 .01010'12 .00020-11 .20020'10 .00000‘11 200.00 .22002‘12 .20000'20 .00170°10 .2200I°12 152 0 0 TABLE B-3 : Probe near a sheathed conductung cylinder. lncudent field I (2,h§ def.) V/m,f-2.QSGH2, (F1950 3020393020993. .15 . 700000001 I .20000010 PIILD I 2 00 AIGLI I 00.00 PM! In LOAD 0000001 00 LOAD CUIIIIT 00 L000 0000007 00 LOAD 0000007 00 000 FOR 0H] '00 I FOR 10 VOYAL o oo .10000-12 . .00000-10 .10100-12 0 00 _70000-13 .00000-11 .20020-10 07700-11 10 00 .72000-10 .17020-10 .10000-10 .17000-10 15 00 .00200-12 .10010-10 .00070-10 .10710-10 20 oo .10030-12 .22070-11 12200-13 .20000-11 20 00 .10100-12 .12020-10 17770-12 .10770-10 30 00 .72700-13 .20020-10 .20010-12 .20120-10 20 00 .17010-12 .20200-10 .02300-12 .20010-10 00 00 .20070-12 10700-10 .00100-12 .10120'10 00 00 .20100-12 .20000-10 .12700-12 .20220-10 0O 00 .20300-12 .02020-10 .21000-12 .02000-10 00 00 .20070-12 .02010-10 .20270-12 .02200-10 00 00 .07000-12 .02170-10 .00200-12 .02200-10 00 00 .00010-12 .00330-10 .00000-12 .00000-10 70 00 .70200-12 .70000-10 .12000-11 77000-10 70 00 .10000-11 .70200-10 .10000-11 .01200-10 00 00 10200-11 .00000-10 .27070-11 .00700-10 00 00 .20820-11 .00120-10 .20070-11 .10100-00 00 00 20170-11 .10000-00 .02200-11 .11700-00 00 00 20720-11 .11000-00 .71710-11 .12100-00 100 00 .00000-11 .10010-00 .00200-11 .12200-00 105 00 .00300-11 .11220-00 .12100-10 .12000-00 110 00 .02700-11 .11000-09 .10200-10 .12000-00 11% oo .10700-10 .11000-00 10700-10 .12000-00 120 00 12700-10 .00000-10 .22000-10 .12020-00 12! oo .17200-10 .00010-10 .20020-10 .12200-00 120 00 .21000-10 .02220-10 .20010-10 .12200-00 130 00 .20100-10 .72000-10 .20200-10 .12100-00 100 00 20700-10 .00030-10 .20100-10 .12000-00 100 00 .20000-10 .00200-10 .01720-10 .12170-00 100 00 00210-10 .20230-10 .00000-10 .11000-00 100 00 .02000-10 .20000-10 .07000-10 .11000-00 100 00 07000-10 .10720-10 .00200-10 .11000-00 100 00 .00000-10 .00020-11 .02200-10 .11270-00 170 cc .02000-10 01030-11 .02000-10 .11100-00 170 00 .00000-10 .10070-11 .00000-10 .11070-00 100 00 .00000-10 .10770-20 .00000-10 .11000-00 100 00 .00000-10 .10070-11 .00000-10 .11070-00 100 00 .02000-10 .02030-11 .02000-10 .11100-00 100 00 .00000-10 .00020-11 02200-10 .11270-00 200 00 07000-10 .10720-10 .00200-10 .11000-00 200.00 .02000-10 .20000-10 .07000-10 .11000-00 210.00 .20210-10 .20220-10 .00000-10 .11000-00 210.00 .20000-10 .00200-10 .01720-10 .12170-00 220 00 .20700-10 .00020-10 .20100-10 .12000-00 220.00 .20100-10 .72000-10 .20200-10 .12100-00 220 00 .21000-10 .02220-10 .20010-10 .12200-00 230 00 .17200-10 .00010-10 .20020-10 .12000-00 200.00 .12700-10 .00000-10 .22000-10 .12020-00 200 00 .10700-10 .11000-00 .10700-10 .12000-00 200.00 .02700-11 .11000-00 .10200-10 .12000-00 200 00 .00200-11 .11220-00 12100-10 .12000-00 200.00 .00000-11 .10010-00 .00200-11 .12200-00 200 00 .20720-11 .11000-00 .71710-11 .12100-00 270.00 .20170-11 .10000-00 .02200-11 .11700-00 270.00 .20220-11 .00120-10 .20070-11 .10100-00 200.00 .10200-11 .00000-10 .27070-11 .00700-10 200.00 .10000-11 .70200-10 .10000-11 .01200-10 200.00 .70200-12 .70000-10 .12000-11 .77000-10 200.00 .00010-12 .00020-10 .00000-12 .00000-10 200.00 .07000-12 .02170-10 .00200-12 .02200-10 200.00 .00070-12 .02010-10 .20270-12 .02000-10 210.00 .20200-12 .02020-10 .21000-12 .02000-10 210.00 .20100-12 .20000-10 .12700-12 .20220-10 220.00 .20070-12 .10700-10 .00100-12 .10120-10 220.00 .17010-12 .20200-10 .02200-12 .20010-10 220.00 .72700-12 .20020-10 .20010-12 .20120-10 220.00 .12100-12 .12020-10 .17770-12 .12770-10 200.00 .10020-12 .22070-11 .12200-10 .20000-11 200.00 .00200-10 .10010-10 .00070-10 .10710-10 200.00 .72000-10 .17020-10 .10000-10 .17000-10 000.00 .70000-10 .00000-11 .00020-10 07700-11 200.00 .10000-12 .00010-00 .00000-10 .10100-12 153 . 0 TABLE B-h : Probe near a conducting cylingir.f-2 h5GHz. Incident fueld - (2.15 deg; m, ° 0 (ms. 3.2.1.3.2.Io.3-2-I 000000001 I .20000010 001 10 L000 0000007 00 L000 0000007 00 LOAD 0000007 00 L000 0000007 00 000 '00 P”! FDI 0 'D0 YDTAL 0 00 .17000-12 0 .71000-10 .10270-12 0.00 .00000-10 .27020-11 .00070-10 .20000-11 10 00 .10730-13 .02720-11 .21000-10 .02000-11 10.00 .00000-13 07000-11 .02010-10 .00000-11 20.00 .22000-12 .20000-11 .17700-1) .22020-11 20.00 .20000-12 .07000-11 .22720-13 .00000-11 00 00 .10000-12 .10220-10 .00770-13 .10020-10 20 00 .20200-12 .11000-10 71020-13 .11010-10 00 00 .00000-12 .10000-10 .11000-12 .11070-10 00 00 .00700-12 .10000-10 .10700-12 .10000-10 00 00 .00000-12 .22000-10 .20170°12 .23020-10 00 00 .00000-12 .20000-10 .00720-12 .20000-10 00 00 .72000-12 .01700-10 .70700-12 .23270-10 00 00 .77010-12 .20000-10 .11000-11 .00020-10 70 00 .00000-12 .00000-10 17000-11 .02120-10 70.00 .02070-12 .01000-10 .20700-11 .00000-10 00 00 .00300-12 .00110-10 .20700-11 .72000-10 00 00 .30000-12 .70000-10 .00000-11 .01000-10 00 00 .10010-12 .00200-10 .70720-11 .00000-10 00 00 .02120-10 .00000-10 .10200-10 .10020-00 100 00 10000-12 .00120-10 .13000-10 .11100-00 100 00 .02220-12 .00270-10 .17270-10 .11000-00 110 00 .17000-11 .00100-10 .21000-10 .12170-00 110 00 .07200-11 .00700-10 .20020-10 .12030-00 120.00 .00720-11 .00000-10 .32210-10 12020-00 120.00 .10730-10 00000-10 .37020-10 .12000-00 130.00 .10000-10 .00700-10 .02020-10 .12030-00 130 00 .22000-10 .00000-10 .00100-10 .12120-00 100 00 .30020-10 .00130-10 .00000'10 .13370-00 100 00 .20000-10 .20020-10 .00000-10 .13030-00 100 00 .00000-10 .20000-10 .00200-10 .13020-00 100 00 .00070-10 .20000-10 .00000-10 .10200-00 100 00 .01000-10 .12000-10 .71720-10 .10000-00 100 00 .00200-10 .72200-11 .70000-10 .10010-00 170.00 .73210-10 .22070-11 .70020-10 .10200-00 170 00 .70200-10 .03100-12 .77020-10 .10070-00 100 00 .77200-10 .00000-07 .70000-10 .10020-00 100 00 .70200-10 .02100-12 .77020-10 .10070-00 I00 00 .73210-10 .32070-11 .70020-10 .10200'00 100 00 .00000-10 .72200-11 .70000-10 .10010-00 200 00 .01000-10 .12000-10 .71720-10 .10000-00 200.00 .00070-10 .20000-10 .00000-10 .10200-00 210.00 .00300-10 .20000-10 .00200-10 .10020-00 210.00 .00000-10 .30020-10 .00020-10 .10020-00 220 00 .00020-10 .00100-10 .00000-10 .10870-00 220 00 .22000-10 .00000-10 .00100-10 .10120-00 220 00 .10000-10 .00700-10 .02020-10 .12030-00 220.00 .10720-10 .00000-10 .27020-10 .12000-00 200.00 .00720-11 .00000-10 .22210-10 .12020-00 200.00 .07200-11 .00700-10 .20000-10 .12000-00 200 00 .17000-11 .00100-10 .21000-10 .12170-00 200 00 .03220-12 .00270-10 .17270-10 .11000-00 200 00 .10000-12 .00120-10 .12000-10 .11100-00 200 00 .02120-10 .00000-10 .10220-10 .10020-00 270.00 .10010-12 .00000-10 .70700-11 .00000-10 270.00 .20000-12 .70000-10 .00000-11 .01000-10 200.00 .00200-12 .00110-10 .20700-11 .72000-10 200.00 .02270-12 .01300-10 .20700-11 .00000-10 200.00 .00000-12 .00000-10 .17000-11 .02130-10 200.00 .77010-12 .20000-10 .11000-11 .00030-10 000.00 .72000-12 .21700-10 .70700-12 .33270-10 000.00 .00000-12 .20000-10 .00700-12 .20000-10 210.00 .00000-12 722000-10 .00170-12 .20020-10 210.00 .00700-12 .10000-10 .10700-12 .10000-10 220.00 .00000-12 .10000-10 .11000-12 .11070-10 220 00 .20200-12 .11000-10 71000-13 .11010-10 220 00 .10000-12 .10220-10 .20770-12 .10000-10 200 00 .20000-12 .07000-11 .22720-10 .00000-11 000.00 22000-12 .20000-11 .17700-10 .20020-11 200 00 .00000-10 .07000-11 .02010-10 .00030-11 000.00 .10700-10 .02720-11 .21000-10 .02000-11 000.00 .00000-12 .27020-11 .00270-10 .20000-11 000.00 .17000-12 .10020-00 .71000-10 .10270-12 154 - : Probe near a sheathed conducting cylinder. 8 5 Incident field . (2,h5 de .) V/m,ft2.0GHz. (Figs. 3.2.5,3.2.11,3.2.l TABLE 000011000? I .20000010 FIILO 0 2.00 AISLE I 00 00 3n1 13 1939 cuaneuv 39 1939 3933331 39 1939 9033331 39 1939 9933331 39 939 393 In1 '93 3 393 13 19131 9.99 .33293-12 9. .33923-13 .12113-12 3 99 .33293o12 .33223-11 .21333-13 .33393-11 10.00 .01200-10 .12000-10 .10070-10 .12070-10 13.99 .13233-12 .12293o19 .33133-13 .12223-19 29 99 .31213-12 .33333-11 .11133-12 .39213-11 23.99 .33323-12 .23913-11 .13333-12 .39933-11 29 99 .19193-12 .11123-19 .22323-12 .11213-19 23 99 33333-12 .13333-19 .23393-12 .13333-19 39 99 .33793-12 .29313~19 .37333-12 .21923-19 33.99 .12133-12 .11923o19 .32323-12 _,,3....° 39.99 .13223-12 .13313-19 .13333-12 .13223~19 33 99 .13313-12 .23323-19 .21333-12 .23323-19 39 99 11233-12 .39933-19 .22393o12 .39313-19 33 99 22233-12 .32333-19 .33323-12 .32333-19 79 99 .23713-12 .32313~19 .12723-12 .32333-19 13.99 .39323-12 .33932o19 .19233-11 .33393-19 39 99 .33313-12 .33123-19 .13393-11 .31323-19 33 99 .33233-12 .33123-19 .13313-11 .11373-19 39 99 .11133-11 .11233-19 .23333-11 .13133-19 33 99 .13333-11 .29323o19 _,.,,..., .23313-19 199.99 .22123-11 .72393-19 .33223-11 .73313-19 193 99 .23393-11 .17193-19 .33173-11 .33313-19 119.99 .23333-11 .13333-19 .12333-11 .33313o19 113.99 .33133-11 .13123-19 .33193-11 .33333-19 129 99 32323-11 .32313-19 .19333-19 .33133-19 123 99 .39223-1f .31233-19 .12223-19 .31323-19 129 99 .33233-11 .33733-19 .13123-19 .73333-19 123 99 .11233-19 .33333-19 .13313-19 .11233-19 139 99 .12323-19 32933-19 .11333-19 .72313-19 133 99 13993-19 .22233-19 .13233-19 .33323-19 139 99 13133-19 .23393-19 .29733-19 .32313-19 133 99 .29233-19 .17333-19 .22123-19 .33333-19 139 99 .22933-19 .11333o19 .22233-19 .33313-19 133 99 .22333-19 .31393-11 .23133-19 .33323-19 179 99 .23333-19 .21333-11 .23333-19 .32333-19 173 99 .23223.19 .39333-12 .23233-19 .31233-19 139 99 .23332-19 .11393-23 23233-19 .39333-19 133 99 .23223-19 .39333-12 .23233o19 .31233-19 139 99 23333-19 .21333-11 .23333-19 .32333-19 133 99 .22333-19 .31393-11 .23133-19 .33323-19 299.99 .22933o19 .11333-19 .22233-19 .33313~19 293.99 .29233-19 .12333-19 .22123-19 .33332-19 219.99 .13133-19 .23393-19 .29233-19 .32313.19 213.99 .13993-19 .22233-19 .13233-19 .33323o19 229 99 .12323-19 .32933-19 .17333-19 .12313-19 223.99 .11133-19 .33333-19 .13313-19 .22233-19 229.99 .33233-11 .33133-19 .13123-19 .23333-19 223.99 .39223-11 .31233-19 .12223-19 .31323-19 239.99 .32323-11 .31313-19 .19333-19 .33733-19 233.99 .33233o11 .13123-19 .33193-11 .33333-19 239 99 .23333-11 .13333-19 .22333-11 .33313-19 233.99 .23393-11 .21193-19 .33713-11 .33373-19 239 99 .22173-11 .22393-19 .33223-11 .13313-19 233 99 .13333.11 .19323-19 .23123-11 .73313-19 219.99 .11233-11 .11233o19 .23333-11 .13133-19 213.99 .33233-12 .33123-19 .13323-11 .71313-19 239 99 .33313-12 .33123-19 .13393-11 .31323-19 233 99 .39323-12 .33933-19 .19233-11 .33393-19 239 99 .23113-12 .32313-19 .12223-12 .32333-19 233.99 .22233-12 .32333-19 .33323-12 .32333-19 299.99 .17233-12 .39933-19 .22393-12 .39313-19 293.99 .13323-12 .23323-19 .21333-12 .23323-19 219.99 .13223-12 .13313-19 13333-12 .13223-19 213.99 .12133-12 .12923-19 .32323-12 .17233-19 229 99 .33193-12 .29313o19 .31333-12 .21923-19 223.99 .33333-12 .13333-19 .23393-12 .13333-19 229.99 .19193-12 .11123-19 .22323-12 .11213-19 223.99 .33323-12 .23913~11 .13333-12 .39933-11 239.99 .31273-12 .33333-11 .11133-12 39213-11 233.99 .13233—12 .12293-19 .33233-13 .12223-19 239.99 .31233-13 .12933-19 .13323-13 .12913-19 233.99 .33293-12 .33223-11 .21333-13 .33393-11 239.39 .33293-12 .13213-23 .33313-13 .22113-12 155 Probe near a conducting cylin ' der. Ine1dent fi Id . (2,“ d . . . . (F195. 3.2. .3.2.12,3?2.1§)) V/m’f 2 OGHZ TABLE 8-6 : PIIOUIICV I .20000010 PM] 10 L000 0000007 00 L000 0000007 00 L000 0000007 00 L000 0000007 09 DEC '00 '01 'D0 0 '00 70 7070L 0.00 .13000-12 0. .00030°10 .10000'12 0.00 .01020-13 .10000-11 .03000-10 .10000'11 10 00 .23000-13 .01000-11 .21000-10 .02120'11 10 00 .30000-13 .00700-11 .01030-10 .00120-11 20 00 .11700-12 .30000-11 .10110'13 .30100-11 20 00 .10000-12 .20000-11 .23100'13 .20000-11 30.00 17000-12 .02020-11 .31100-13 .00000-11 30 00 13720-12 .00000-11 .07000-13 .10100-10 00 00 17100-12 .12000'10 .01000'13 .12020’10 00 00 .20070-12 .12000-10 .13100-12 .13010'10 00 00 .37700'12 .13030-10 .20320'12 .10010-10 00 00 .30000'12 .10300-10 .30070-12 .10000-10 00 00 .30300-12 .20700-10 .07170-12 .20000-10 00 00 30000-12 .31000°10 .70720'12 .32700-10 70 00 02000-12 .30000°10 .10300-11 .30320-10 70 00 .00000-12 .30000-10 .10700-11 .00000'10 00 00 .20020-12 .00270-10 .20700-11 .07000-10 00 00 17330-12 .03300-10 .20710-11 .00300-10 00 00 .07300-13 .00310-10 .30000-11 .03200-10 00 00 .07300-13 .02000-10 .01000-11 .07210-10 100 00 .02300-13 .03200-10 .00000'11 .70020-10 100.00 .33030-12 .00020'10 .00000-11 .73000-10 110.00 .00000-12 .00000-10 .10000-10 .70030-10 110 00 .10100-11 .00100-10 .12020-10 .70000'10 120.00 .32000-11 .00000-10 .10270'10 .70000'10 120 00 .00070-11 .00000-10 .17020-10 .77000-10 130 00 .70700-11 .07000-10 .20030-10 .70000-10 130 00 .10020-10 .01000'10 .23020-10 .70000-10 100 00 .10100-10 .30330-10 .20030-10 .70000'10 100 00 .17000-10 .27010-10 27000-10 .73300-10 100 00 .21000-10 .20000-10 .30000-10 .72710’10 100 00 .20000-10 10000-10 .32010-10 .72200-10 100.00 .20100-10 .00000-11 .33000-10 .72200-10 100 00 .32100'10 .02000-11 .30000-10 .72010-10 170.00 .30000-10 .23030-11 .30010'10 .72700‘10 170 00 .30000-10 .00000-12 .30000'10 .73020-10 100 00 .30000-10 .00000'37 .30000'10 .73130-10 100 00 .30000-10 .00000-12 .30000-10 .73020'10 100 00 .30000-10 .23030-11 .30010-10 .72700-10 100.00 .32100-10 .02000-11 .30000-10 .72010'10 200.00 .20100-10 .00000-11 .33000-10 .72200'10 200 00 .20000-10 .10000-10 .32010-10 .72200-10 210 00 .21000-10 .20000-10 .30000-10 .72710-10 210 00 .17000-10 .27010-10 .27000-10 .73300-10 220 00 .10100-10 .30330'10 .23030-10 .70000-10 220.00 .10020-10 .01000-10 .23020-10 .70000'10 230 00 .70700-11 .07000'10 .20030-10 .70000'10 230 00 .00070-11 .00000-10 .17020-10 .77000-10 200 00 .32000-11 .00000-10 .10270-10 .70000-10 200.00 .10100-11 .00100-10 .12020-10 .70000-10 200 00 .00000-12 .00000-10 .10000-10 .70030-10 200 00 .33030-12 .00020-10 .00000-11 .73000-10 200.00 02300-13 .03200'10 .00000°11 .70020'10 200 00 .07300-13 .02000-10 .01000-11 .07210-10 270.00 .07300-13 .00310-10 .30000-11 .03200-10 370.00 .17330-12 .03300'10 .20710-11 .00300'10 200.00 .30020-12 .00270'10 .20700-11 .07000-10 300.00 .00000-12 .30000'10 .10700-11 .00000°10 200 00 .02000'12 .30000'10 .10300-11 .30320-10 200.00 .30000'12 .31000-10 .70720'12 .32700'10 300.00 .30300'12 .20700'10 .07170-12 .20000'10 300.00 .30000'12 .10300'10 .30070-12 .10000-10 310 00 .37700'12 .13030'10 .20320-12 .10010-10 310.00 .30070'12 .12000‘10 .13100‘12 .13010-10 320.00 .17100-12 .12000-10 .01000-13 .12030’10 320.00 .13720'12 .00000-11 .07000-13 .10100-10 330.00 .17000'12 .02020-11 .31100'13 .00000‘11 330.00 .10000'12 .20000'11 .23100'13 .20000'11 300.00 .11700'12 .30000-11 .10110-13 .30100'11 303.00 .30000'13 .00700-11 .01030-10 .00120-11 300.00 .23000-13 .01000'11 .21000-10 .02120'11 300 00 .01020'13 .10000'11 .03000'10 .10000'11 300.00 .13000'12 .01030'30 .00030-10 .10000-12 156 Probe near 3 cy Incident field (Figs. 3.2.19.3. . TABLE B-7 : i iflectric shell. V/m,f-3.0GH2. 000000001 8 .30000910 '10L0 I 2.00 000L0 I 00 00 001 10 L000 0000007 00 L000 0000007 00 L000 0000007 00 L000 0000007 00 000 '00 001 '00 0 '00 70 7070L 0 00 .70370-10 0 .30100-00 .02700-00 0 00 .77000-10 .03030-13 .20730-00 .33010-00 10.00 .00020-10 .33210-12 .70000-10 .10000-00 10 00 .00020-10 .20000-11 .00000-11 .02200-10 20.00 00030-10 .00700-11 .10070-11 .00070-10 20 00 .02000-10 .17000-10 .03000-11 .10000-00 30.00 .71000-10 .20000-10 .07700-10 .10700-00 30 00 .00000-10 .00000'10 .10700-00 .20000-00 00.00 .00000-10 .71020-10 .17100-00 .20700-00 00 00 .01170-10 .07000-10 .10300-00 .27170-00 00.00 .00700-10 .00100-10 .10000-00 .20300-00 00 00 .30130-10 .00000-10 .10110-00 .31070-00 00.00 .20020-10 .11700-00 .17030-00 .30020-00 00 00 .11030-10 .13070-00 .17220-00 .32000-00 70 00 .00000-11 .13000'00 .20000°00 .30010-00 70 00 .11300-10 .11000-00 .17320-00 .30000-00 00.00 .10220-10 .11000-00 .10000-00 .23020-00 00 00 .70330-11 .13220-00 .11030-00 .20000-00 00 00 .01200-11 .13000-00 .10000'00 .20000-00 00 00 .30000-11 .11300-00 .11000-00 .23000-00 100 00 00030-11 .10000-00 .03020-10 .10000-00 100 00 .11000-10 .10170-00 .07300-10 .10100-00 110 00 23000-10 .10700-00 .00000-10 .21100-00 110.00 .20700-10 .10000-00 .03000-10 .22030-00 120.00 .20000-10 .03020-10 .70000-10 .10000-00 120 00 .10000-10 .00000-10 .00000-10 .10000-00 130 00 10030-10 .70310-10 .03000-10 .13200-00 130 00 .20120-10 .03000-10 .02000-10 .13300-00 100 00 .03030-10 .00030-10 .01200-10 .10100-00 100 00 .00020-10 .00720-10 .00730-10 .10030-00 100 00 .00000-10 .30100-10 .00000-10 .20000-00 100 00 .71000-10 .20000-10 .01000-10 .10200-00 100 00 .00000-10 .10010-10 .77010-10 .10070-00 100 00 .00000-10 .11200-10 .00700-10 .10000-00 170 00 .00000-10 .00700-11 .07000-10 .13200-00 170 00 .00000-10 .12700-11 .00010-10 12770-00 100 00 .00300-10 .12100-30 .71200-10 12000-00 100 00 .00000-10 .12700-11 .00010-10 .12770-00 100 00 00000-10 .00700-11 .07000-10 .13200-00 100.00 .00000-10 .11200-10 .00700-10 .10000-00 200.00 .00000-10 .10010-10 .77010-10 .10070-00 200.00 .71000-10 .20000-10 .01000-10 .10200-00 210 00 .00000-10 .30100-10 .00000-10 .20000-00 210 00 .00020-10 .00720-10 .00730-10 .10030'00 220.00 .03030-10 .00030-10 .01200-10 .10100-00 220.00 .20120-10 .03000-10 .02000-10 .13300-00 230.00 .10030-10 .70310-10 .03000-10 .13200-00 230 00 .10000-10 .00000-10 .00000-10 .10000-00 200.00 .20000-10 .03020-10 .70000-10 .10000-00 200 00 .20700-10 .10000-00 .03000-10 .22030-00 200 00 .23000-10 .10700-00 .00000-10 .21100-00 200 00 .11000-10 .10170-00 .07300-10 .10100-00 200.00 00030-11 .10000-00 .03020-10 .10000-00 200.00 .30000-11 .11300-00 .11000-00 .23000-00 270.00 .01200-11 .13000-00 .10000-00 .20000-00 270.00 .70330-11 .13220-00 .11030-00 .30000-00 200.00 .10220-10 .11000-00 .10000-00 .23020-00 200 00 .11300-10 .11000-00 .17320-00 .30000-00 200.00 .00000-11 .13000-00 .20000'00 .30010-00 200 00 .11030-10 .13070-00 .17220-00 .32000-00 300.00 .20020-10 .11700-00 .17030-00 .30020'00 300 00 .30130-10 .00000-10 .10110-00 .31070-00 310 00 .00700-10 .00100-10 .10000'00 .20300-00 310.00 .01170-10 .07000-10 .10300-00 .27170-00 320.00 .00000-10 .71020-10 .17100-00 .20700'00 320.00 .00000-10 .00000-10 .10700-00 .20000-00 330.00 .71000-10 .20000'10 .07700-10 .10700-00 330.00 .02000-10 .17000'10 .03000-11 .10000-00 300.00 .00030-10 .00700-11 .10070-11 .00070'10 300.00 .00020-10 .20000-11 .00000-11 .02200-10 300.00 .00020-10 .33210-12 .70000-10 .10000-00 300.00 .77000-10 .03030-13 .20730'00 .32010-00 300.00 .70370-10 .30030-30 .30100'00 .03700-00 157 TABLE B-8 : Probe near a cylindrical dielectric shell. Incident field - (2,h§ deg.g V/m,f-2.LSGH2. (Figs. 3.2.20,3.2.23, .2. 6 000000007 I .20000910 010L0 3 2 00 000L0 0 00.00 '01 10 L000 0000007 00 L000 0000007 00 L000 0000007 00 L000 0000007 00 000 '00 001 000 0 000 70 7070L 0 00 .00030-10 .73130-10 .12700-00 0 00 .00010-10 10100-12 .02000-10 .11700-00 10 00 .00200-10 .02300-12 .00030-10 .10310-00 10 00 .00000-10 .32000-11 .00020-10 .10030-00 20 00 .00710-10 .70000-11 .02000-10 .12020'00 20 00 00770-10 10070-10 .02000-10 .13170-00 30 00 01000-10 .21000-10 .00030-10 .12300-00 35 00 00310-10 .20000-10 .00000-10 .13120-00 00 00 37000-10 .30720-10 .00070-10 .10000-00 00 00 .27000-10 07030-10 .13370-00 .20030-00 00 00 10310-10 .00010-10 .13000-00 .21070-00 00 00 .10070-10 .00000-10 .11030-00 .10210-00 00 00 13000-10 .00000-10 .00070-10 .10010-00 00 00 11000-10 .00000-10 .00020-10 .10010-00 70.00 .70000-11 .00230-10 .00020-10 .17120-00 70 00 .37330-11 .70000-10 .02000-10 .17020-00 0O 00 10000-11 .00110-10 .00070-10 .17010-00 00 00 .23010-12 .01010-10 .00000-10 .17210-00 00 00 .32300-12 73000-10 .02030-10 .10000-00 00 00 10000-11 .07000-10 .00030-10 .13000-00 100 00 .02000-11 .00000-10 .00000-10 .12000-00 100 00 .11030-10 71200-10 .03000-10 .13030-00 110 00 10130-10 70320-10 .00000-10 .10000-00 110 00 17020-10 .00200-10 .72200-10 .10000-00 120 00 10010-10 .00720-10 .00300-10 .13100-00 120 00 10770-10 .07000-10 .00000-10 .10320-00 130 00 10000-10 02200-10 .20200-10 .07300-10 130 00 .20010-10 37030-10 .20010-10 .00300-10 100 00 20700-10 .33300-10 .30700-10 .00020-10 100 00 .37200-10 .20000-10 .00000-10 .11010-00 100 00 00000-10 .22000-10 .01130-10 .11700-00 100 00 00000-10 .10100-10 .00170-10 .12120-00 100 00 03130-10 .10720-10 07100-10 .12100-00 100 00 .00070-10 .01070-11 .07020-10 11000-00 170 00 .00000-10 .20100-11 .00000-10 .11030-00 170 00 .00000-10 .71130-12 .00000-10 .11200-00 100 00 00020-10 .00030-37 .00000-10 .11100-00 100 00 00000-10 .71130-12 00000-10 .11200-00 100 00 .00000-10 .20100-11 .00000-10 11030-00 100 00 .00070-10 .01070-11 .07020-10 .11000-00 200 00 03130-10 .10720-10 .07100-10 .12100-00 200 00 .00000-10 .10100-10 .00170-10 .12120-00 210 00 .00000-10 .22000-10 .01130-10 .11700-00 210.00 .37200-10 .20000-10 .00000-10 .11010-00 220 00 .20700-10 .33300-10 .30700-10 .00020-10 220 00 .20010-10 .37030-10 .20010-10 .00300-10 230 00 .10000-10 .02200-10 .20200-10 .07300-10 230.00 .10770-10 .07000-10 .00000-10 .10320-00 200 00 .10010-10 .00720-10 .00300-10 .13100-00 200 00 .17020-10 .00200-10 .72200-10 .10000-00 200 00 .10130-10 70320-10 .00000-10 .10000-00 200 00 .11030-10 .71200-10 .03000-10 .13030-00 200 00 .02000-11 .00000-10 .00000-10 .12000-00 200 00 .10000-11 .07000-10 .00030-10 .13000-00 270 00 .32300-12 .73000-10 .02030-10 .10000-00 270.00 .23010-12 .01010-10 .00000-10 .17210-00 200 00 .10000-11 .00110-10 .00070-10 .17010-00 200.00 .37330-11 .70000-10 .02000-10 .17020-00 200 00 .70000-11 .00230-10 .00020-10 .17120-00 200.00 .11000-10 .00000-10 .00020-10 .10010-00 300.00 .13000-10 .00000-10 .00070-10 .10010-00 300.00 .10070-10 .00000-10 .11030-00 .10210-00 310.00 .10310-10 .00010-10 .13000-00 .21070-00 310.00 .27000-10 .07030-10 .13370-00 .20030-00 320.00 .37000-10 .30720-10 .00070-10 .10000-00 320.00 .00310-10 .20000-10 .00000-10 .13120-00 330.00 .01000-10 .21000-10 .00030-10 .12300-00 330.00 .00770-10 .10070-10 .02000-10 .13170-00 300.00 .00710-10 .70000-11 .02000-10 .12020-00 300.00 .00000-10 .32000-11 .00020-10 .10030-00 300.00 .00200-10 .02300-12 .00030-10 .10310-00 300.00 .00010-10 .10100-12 .02000-10 .11700-00 300.00 .00030-10 .00000-37 .73130-10 .12700'00 158 TABLE 8-9 : Prope near a cylindrical dielectric shell. Incident field - (2 b deg. V/m,f-2.0GH2. (Figs.3.2.21,3.2.2!1, .2. 7 '00000001 0 .20000010 F10LD 8 2 00 000L0 I 00.00 D"! 1N L000 0000001 30 L000 0000007 00 L000 00000-7 00 L000 0000007 00 000 '00 PM! '00 0 '00 70 7070L 0 00 ,00100-10 , .71030-11 07330-10 0 00 .30770-10 .27720-12 01000-11 .00200-10 10 oo .30000-10 .11000-11 .17120-10 .00000-10 10 oo .30700-10 20030-11 .33000-10 .72070-10 20 00 .30000-10 .00030-11 03700-10 .00000-10 20 00 .32200-10 .07030-11 .70100-10 11220-0. 30 00 .20000-10 10730-10 .73300-10 11000-00 30 00 .27010-10 10000-10 .03000-10 .11030-00 00 00 20000-10 .23330-10 .00000-10 .00200-10 00 00 .20000-10 .20000-10 .00030-10 .03070-10 00 00 .10070-10 .30000-10 .00000-10 10210-0! 00 00 .10070-10 .30110-10 .00000-10 .11000-00 0o 00 .07000-11 02000-10 .70020-10 .12070-00 00 00 .30710-11 07100-10 .71000-10 .12270-00 70 00 .27200-11 .00070-10 .00030-10 .11000-00 70 00 .22100-11 .00070-10 .00000-10 .00000-10 00 OO 17000-11 .00000-10 .00000-10 .01000-10 00 00 13700-11 00330-10 .00000-10 .02700-10 00 00 .10700-11 07700-10 .00110-10 .07000-10 00 00 .20120-11 .00130-10 .00210-10 .10100-00 100 00 .00100-11 .00120-10 .00320-10 .10300-00 100 00 .00210-11 .07100-10 .00220-10 .10030-00 110 00 03700-11 .02200-10 .00000-10 .02000-10 110 00 ,07000-11 .37020-10 .30000-10 .02020’10 120 00 70000-11 .33000-10 .32200-10 72000-10 ntoo mac-to .30700-10 .27710-10 .00030-10 130 00 .10010-10 .20270-10 .27330-10 .70010-10 130 00 .20200-10 .20300-10 .30000-10 .70270-10 100 00 .20300-10 .21000-10 .30000-10 .02020-10 100 00 20000-10 .17000-10 .30010-10 .07170-10 10° 00 .32270-10 .13700-10 .02170-10 .00100-10 100 00 33000-10 .00200-11 .02000-10 .00300-10 100 00 .30000-10 .00000-11 .01730-10 .02770-10 100 00 .30000-10 .30000-11 .00300-10 .70030-10 170 00 .30030-10 .10320-11 .30100-10 .70700-10 170 00 .30000-10 .00000-12 .30320-10 .73020-10 100 00 .30070-10 .00300-37 .30000-10 72010-10 100 00 .30000-10 .00000-12 .30320-10 .73020-10 100 00 .30030-10 .10320-11 .30100-10 .70700-10 100 00 .30000-10 .30000-11 .00300-10 70030-10 200 00 .30000-10 .00000-11 .01730-10 .02770-10 200 00 .33000-10 .00200-11 .02000-10 .00300-10 210 cc .32270-10 .13700-10 .02170-10 .00100-10 210 cc .20000-10 .17000-10 .30010-10 .07170-10 220 00 .20300-10 .21000-10 .30000-10 .02020-10 220 00 .20200-10 .20300-10 .30000-10 .70270-10 230 00 .10010-10 .20270-10 .27330-10 .70010-10 230 00 .10100-10 .30700-10 .27710-10 .00030-10 200 00 .70000-11 .33000-10 .32200-10 72000-10 200 00 .07000-11 .37020-10 30000-10 .02020-10 200.00 .03700-11 .02200-10 .00000-10 .02000-10 200 00 .00210-11 .07100-10 .00220-10 .10030-00 200.00 .00100-11 .00120-10 .00320-10 .10300-00 200.00 .20120-11 .00130-10 .00210-10 .10100-00 270.00 .10700-11 .07700-10 .00110-10 .07000-10 270 00 .13700-11 .00330-10 .00000-10 .02700-10 200 00 .17000-11 .00000-10 .00000-10 .01000-10 200 00 .22100-11 .00070-10 .00000-10 .00000-10 200 00 .27200-11 .00070-10 .00030-10 .11000-00 200.00 .30710-11 .07100-10 .71000-10 .12270-00 300,00 .07000-11 .02000-10 .70020-10 .12070-00 300.00 .10070-10 .30110-10 .00000-10 .11000-00 310 00 .10070-10 .30000-10 .00000-10 .10210-00 310.00 .20000-10 .20000-10 .00030-10 .03070-10 320.00 .20000-10 .23330-10 .00000-10 .00200-10 320.00 .27010-10 .10000-10 .03000-10 .11030-00 330.00 .20000-10 .10730-10 .73300-10 .11000-00 330.00 .32200-10 .07030-11 .70100-10 .11220-00 300.00 .30000-10 .00030-11 .03700-10 .00000-10 300.00 .30700-10 .20030-11 .33000-10 .72070-10 300.00 .30000-10 .11000-11 .17120-10 .00000-10 300.00 .30770-10 .27720-12 .01000-11 .00200-10 300.00 .00100-10 .10170-30 .71030-11 .07330-10 TABLE PH! DID 300 10‘ 110 IIS. ‘20 12' 130 '3' 1‘0 105 iDO 1" 1.0 I‘D 170 175 100 IDS 1.0 IDS 200. 205. 210. 2:5. 230. 223. 230. 235. 200, 208. 2'0, 260. 2‘5. 270. 278‘ 2A0 20'. 2’0‘ 203. 300. 303, 3'0. .00 .00 31' 320 32'. 330. III. 300. 348. 330 ll. 3.0 00 00 00 ‘00 .00 .00 00 ‘00 00 .00 00 .00 .00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 _00 00 00 .00 .00 .00 B-IO : .IDODI' .DDO?!‘ .2‘!!!‘ .IIDII' .IITDI' .1}DDI’ .ZZADE' .IIIO!‘ .JIDJD°12 .04.!!- .IDDOI‘ .DIDOE' .DDAOI' .awsaz- .IUCOI-II .3910:- .1.71!-I1 .1ssse- .2321!- .3323!‘ .4351!- .Ii70l' .DBZIE° .IAVIE' .1340!’ .0730!- .IIIIE’ .3010!- 159 Prop: near a c lncndent field (Fig. 3.3.1) FIIOUIICY I LOAD CUIIII? 80 '0. PM! 12 i: 13 I2 12 ‘0071‘1! .I007I-1I .DO7ID’ .DZDOI~I2 .30iDl’ .‘DOJI' '0 10 10 ‘0 VDZJI'IO 10 IiiDl'OD .IITOI-OD ‘IIO7E-OD .‘ADAI'OD .iDIDI'OI .II7DI'0! .IIDIE°OD IADAI°00 .13.?!‘0’ .‘270E'OD .1IIIE-0O .ODDDI-10 .TDZDI' .II?0I° .ADDII-10 .3322l-10 .222Al'10 .IIDSI' .7D1|l° .02301-12 .ID?DI° .1007!- .1120!’ .IOOVI'II I! 11 I! .DDAOI'12 .0150!- .0000!- .AADil' .SODII‘12 12 12 12 .IDIDI-Ifl .IIADI-I2 .SIDDI'II .iDVOI‘IZ .iODll'ia .Ilfill-‘J .DIIVI-IJ .IDDDI'I2 .3000l910 FDI .3201l'1| .03111’11 .2087I~11 .ZOAll-ii .D211I'11 .OOODI‘II .TDDAl-Ii .10.!!‘10 .2077I°10 .22771-‘0 .DOODI'io .AICZE-Io .01371°i0 .DIDII'IO .7DDIE~10 .IDIAI'iO .100II-0I .‘OOJI'OD .1334!°0I .IIOAI'OD .1AOII°00 .1AOII'OI .iJSOI'OD .123DI'00 .QIOJI'OD .DDDDI'10 .AO‘DI-‘O .DC07I'VO .IOIAI'IO .DIIDI-IO .230ll'10 .18001-10 .A1DAI°II .IDAII-Il ,ODOII'IZ .10713-30 .DDOJl-tz .SAACE'II .AVDAl-II .IDDDI°I0 .ZDODl-IO .IOIOI'IO .ADIAI-‘O .DAOVI-iO .00101-10 .ODADI“0 .1103l-OD .123DI'OD .IDDOI'OI .iAO'I'OD .IAOII~00 .IDDAI'0D .LSJAI‘OD .i203l'00 .10DOI'0D .DDiAI'IO .7ODDI'10 .DIIII‘10 .D337I'10 .AIAII-IO .SOIII010 .OZTVI'I0 2077l-I0 .1AD2I'I0 .VIODl-II .DJOIl-II .Datil'Ii .IDDAI'II .20I7I'11 .I371l'11 .DZIVE-I1 .2.22l°3$ Y I In ( LOAD CURRENT 80 NO. 1 LOAD FOR .TOlil-vd .3D7IB'IA .ODOII-ll .1’0‘1'13 .2037I-13 .JOADI°13 .DOISE-l: .1022I-‘2 .IIDJI-i? .IDlil-Iz 13‘TI'I1 .Dtd7l'1l .3307l'i1 .IIOOI'II .VDAAI'II .110Dl‘i0 .‘DDII-DO .2‘3OI'1O .IDAOI-‘O .DDD7I‘10 .ADVOE-10 .IVDDI'IO .DDZDI'!0 .DIIDI"0 .DJZII-IO .10071-00 .‘IIDI'OD .IIDOI'OD .1DAII'0D .‘AIOI'OD .10021'0D .1I32I'0D .IDODI-OD .1IDOI°OD .‘IDT!°OD .IDDOI'OI .1OOAI°0D .ISOZI'OD .IADIE'OD .IAIII'OD .1DCJI'OD .IZIAI'OD .11333'00 .1007l-0D .I32Il‘10 .DIDDE'io .oozot-to .D7ODI'|0 .AI7OI-10 .30978'00 .OA‘OI'IO .IilDl-io .SDDZI'IO .11002-10 .VDAAI'Ii .IIQOI'Ii .33.?!‘11 .DICVI'II .1347I'11 .AZDSI-iz .I000I’12 .ZODII'IZ .iIDDI-I: .1022I'12 .IOIII-13 .O0AOI°13 .2037I'13 .‘DOII‘lD .IDODI'IA .IDVDI-IA .VDAil'IA CUIIINY 80 Y! ical bod m.f-3.0G .1.7AI°12 .333.I°1t .OAOOI‘II .22A2I-Il .IIOZI'IQ .DIDTI-ii .DDIil-ii .DIDII‘II .IO'DI-IO .DIDII'IO .23D7l*‘0 .32213'10 .AIIII-‘O .DCDTI'iO .0701I‘30 .IDIDl-Io .I037I'OD .ItDAI°0. .I3D3l'0. .1DIOI'OD .‘IDAI'0O .I7DAE-0D .‘Oizl-OD .20001‘00 .2070l°09 .ZIDDI-OD .32233'00 .2310I-00 .2A13I'0D .IDIDI'0D .IOIVI'OD .IVOAE-OD .ZOltl'OI .DOill-OD .IIOil'0D .IVIDI°0O .DITJI'OD .IIDDI-OD .3101l'00 .IOIAI‘OO .ZO‘tI-OD .ZTAAI-OI .IDITI-OD .2DZDI°OO .2AIDI-0D .23!‘I°0| .2223I°09 .IIJA!°OD .2010!°0. .20001-0D .‘OiII-0O .17DAI°0I .‘DAAE-OD .1I30l'00 .IODII‘0D .1IDAI°0O .IOJVI-OD .DDDDI-I0 .D7OII-i0 .DDDVI'10 .03031-10 .322|l-10 .23073'10 .31.!!‘10 .1D'Dl°10 .DDDII-it .DDD‘I'II .DII7I-11 .32021-11 .DIAII-ii .OAOOI-i‘ .JDODl-II .10702'13 fig. LOAD CUDIIIT 80 YOTAL TABLE OH} DID ‘00 108 '10 I'D 12D '30 135 100‘ ‘DO 13‘ 1.0 1.5 '70 17‘ 1.0 III 1.0 '0' 200‘ 203 2'0 3‘8 220. 235 240 III 230. 2'3. 260. III. 270. 27. III 2.3 300‘ 30.. 3‘0 00 00 00 00 00 00 .00 700 .00 00 00 ‘00 ‘20. 00 00 00 00 00 00 00 00 00 00 .00 230, 00 00 .00 .00 300, .00 2'0. .00 00 ‘00 .00 .00 .00 .00 .00 DID. 3'0, 00 B-ll FIDO LOAD CUIIIIT 80 '0! .13031' .7320I' .1111!- .V’ADE' .IIOOI' .130‘1‘ .1132!- .IIDII‘ .3200!- .II2II‘ .SDOVI' .AATII- .IDDOI- .ODAII' .IAZAI' .IDITI' .ADJAI- .3402!’ .1IDDI' .1IDII' .33.!!- .A6701' .IDIII' .DAOAI' .tOVDI’ .1500!‘ ‘22231' .DDAII' .ADADI- .IIIJI- .DOCJI' .IDAAI- .7iIII' .VAIAI' .7530!- .1ADA!° .71DAI' .OODAI' 160 : Probe near a lngident fiel (Fug. 3.3.2) UIICV I .20302010 IDDVI' i0 ‘0 |0 |0 STJOI'IO ‘0 10 ‘0 l0 .IOIJI'IO .SIJJI‘ .0802!- .3730!‘ .IIAOI' .IDIOI-Io .IIDOI' .IOVDI' .IDOAI' .SDIII' .IDDTI' .AIVAI- .DIDII' .IIAII' 10 II II .IADOI°I2 .SAOZI- .0034!- .DI17I° .IAZA!‘ .OIDII' ‘2 ‘2 12 I2 12 .IADOI'iz .4010!- .30.?!‘ .IDIOI‘ .3200I-12 .SDD‘l-IZ .1132I°12 .‘ID‘I-IZ .1I00l'12 .7IAII'i3 .1IIII-13 .VIDDI-il .lJODI-i! .23.!!- ‘DJIOI' .AOIDI' .|D07I~ LOAD CUIIIIY 30 ID! I .AIDII' .IITJI' .OJIDI’ .13IOI' .2062!‘ .338‘l° .2D7Al° .JDIII' .ACAII' .8003!- .0234!- .7027!- .803!!- .AAIII- !I II .1OODD'10 ‘ I IO IO 10 I0 .II2DI-‘0 .OIIJI-IO .DOODI' .DAIAI' .VIDOI' .I012I° .DODJI' .00.!!- .JIIII~ .2732!- .iDOIE‘ .|22|I' .IDODI- .IIAII- .70301-12 .AIJII‘)? .VDIOI' I2 .31..I-'! .IIIDI-‘O .IDOOI-io .2722!- .3801!- .0082!- .DOOJI'IO .DDIZI‘IO .VDDAI‘VO .DAIAI°i0 .O0ODI' . . O 0 I. . ‘0 10 IO .DIZDI-‘O .ADIJI°|0 .DOJII°IO .7027I-10 .DODAI-IO .DDODI"0 .ADADI-io .3..2I-|0 .DDTAI-‘O .ODDiI'io .IOOZI"0 .IIIOI-IO .IOODI'10 .DO73I°1i .ADD‘I-ii .‘DOTI-Ii .AO‘DI°II .IDO0I‘1I .IDDIl-I! .I'AII‘JI c Ii d. .8273!- .AIIA!’ .IO‘O!‘ .IO7I!‘ .2329!- .62011° .7.2DI° ,!310£' .2043!‘ .JIIAI- .I2CI!°12 .02201' ,IIIOI' .SDIII' .IDIAO'I .AOAAI’I .I7AII'V .TDDII'I .1000I°I .1A19I° .0373!- .ADiDI’ 7.43!!- .IDiil‘ .DIADI' .0728!- .TOAII-OO .70...‘ .7008!‘ .073II-10 .DIAS£° .ODII" .DAIII' 237!!- I! .i302l~10 OIVDII' .ZIJII' .27JDl-10 .IZIII°IO I0 10 7300l°10 .VDDDI°‘0 .TOJAI-IO .7IDII-10 .7‘001-10 .7300I"0 .ADIII-l0 .0373!“ .IAIOD010 .3200!- .IVIII° .IOIDI-‘0 .IVDDl-IO .‘3D2I'10 .10001-10 .7001I° .DTAil'!i .AODAI-I! .DOIAI'il .IDIDI-l! .12DII'|1 .Dzlll'iz .IDADI'ifl .DOOII°12 .20A3I-12 .1310I'I2 .7DDIl-1I .AII‘I‘!) .IIIOl-SJ .IDTDI‘ID .10101013 .IIVDI'IA .AODAI-IA .0273I°IA lo V LOAD CUIIENY 80 FOR TI 9... 3:31 bod ,f-2.h5 .IIDVI'ID .IADDI'II .ID7OI‘II .AODDI’!1 .IDOII'II .AADDI°11 .D‘IDI-i! .‘0JDI'10 .OD’OI'il .IIO7I'IO .31303'l0 .IIVDI"0 .30!0I°‘0 .37III-I0 .ADDDI°|0 .DDAII'!0 .I7III-10 .7OIDI-10 .DDIII-‘O .DDDDI-IO .1ODDI'OD .1100I°OD .1IDOI'OO .12IAI°0D .ialOI-OD ‘13ADI°0O .12001-00 .127OI'0D .IIOAI-OD .Illfil'OD .13011'00 .IDOII-0. .IAIAI'OD .‘0IDI'OD .LAIOI'OI .ID‘DI'OD .10101-00 .|D|1I'OI .1CDOI'OO .|ADDI-0. .IAIAI°0D .IIDDI'OI .13.!!‘0' .IISII.0O .i30AI-OD .IIVOI‘OI .1ODDl-OD .IIAII'OI .IZDDI-OD .‘IICI'0D .liODI-OI .IO0DI'0D .IOOII'OO .ODDIl-IO .DDODI'IO .7ODDI-10 .0711I'10 .IOAII'10 .ADDOI-lo .3731I‘10 .IOIII"0 .IIVDI-IO .3130I°|0 .IID1I-10 .DDIOI-I‘ .IOSDI'I0 .DIIDI“! .ACOSI’!‘ .IOODI°II .AODDI'ii .ID1DI-‘1 .IOIOI°1I .‘307I-12 5A2. LOAD CUIRIIT 80 TOYAL TABLE PH! OES 100 100 110. 110 120 120. 130. 120 100 100 100 100 100 100 170 170. 100 100. 100. 100 200. 200. 210, 220. 220. 220. 220. 200. 200. 200 200. 270. 270 200 200 200 200. 200. 210. 210. 220. 220. 220. 220. 200. 200. 200. .00 00 ,00 .00 00 .00 00 00 .00 00 00 00 00 00 0O 00 00 00 00 00 00 00 .00 .00 .00 200. .00 8-12 : 'R!0U!RCY I LOAD CURR!07 00 FOR P”! .0071!“12 .0107!“12 .2000!“12 .0002!“10 .2212!“12 .0700!“ .0020!“ .0001!“ .0002!“ .7011!“ 12 12 12 12 12 .0201!“ .1120!“ .1207!“ .1207!“ .1101!“ 12 12 12 12 12 .7000!“ .0702!“ .0000!“ .0000!“ .0002!“ 12 12 12 12 12 1000!“ .2020!“ .0002!“ .1012!“ .1000!“ .2210!“ .2220!“ .0210!“ .0002!“ .0001!“ .0200!- 0002!“ .1070!“ .1100!“ .1207!“ .1200!“ .1222!“ .1200!“ .1207!“ .1100!“ .1070!“1 .0002!“1 .0200!“1 .0001!“1 .0002!“1 .0210!“ .2220!“ .2210!“ .1000!“ .1012!“ .0002!“ .2020!“ .1000!“ .0002!“ .0000!“ .0000!“12 .0702!“12 .7000!“12 .1101!“12 .1207!“12 .1207!“12 .1120!“12 .0201!“12 .7011!“12 .0002!“12 .0001!“12 .0020!“12 .0700!“12 .2212!“12 .0002!“10 .2000!“12 .0107!“12 .0071!“12 1 .10000010 .1100!“ .2000!“ .0070!“1 .2002!“1 .2071!“1 .0010!“1 1 .1220!“ .1010!“ .1001!“ .1000!“ .1000!“ .2002!“ .2000!“ .2120!“ .2220!“ .2200!“ .2202!“ .2010!“ .2000!“ .2020!“ .2217!“ .2200!“ .1007!“ .1200!“ .2700!“ 1 1 .0700!“1 1 1 61 Probe near a Ingident fiel (Fug. 3 .3.3) 0000!“ 1000!“ 2000!- 2022!“ 1000!“ 0720!“ .0000!“27 .2700!“ .1002!“ .2222!“ .0700!“ .0720!“ .1000!“ .1007!“ .2200!“ .2022!“ .2000!“ 12 11 11 11 11 10 10 10 1200!“ 10 10 10 .2217!“10 .2020!“10 .2000!“10 .2010!“10 .2202!“10 .2200!“10 .2220!“10 .2120!“10 .2000!“10 .2002!“10 .1000!“10 .1000!“10 .1001!“10 .1010!“10 .1220!“10 .1000!“10 .0010!“11 .2071!“11 .2002!“11 .0070!“11 .0000!“11 .0000!“11 .2000!“11 .1100!“11 .0002!“20 CY d LOAD CURR!NT 00 FOR R ind (2 r ical ,hS dc b 9 ol ) LOAD CURR!RT 00 FOR 7! .0020!“10 .0270!“10 .2070!“ .2000!“ .0072!“ .1700!“ .2000!“ .2002!“ .0100!“ .7022!“ .1102!“ .1720!“ .2070!“ .2000!“ .0000!“ 12 12 12 12 12 .0072!“12 .2002!“ .2102!“ .2000!“ .0000!“ .0021!“ .0270!“ .7100!“ .0022!“ .0077!“ .0007!“ .1002!“ .1110!“ .1100!“ .1212!“ .1200!“ .0007!“ .1207!“ .1070!“ .2020!“ .1200!“10 .1272!“ .1200!“ .1200!“ .1212!“ .1207!“11 .0007!“12 .0072!“12 .0000!“12 .2000!“12 .2070!“12 .1720!“12 .1102!“12 .7022!“12 .0100!“12 .2000!“12 .1700!“12 .0072!“10 .2000!“10 .2070!“10 .0270!“10 .0020!“10 0 V ical bod m,f-1.SG 242. LOAD CURR!IT 00 YDYAL .0100!“ .2000!“ .7007!“ .1070!“ .1200!“ .1000!-10 .1000!“ .1000!“ .2020!“ .2017!“ .2000!“ .2207!“ .2000!“ .2001!“ .2001!“ .0020!“ .0007!“ .0017!“ .2000!“ .2071!“ .2000!“ .2200!“ .2202!“ .2000!“ .2001!“ .2022!“ .2720!“ .2002!“ .2000!“ .2002!“10 .2000!“ .2002!“ .2720!“ .7100!“12 .1101!“11 .2071!“ .0002!“ .0020!“ 1 1 0000!“1 1 1 2202!“ 10 10 10 10 .2022!“10 .2001!“10 .2000!“10 .2202!“10 .2200!“10 .2000!“10 .2071!“10 .2000!“10 .0017!“10 .0007!“10 .0020!“10 .2001!“10 .2001!“10 .2000!“10 .2207!“10 .2202!“10 .2000!“10 .20170“10 .2020!“10 .1000!“10 .1000!“10 .1000!“10 .1200!“10 .1070!“10 .7007!“11 .0000!“11 .2000!“11 .0100!“11 .0020!“11 .0002!“11 .2071!“11 .1101!“11 .7100!“12 TABLE B-i3 : FR!0U!RCV I F"! D00 10.00 20 00 20. 20 20 0O 00 00 00 00 00 .00 .00 00 00 00 100. 100 110 110. 120 120 120 120 100. 100 00 00 00 00 00 100. 100 100 100 I70 00 00 00 00 00 170 100. 100 100 100. 00 00 00 00 200. 200. 210. 210. 220. 220 220. 220 200. 200. 200. 200. 200. 200, 270. 270.00 200.00 200.00 200.00 200.00 200. 200. 210. 210. 220. 220. 220. 220. 200. 200. "° . '.' - ’0. ~ Probe near a cy Incident field - (2,0 deg.) V/m,f-3.0GH2. (Fig. .2000!010 LOAD CURRINT 00 FOR PHI 001300 001300 001300 00WM00 001300 0130130 001300 001300 001300 001300 004300 001300 001300 001300 0130 162 iindr 3.3.h) F|!LO I 2.00 LOAD CURRIRY 00 FOR I 001300 0130013 001300 0130130 001300 0130130 001300 001300 001300 001300 00W300 001300 00W300 001300 0130 icai b AREL! 3 .0001!“10 .7012!“10 .2002!“12 .0070!“12 .0000!“12 .1212!“12 .2000!“12 .2207!“12 .0002!“12 .1020!“10 .10200“10 .2217!“10 .2122!“10 .02770“10 .0000!“10 72000-10 .0202!“10 .1102!“00 .1200!“00 .1020!“00 .1000!“00 .2000!“00 .2211!“00 .2000!“00 .2000!“00 .2020!“00 .2000!“00 .2000!“00 .2127!“00 .21000“00 .2100!“00 .21000'00 .2127!“00 2000!“00 .2000!“00 .2020!“00 .2000!“00 .10000“00 .1020!“00 .1200!“00 .1102!“00 .0202!“10 .7200!“10 .0000!“10 .0277!“10 .2122!“10 .2217!“10 .1020!“10 .1020!“10 .0002!“11 .0200!“11 .2000!“11 .10000-11 .1012!“11 .0002!“12 .2207!“12 .1212!“12 .0000!“12 .0070!“12 .2002!“12 .7012!“10 .0001!“10 .1020!“12 LOAO CURR!07 00 FOR 7! LOAD CURRIN? 00 707 uologicai body. AL .1020!“12 .0001!“10 .7012!“10 .2002!“12 .0070!“12 .0000!“12 .1212!“12 .2000!“12 .2207!“12 .0002!“12 .1012!“11 .1000!“11 .2000!“11 .0200!“11 .0002!“11 .1020!“10 .1020!“10 .2217!“10 .2122!“10 .0277!“10 .0000!“10 .7200!“10 .0202!“10 .1102!“00 .1200!“00 10200-00 .1000!“00 .2000!“00 .2211!“00 .2000!“00 .2000!“00 .2020!“00 .2000!“00 .2000!“00 .2127!“00 .2100!“00 .2100!“00 .2100!“00 .2127!“00 .2000!“00 .2000!“00 .2020!“00 .2000!“00 .2000!“00 .2211!“00 .2000!“00 .1000!“00 .1020!“00 .1200!“00 .1102!“00 .0202!“10 .7200!“10 .0000!“10 .0277!“10 .2217!“10 .1020!“10 .1020!“10 .0002!“11 .0200!“11 .2000!“11 .1000!“11 .10120“11 .0002!“12 .2207!“12 .2000!“12 .1212!“12 .0000!“12 .00700“12 .2002!“12 .7012!“10 .00010“10 .1020!“12 TABLE B-ih : Probe near a cyiund ncal bnol lnondent field = (2 30 deg.) (Fig. 3.3.11) FRO0UENCV 1 .20000010 Fl!LD 8 2.00 AICL! 3 2O 00 PH! 10 L000 CU000NY 00 L000 CURRENY 00 LOAD CURR007 00 D00 FOR FM! FOR I FOR 7! O OO .70000-12 0. .11000-12 S 00 .22000-12 10200-11 .00000-10 10 00 12000-12 .20050-11 07000-10 10 OO 00710-12 .10200-11 .22020-12 2O 00 00010-12 10020-11 20000-12 20 00 .07010-12 01000-11 .00000-12 20 00 11220-12 .01020-11 00070-12 25 0C 10000-12 .20200-11 10220-12 00 OO 10070-12 72100-11 .20000-12 00 00 22000-12 10200-10 00720-12 0O 00 20000-12 11200-10 70000-12 00 OO 00700-12 .10200-10 .12000-11 0O 00 02200-12 21710-10 .20210-11 GS 00 02250-12 20100-10 .22200-11 7O 00 00070-12 21270-10 .00200-11 75 OO 00200-12 .20700-10 .70000-11 0O 00 .02000-12 07000-10 .11070-10 05 OO 21200-12 02220-10 .10020-10 00 00 10000-12 .00170-10 .22020-10 00 00 00050-12 0071!-10 .22000-10 100 00 22770-12 00710-10 .02700'10 105 00 77010-12 70000-10 .00000-10 110 00 10200-1! .70200-10 .70100-10 115 00 20200-11 .07020-10 .00070-10 120 00 00200-11 .01020-10 .10200-00 12S 00 11120-10 .00100-10 12100-00 120 00 10010-10 07000-10 .12000-00 12$ 00 22200-10 00000-10 .10710-00 100 00 20050-10 .22020-10 1722!“00 100 00 20110-10 .20070-10 .10020-00 100 00 07000-10 .10000-10 .20100-00 100 00 00000-10 .12020-10 .21200-00 100 00 02000-10 .70000-11 22200-00 105 00 00000-10 .02000-11 .22000-00 '70 oo 70720-10 10220-11 .22020-00 170 00 77700-10 .07020-12 22000-00 100 oo 70000-10 .02000-27 22000-00 100 00 77700-10 .07020-12 22000-00 100 00 70720-10 .10220-11 .22020-00 105 00 00000-10 .02000-11 .22000-00 200 00 02000-10 .70000-11 .22200-00 20$ 00 00000-10 .12020-10 .21200-00 210 00 07000-10 .10000-10 .20100-00 210 00 .20110-10 .20070-10 .10020-00 220 00 20000-10 .22020-10 .17220-00 22S 00 .22200-10 .00000-10 10710-00 220 00 .10010-10 .07000-10 .12000-00 220 00 .11120-10 .00100-10 .12100-00 200 00 .00200-11 .01020-10 .10200-00 200 00 .20200-11 .07020-10 .00070'10 200 00 .10200-11 .70200-10 .70100-10 200 00 77010-12 .70000-10 .00000-10 200 00 .22770-12 .00710-10 .02700-10 205 00 .00000-12 .00710-10 .22000-10 27° 00 .10000-12 .00170-10 .22020-10 270 00 .21200-12 .02220-10 .10020-10 200 00 .02000-12 .07000-10 .11070-10 200 00 .00200-12 .20700-10 .70000-11 200.00 .00070-12 .21270-10 .00200-11 200 00 .02200-12 .20100-10 .22200-11 200 00 .02200-12 .21710-10 .20210-11 200.00 .00700-12 .10200-10 .12000-11 210 00 .20000-12 .11200-10 .70000-12 210 00 .22000-12 .10200-10 .00720-12 220.00 .10070-12 .72100-11 .20000-12 220.00 .10000-12 .20200-11 .10220-12 220 00 .11220-12 .01020-11 .00070-12 220 00 .07010-12 .01000-11 .00000-12 200.00 .00010-12 .10020-11 .20000-12 200.00 .00710-12 .10200-11 .22020-12 200.00 .12000-12 .20000-11 .07000-10 200.00 .22000-12 .10200-11 .00000-10 200 00 .70000-12 .10010-20 .11000-12 163 9 .2700!- .1120!- .1021!- .0200!- .7700!“ .1002!“ .2010!“ .0700!“ .7027!- .7027!- .0000!- .0700!- .2000!- .2002!- .2010!- .1002!- .1200!- .1100!“ .7700!“ icai bod ,f=3.0G 1071!- ‘a‘-I“ and-.." 0200!- 0270!- ““‘ One-u... 1100!- 12000- 2002!- 0270!- 0007!- 11270-00 .12070-00 10220-00 .10700-00 17200-00 10020-00 .20000-00 .22000-00 22020-00 .20100-00 20710-00 20120-00 .20200-00 20010-00 21100-00 .21000-00 .21000-00 21000-00 21100-00 20010-00 .20200-00 .20120-00 .20710-00 .20100-00 .22020-00 .22000“00 .20000-00 .10020-00 .17200-00 .10700-00 10220-00 12070-00 .11270-00 .0007!“ .0270!- 10 10 10 10 10 10 10 10 10 10 10 11 .02700-11 .02000-11 .0200!“11 .10210-11 .11200-11 .27000-11 10710-11 I... LOAD CURRON7 00 TOTAL TABLE 9H1 DEC 10 1s 20 20 20 25 00 00 00 SS 00 70 75 00 00 0O 00 100 105 110 115 120 120 120 125 100 105 150 105 100 105 170 170 100 100 100 100 200 200 210 210 220 220 220 220 200 200 200 200 200 200 270 270 200 200 200 200 200 200 210 210 220 220 200. 200 200 200 '000UONCY IN 000 00 00 00 00 00 00 OO 00 00 00 00 00 00 00 00 00 00 00 00 OO 00 OO 00 00 00 DO 00 00 00 00 00 OO 00 00 0° 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ,00 .00 00 ‘00 00 .00 100 .00 .00 B-IS : .2207!- .0000!- .2700!- .2001!- .2000!- .1720!- .2207!- .0722!- ,00000- 11000!- 11570!- ,10000- .2220!- ,02000- 111720-00 .0077!- .0002!- .2220!- .2070!- ,11010- .1000!- 1 1 .10110'1 1 .10700-1 .12070-1 .12220-1 .10000-1 .07200-1 .00000-1 164 Prope near a lncndent fie] 0.0 (Fig. 3.3.l.) ‘ 20000010 LOAD CUIIINY 00 PM! 07200- 1 12220-1 12070-1 1 1 nun-tun- 10110-11 .12000-11 ,02000- 100220- 2000!- 71210-12 23100-11 00100-11 11010-10 120700-10 10 1o 1O 10 00020- 00770- 110200-00 10700-00 10000-00 20000-00 122020-00 ,22220-00 .22000-00 .22220-00 .22020-00 120000-00 .10000-00 .10700-00 .10200-00 .11720-00 .0200!- 10 .22100-11 .7131!- .2040!- 0022!- .07220-12 .2207!- .1720!- .20000-12 .20010-12 .27000-12 .00000-12 .22070-12 '10LD I 2 00 L000 CURI!NY $0 I POI .0001!- 0000!- 11 11 .20000-11 11 ,11000- .21020- .2010!- .00000- .0012!- .02000- 00700- 12220- 12000- 21100-10 10 10 10 1O 10 7000!- 11020-00 10200-00 110000-00 10000-00 20010-00 20010-00 21100-00 .21000-00 20200-00 .10000-00 10000-00 10200-00 .12020-00 .00100- ,00220- .27000- .22000- 10 72720-10 10 10 10 12200-10 07000-11 10200-11 .10070-20 .10200-11 .1220!- .22000- .27000- 100220- .7272!- .0010!- 27000-11 10 10 10 1O 10 10 12020-00 .10200-00 110000-00 .10000-00 .20200-00 .21000-00 .21100-00 .20010-00 .20010-00 .10000-00 .10000-00 .10200-00 .11020-00 .02000- .7000!- 10 10 .00120-10 .0000!- .20100- .21100- .2102!- .11000- 10 .12000-10 .12220-10 .0070!- 11 .20000-11 .0000!- .0001!- 11 11 .02000-20 INCL! ' bio] 9 o .)V 00 00 LOAD CUIIINT 00 000 70 .20210- 10000- .1002!- 7007!- .1010!- 10220- .20220- .0110!- 00000- 10010- .2020!- 101000- .0720!- ,10720- 10720- 20000- 120220- .0002!- 70000- 10000- .1020!- 1000!- 22200- .2002!- 20000- 00000- 0000!- .0220!- .0777!- .0272!- .0712!- ,70000- 170120- 7002!- 70020- 17001!- 70070- 70010- 70020- .7002!- .70120- .7000!- .0712!- .0272!- ,07770- .0220!- .0000!- .0000!- .20000- 2002!- .2220!- .10000- 10200- .1000!- ,70000- .0002.- .20220- .2000!- .10720- .10720- .0720!- .0100!- .2020!- 1001!- .0000!- .01100- .2022!- .1022!- .10100- .70070- .1002!- .1000!- .2021!- 12 12 12 12 10 1O 10 10 10 10 10 10 1O 10 10 10 10 10 1O 10 10 10 1° 10 10 1° 11 ‘d“. d‘d“ 12 12 12 12 12 12 12 12 12 10 3 ice] m,f=3.0G bod 20200-12 .00010-11 .00000-11 22000-11 .07020-11 .12010-10 12020-10 12020-10 22070-10 .21000-10 .20000-10 ,07000-10 07100-10 01200-10 ,07100-10 .12200-00 110700-00 10000-00 10000-00 21110-00 .22010-00 22220-00 20000-00 .20220-00 .20120-00 .22000-00 20020-00 120200-00 20000-00 .20200-00 20020-00 27000-00 20000-00 20000-00 .20020-00 .21020-00 .21020-00 21020-00 .20020-00 22000-00 .20000-00 .27000-00 .20020-00 .20200-00 .20000-00 20200-00 .20020-00 .22000-00 .20120-00 .20220-00 .20000-00 .22220-00 .22010-00 .21110-00 .10000-00 .10000-00 .10700-00 .12200-00 .07100-10 .01200-10 .07100-10 .07000-10 .20000-10 .21000-10 .22070-10 .12020-10 .12020-10 .12010-10 .07020-11 .22000-11 .00000-11 .00010-11 .20200-12 Kg. LOAD CUIN!NY $0 YOTAL TABLE 'Hl DEC ‘0 ‘5 20 2S 30 35 00 ‘5 SO 55 50 ‘5 7O 75 .0 IS :00 ‘05 Ivo "S I20 125 130 135 ‘00 1“ ISO ‘5! ‘50 1'5 170 ‘75 IIO ‘35 ‘.O 1.5 200 205 2‘0 2‘5 220 22! 230 235 2‘0 205 250, 255 260 2" 27° 27! 2.0 20$ 2.0 20$ 300 30‘ IIO, 338 830 333 300 B-l6 VIIOUENCV I 30008010 IN LOAD CURRENT 30 FOR PHI 00 VIICIE"2 OO ISIIE'12 00 .IO2UE-i3 OO 33.8E‘12 00 .JISZI'I2 OO 2312E-12 OO AAOOE-12 OO 7‘JlE-I2 OO 7387l'12 OO VIIIZI-Iz 00 13QII‘11 OO 'CJOE'!‘ OO ‘73OE‘11 00 2°.AE-‘1 OO 22$.E"| OO 42OIAE-!! OO 171$I-1l OO ‘2S2E-1I OO COJil-XZ 00 JIAII-I? 00 OSOIE'I2 OO JOIOE°31 OO 77SJE°!1 OO IS7IE'IO 00 27702'10 OO AAAIE'YO OO I‘lBE-IO OO IJOJI-IO OO 123ll-O! 00 ISCAE‘OI 00 1’06E'O9 00 2237E-O’ OO 253.!‘09 00 .ITISE-O. OO ZIIIE'OI 00 31IOE-0’ 00 ,3'§2E'O! 00 .31tot-OI OO 2...!‘09 00 .27OII-OI 00 .2‘JIE'OI 00 ‘22371-09 OO IIOCI-O’ OO ,IICSI-O! ‘00 1234E'0I 0° Alioll-IO 00 .C‘AII‘iO 00 .AAAII-‘O 00 _ITVOI'!O OO .‘IVAI"O 0° ‘VYASE-Ii 00 JOOOE'iI OO .I‘OIE"! 00 33|‘E'|2 0° .OJIE'12 ‘00 12'2l'1‘ 0° .171'I'11 ,OO ZOiAI'il 00 .22§.I'11 00 .ZOIAI'II 0° .I7JOI'11 .00 .II30!°1I 0° .IJ.AE-'I DO .ICAZI-I2 0° .73372-12 .00 .7OIII°13 00 .A..°I"2 .90 .2auze-12 .00 .JUAZI'33 OO .aaasc-az 0° .‘OICI-‘J 0° .l’i’l"1 00 .IIOUI"3 : Probe near 3 cy 165 Incident field (Fig. 3.3.h) FlELD ‘ ‘3‘3AI-11 IOVAI'IO AiiSl‘li {IOAIE-11 i‘AZE‘IO ICIil~IO ‘1§7AE-IO .2.:AI'1O A1§AI‘IO ACSJI-ic CiiJE-IO CUIAI‘10 ,IOA7I-08 IZAIE-OI AiI’ll'OQ IOOAl-O! .2‘33l'09 leTl-O’ {ZCIAI-O. 27.82-00 .2I1AI-OI Zliol-O. .ZTOtl-O! ,2A77I'O! ZZOAE-O’ 1IlAE-O’ ilOAE'O9 12IiE-OI .OIZOI'1O .723‘£-'O $013l'to JIVII'UO IVIOE'IO TC.2E'!I iOO!I-‘I ‘2102l—J‘ ,1’011-1! .7IO2E-!I SVCOE~IO .JI7AI'IO .3013E-IO 72311-10 .OA2IE-io .12.|I-OI .‘OOAI'O. .!.1I!'O’ IZOIl-OI ZAVTI-O. .27OII'0. .2AIOI-OI .2A18E'O’ .27AAI-OI 20.8I-OI .2.0?l°°. .11332'03 .1IOAI-O. .1..|I°0. .‘2’11'00 .1OA7I°OO .IIOAI-10 .I!III°IO .4353l'i0 .AiIAE'IO .2OZAl-IO .‘C7AI'1O .Iflflil-io .1I42I-‘0 .IICII°II .AIIII-‘I .1OTAI-IO .OIIOE-ii .CIABI'SI in ( I 2 00 LOAD CUIIEIY SO POI I drical AICLI U .0 00 LOAD CUIIINT SO '0! Y! .ISOCE-Ai .O2OJE‘42 .IiIOE‘li AIIQE-AI CSSZE'A! .30.!-4$ .lI'AI'AO 31.2!‘CO IZIIl-AO IJIlI-AO I‘AOI'3. .2‘OOE-3. A207E'3' CVOAI'3’ IOISI'JI ‘IOOE-3O .2JI7E'38 .JAOZI‘JI 0.77I‘JA .IITAI'JI 1155I°J7 'ACOE'J7 ‘AOOI°J7 .2i50I'37 .2538E°37 2’11l°37 3270I‘37 JCOAE‘J? 3.17E'37 A'AJE'SV OIJIE'37 .A‘2’E'37 .A7ACE'37 AUDIE-37 ACCII'JV .AOIOI'JV AIACI'3T AAIAI'IT .AVAII'37 OOZDE'37 CASIE-ST .liIJE'IT .JOI7I'37 .J‘OII'37 .IZVOI-SV .2.!!!‘37 .23331'37 ,21641'37 .IAOOE'JV IACOI°37 Il$35°37 .00081‘30 .II7II-JI AIVTI'II .IAC2I'JI .23.?!‘18 ‘15002-38 .|OAII°3| .OVOAI'JO 8207I°3I .IAOOE'SI .‘IIOE'II .IIIII°A° .IZIII-AO .3!.2!~A¢ .IIUAI-OO .OIOII'Oi .IIIQI'A! .AOIII'AI .IIOIl-AI .OQOJI'Ql .ZJIII'Ai biolo ical bod 2,90 deg.) V m,f=3.0G a. LOAD CUIIEIY SO TOYAL liISI-12 .ICCSE'!‘ .107'l°‘0 AISAI"‘ .3333!°$1 17°3I°IO ‘0680E'10 .QOOII'!O ‘AZAAI'IO AIIJE'iO .27Cl-IO .IIS7I'IO .iOCIE'O, ,IZTJE'O’ 1.1'I°OI .‘IZIE'OI .2IACE~O. 2lt3l-OI 2‘72l-OI 27.8!‘0. .2IAOE-O! .IOAAl-OI 30508-0! ITAAI‘O. .2831l-OI ISIZI-OI ZSJAE-OI 2S!‘I‘OI 2‘071'09 2'2’l'00 77391-0. .2.37l-09 .IQTOE-O. .IOCCI-OO .SIROI-OI 31528.0. 31291-0! AJOSIE-OI .ZIVOl-O. ZIS7I'OI ‘27JOI'O. 2‘2.I°OO .23.?!‘0! .25!§I°OI .2'3.!°O. .2§A2I'O. .2CSlI'OO .IVSAI-O. .IIIAI'OI .QAAIl-O! 27IIE-OI {2‘72I'OI .2AIJI'OI .IIAII°OI 1.2‘I-OI 16111-0. 12TJI°OO .iotll-O. .AAIVI-‘O .CZVAE-io .AIIII-IO .AQAAE-IO .IIIA£°IO IIAOI'IO .IVOII-IO .‘II'I-io .II‘JI-l‘ .AAIAI-Ii ,IOTOI-IO .OICII'II .III3I'I2 TABLE RH] DEC 50 $5 50 SS 70 100 105 1‘0 ilS 120 I25 ‘30 135 ‘40 IA. ‘50 ‘5‘ ‘DO II. I70. 17‘ 380 IDS ‘00 1.5 200 205 210 215 220 228 230 2.0 285. 2‘0. 255. 200. 20'. 270 273. 2.0. 205‘ 2.0. 300 30' 3‘0 315. 320. 32$. :30. III. 360‘ III. FREOUERCV B-l7 : Probe near a cylindrical b Incident field = (2.0 deg.) V/m,f- 166 (Fig. 3.3.5) 72‘501010 IN LDAO CURRIN? $0 FOR PHI 0 0 001300 00 00 00 00 001100 00 00 00 00 00 00(300 0 0 00(300 00 00 00 00 00 O 0 0 0 00(300 0¢)0<)0 00(300 0 0 00(200 00 00 00 00 00 0 0 0 0 001500 00(300 00(300 0 0 001,00 00 00 00 00¢>00 00 0 0 00C’00 0130 FIELD ' 2 00 LOAD CURRER? $0 FOR A 00¢)00 00(300 00(300 00(500 00¢)00 00'300 00¢)00 00(300 0<>0¢D0 001,00 0¢>0¢>0 00(300 (300(30 00(300 00¢, .‘I2OE-l .lOADE-I .IDADI‘l I 1 .1IADI'i .IIIDI'I .IDDOI" I i . .2030! ANGLE 3 .1IDDl-13 ,IiZDE-lA .ITIOI-IA .IOIOI‘ID OIDOE°13 .S2DQE‘13 .83825-13 ISIDE-I! ,26202'12 ‘AOIVI'ifl 2330!- 3.30!' i...“" .OiDIE-Il .llADI'IO iSVOE'VO .212IE‘IO .ZTI‘E'IO .JSTil'IO .OA722'10 DATOE'ID lIDJDI-‘O .733ll'l0 DVAOI-IO .DIJOI'VO .IODIE‘OD ilIODI'OO .lZDOI-OI .IJADE'O’ ltAODI-OI .IACOI'OI .IAD7I.OI .tSiDI'OD 1827I-OD .IIIDD'OD .iADTI-OI .IAIOI'OI .‘AODI’OI .IJADE'OI .IODDE'OD .11.!!‘0. .!ODDI°OI .DD30l-10 ,87AOI-10 .7DDII'10 .IDJDI-IO .DATOI~10 .6172E-10 .SDVII'IO .IVDAI'IO .2!21I-IO .IS7OE'10 .1IAD!°11 .SOADI"1 .DDZDI‘II .AODTB“! .2320I'12 .1DDDI°‘2 .ADA2I-I3 .IZDOI°13 .DDDOI°I3 .IOJII°13 .87IOI°OA .IIZDI". .1IIDI-l3 0.00 LOAO CURRIIY 80 'OR YE iologica LOAD CURRENT 80 TDYAL ,‘DDII'VJ ‘DlZIE’lA A7IOI'!‘ IOIDE-ll .JDDOI'IJ iDQSDE'II ‘IIIII'lO .lIIII-IZ ~262OE'I2 AOD7I"2 .33201'12 .IOCOI-ll 'IAII'II IDJOE-ll DIJOI'II .DDDDE"! ,OIDII-ll llA‘l'IO .ISVAI'IO 21213'10 AZVAAI‘IO 3‘71E-10 .AAT2I'IO .DATOI‘IO .IDJCI'IO 77.3.E-lo DVAIE'DO VDDJOE-IO .IODII°OI IZIDI°0D IIADE'OD lOOII-OI IAIOE-O. .|ADTI°0! _IIIDE'O’ IDI7E'00 .1I‘DI'OD IAOTI-OD ,OADOE°00 IAOIE-O’ ,IIAIE°09 .1ZDDl-OI .‘1I2I'OD .i0l.£°0. .ODJOI-IO .IVAIl-IO 733|I°I0 ‘ODJIE-IO .SA702-l0 .AITZI'IO .IDVII'IO .2TIAE°!0 .2121l'10 .1IVDI'10 .IIAIE'10 .DiDII'II .DDDOI-‘I .IIJOI'Il .DDJOI-Il .‘IAAI‘lI .IOADl-II .DIZII'UZ .COI7E'12 .23201-12 .IIIIl-IZ .AIAII'IJ .DziIl-II .IDDOI-ifl IOIII°‘3 AVIOI-|A l bod 2.b56 lg. 167 TABLE B-18 ' Pr - - - |ng?§egga;.alcyllndr1cal buoloaical bod . (Fi 'e d 8 (2’30 deg.) V mpf'2.h56HZ. 9- 3-3-5) ru2ou2ucv.1 .22202-10 21210 1 2 oo aucL2 a :o 00 on: In 1022 cu222u7 so 1020 2022227 so 1020 can-227 so 1020 2022227 so 022 202 vn1 ran a 202 72 70721 0100 722222-13 . .12212-12 .77222-12 2 00 ,22232-12 .11222-11 .22272-12 12:22-11 10 oo 22222-12 122202-11 .22222-12 422222-11 12 oo .22722-12 20072-11 12222-12 .20222-11 20 oo .22002-12 .20322-12 .22222-12 .10122-11 22 oo .72022-13 .21202-11 22222-12 .22222-11 20 00 22222-1: .22222-11 422222-12 .22072-11 as 00 23022-1: ,20202-11 11222-12 .22222-11 20 oo 12002-12 22222-11 .12222-12 .20212-11 22 oo .12122-12 .22222-11 .20222-12 .70202-11 2o 00 17222-12 .10312-10 22272-12 10222-10 22 oo .22222-12 .12202-10 ,72222-12 .13222-10 20 oo 22222-12 .12372-10 ,12322-1: .12202-10 22 on 21202-12 17712-10 ,12272-11 .12222-10 70 oo .22122-12 .22222-10 .22722-11 .22222-10 72 00 27222-12 .22022-10 .22212-11 .22222-10 20 oo 22272-12 .21272-10 .21222-11 .27222-10 22 oo .17012-12 .22122-10 22122-11 .22222-10 so oo 21222-12 ,2o122-1o 11222-10 .22022-10 22 00 72022-1: .22072-10 12202-10 .20022-10 100 00 712212-12 .22222-10 .20222-10 .22222-10 105100 22272-12 22022-10 .22722-10 .72222-10 110 00 22222-12 .22122-10 .22222-10 .20222-10 112 00 12272-11 .22022-10 .21022-10 .22022-10 120 00 22022-11 22072-10 .22022-10 .22222-10 122 00 23722-11 .27772-10 27222-10 .10022-02 1:0 00 .72222-11 .22022-10 22202-10 .10222-02 122 00 11122-10 122222-10 .72722-10 .11212-02 120 00 12722-10 .22212-10 21272-10 .11222-02 122 00 12272-10 12212-10 .22272-10 .12222-02 120,0o 22712-10 12212-10 22122-10 .12122-02 122 00 .22272-10 .22172-11 ,10022-02 712712-02 120 00 20212-10 21222-11 .10272-02 .12212-02 122 00 .23222-10 .22272-11 10222-02 .12222-02 170 00 .22722-10 12722-11 .11222-02 .12222-02 172 00 .27272-10 .22222-12 .11222-02 .12122-02 12o oo .27772-10 .22122-27 111222-02 .12222-02 122 00 .27272-10 .22222-12 .11222-02 12122-02 120 00 .32722-10 112722-11 11222-02 12222-02 125 00 .22222-10 .22272-11 10222-02 .12222-02 2oo.oo .20312-10 .21222-11 .10272-02 .12212-02 202 00 .22272-10 .22172-11 .10022-02 ,12712-02 210 00 722712-10 .12212-10 .22122-10 .12122-02 212 oo 12272-10 .12212-10 .22272-10 .12222-02 22o.oo .12722-10 .22212-10 .21272-10 .11222-02 222 00 .11122-10 .22222-10 .72722-10 .11212-02 220.00 .72222-11 .22022-10 .22202-10 .10222-02 222 00 .22722-11 .27772-10 .27222-10 .10022-02 220100 .22022-11 .22072-10 .22022-10 .22222-10 222 00 .12272-11 .22022-10 .21022-10 .22022-10 220 00 .22222-12 .22122-10 .22222-10 .20222-10 222 00 .22372-12 .22022-10 .22722-10 .72222-10 220 00 12212-12 .22222-10 .20222-10 .22222-10 222.00 .72022-12 .22072-10 .12202-10 .20022-10 270.00 .21222-12 .20122-10 .11222-10 .22022-10 272.00 .17012-12 .22122-10 .22122-11 .22222-10 220 00 .22272-12 .21272-10 .21222-11 .27222-10 222.00 .27222-12 .22022-10 .22212-11 .22222-10 220 00 .22122-12 .22222-10 .22722-11 .22222-10 222.00 .21202-12 .17712-10 .12272-11 .12222-10 200.00 .22222-12 .12272-10 .12222-11 12202-10 202.00 ,22222-12 .12202-10 .72222—12 .12222-10 310.00 .17222-12 .10312-10 .22272-12 .10222-10 212.00 .12122-12 .22222-11 .20222-12 .70202-11 22o.oo .12002-12 .22222-11 .12222-12 .20212-11 222.00 22022-12 .20202-11 .11222-12 22222-11 :20 oo .22222-12 .22222-11 .22222-1: .22072-11 322.00 .72022-1: .21202-11 .22222-13 .22222-11 220 00 .22002-12 20222-12 .22222-12 .10122-11 222 00 .22722-12 20072-11 .12222-1: 20222-11 220.00 .22222-12 .22202-11 .22222-12 .22222-11 222 00 .22222-12 .11222-11 .22272-12 .12222-11 22o.oo .22222-12 .27022-22 .12212-12 .77222-1: 168 TABLE B-l9 : Probe near a cyl Incident field = biolo ical bodE. . Hz. (th- 3.3.5) 1 deg.) V m,f=2.h§ PRIOUERCV 2 .20000‘10 010LD 8 2.00 ARCLI 1 00 00 PH! 1N LOAD CURRENT 00 LOAD CURRONT 00 LDAD CURRON7 00 LOAD CURRORY 00 000 FOR RH] 00R R FOR 70 TDYAL 0 00 .10070-12 0 .01300-10 .10000-12 0 00 10000-12 30070-11 .22020-10 .30000-11 10 00 .10000-13 .00000-11 .11070-10 .00000-11 10 00 10720-12 100220-11 00070-10 .01300-11 20 00 .20000-12 .27100-11 700700-10 .20000-11 20 00 .23010-12 .00210-11 .13100-13 .00000-11 30 OO 110000-12 13000-10 21000-13 .13000-10 30 OO .27020-12 .10120-10 130030-13 .10000-10 0O 00 00000-12 ,10000-10 00000-13 10000-10 00 00 .00300-12 10000-10 10220-12 .20300-10 0O 00 03000-12 .30030-10 .10320-12 31020-10 55 00 07100-12 .30710-10 .20230-12 .30000-10 0O 00 .00300-12 03110-10 01100-12 .00000-10 05 00 ,00210-12 03130-10 .03200-12 .00710-10 70 00 .07300-12 .00000-10 .00700-12 71020-10 70 00 .02700-12 100070-10 10170-11 .00310-10 00 00 .70000-12 .03010-10 .20020-11 .00000-10 05 00 01030-12 10000-00 .20710-11 10000-00 00 00 27000-12 112000-00 .30000-11 12070-00 00 OO 23720-12 .13220-00 ,03010-11 13770-00 100 00 00720-12 ,13000-00 100000-11 ,10000-00 10$ 00 13010-11 .13010-00 .00270-11 10000-00 I10 00 20000-1l 713000-00 ,11100-10 .10200-00 115 00 00010-11 13010-00 13070-10 .10070-00 120 00 10210-10 .12020-00 .10300-10 .10200-00 120 00 ,10130-10 .11330-00 110100-10 .10000-00 130 00 23000-10 .00170-10 .21070-10 .10000-00 135 00 .33300-10 .00700-10 .20070-10 110270-00 100 00 00200-10 .00020-10 .27100-10 .10130-00 100 00 00020-10 .00020-10 .20000-10 .10000-00 100 00 00100-10 100030-10 31730-10 .10070-00 155 00 .00000-10 .20000-10 .33030-10 .10220-00 100 00 00000-10 .10030-10 .30230-10 110000-00 100 00 10030-00 .10000-10 .30000-10 .10730-00 170 00 10700-00 .07100-11 .37020-10 .10000-00 170 00 11100-00 .11000-11 .37000-10 .10100-00 100 00 11330-00 .12000-30 .30170-10 10100-00 100 00 .11100-00 .11000-11 .37000-10 10100-00 100 00 10700-00 .07100'11 .37020-10 10000-00 100 00 10030-00 .10000-10 .30000-10 .10730-00 200 00 .00000-10 .10030-10 .30230-10 .10000-00 200 00 .00000-10 .20000-10 .33030-10 10220-00 210 00 .00100-10 00030-10 .31730-10 110070-00 210 00 .00020-10 .00020-10 .20000-10 .10000-00 220 00 100200-10 .00020-10 .27100-10 .10130-00 220 00 .33300-10 .00700-10 .20070-10 .10270-00 230 00 .23000-10 .00170-10 .21070-10 .10000-00 230 00 10130-10 .11330-00 10100-10 .10000-00 200 00 10210-10 112020-00 110300-10 .10200-00 200 00 .00010-11 113010-00 .13070-10 .10070-00 200 00 .20000-11 .13000-00 .11100-10 .10200-00 200 00 13010-11 13010-00 .00270-11 .10000-00 200 00 .00720-12 .13000-00 .00000-11 .10000-00 200 00 .23720-12 .13220-00 .03010-11 .13770-00 270 00 .27000-12 .12000-00 .30000-11 .12070-00 270 00 .01030-12 .10000-00 .20710-11 .10000-00 200.00 .70000-12 .03010-10 .20020-11 .00000-10 200 00 .02700-12 .00070-10 .10170-11 .00310-10 200 00 .07300-12 .00000-10 .00700-12 .71020-10 200 00 .00210-12 .03130-10 .03200-12 .00710-10 300 00 .00300-12 .03110-10 .01100-12 .00000-10 300 00 .07100-12 .30710-10 .20230-12 .30000-10 310 00 .03000-12 .30030-10 .10320-12 .31020-10 310 00 .00300-12 .10000-10 .10220‘12 .20300-10 320.00 100000-12 .10000-10 .00000-13 .10000-10 320.00 .27020-12 .10120-10 .30030-13 .10000-10 330.00 .10000-12 .13000-10 .21000-13 .13000'10 330.00 .23010-12 .00210-11 .13100-13 .00000-11 300.00 .20000-12 .27100-11 .00700-10 .20000'11 300.00 .10720-12 .00220-11 .00070-10 .01300-11 300 00 .10000-13 .00000-11 .11070-10 .00000-11 300.00 .10000-12 .30070-11 .22020-10 .30000-11 300.00 .10070-12 .17110-30 .01300-10 .10000-12 169 TABLE 8-20 : Prope near a cylundrucal bnolo Ical bodE. Ineldent fleld - (2,90 deg.) V m,f-2.h5 Hz. (Fug. 3.3.5) '00OUENCV I .20000610 '10L0 I 2.00 AICLI I 00 00 'Nl IN LOAD 0000007 00 L000 00000“? 00 L000 CUIIINT 00 L000 0000001 00 000 '00 '01 '00 I '00 70 7010L 0 00 ,20000-12 0. .20000-01 20000-12 0.00 10000-12 07030-11 .10200-01 .00200-11 10 00 722220-13 10720-10 .70100-02 .10700-10 15 00 10200-12 .00200-11 31000-01 .01720-11 20 oo 33200-12 .30100-11 ,01000-01 .30000-11 20 00 .31220-12 .00010-11 .02110-01 .00730-11 3O 00 122000-12 .17000-10 13000-00 .10170-10 35 00 .37220-12 .20100-10 .20700-00 20030-10 06 00 100000-12 10700-10 00010-00 .10300-10 00 00 .72020-12 .20210-10 03010-00 .20030-10 00 00 71330-12 .01230-10 .10100-30 101000-10 05 00 00020-12 .01020-10 .10300-30 .02010-10 00 oo .11700-11 87000-10 .20000-30 100000-10 00 00 12000-11 70000-10 30000-30 .72100-10 70.00 11000-11 .02020-10 .00000-30 .00000-10 70 00 .11030-11 .11210-00 00010-30 111320-00 00 00 00070-12 112010-00 12700-30 .12010-00 05100 00000-12 10000-00 .17030-30 _10120-00 00 00 ,30730-12 .10000-00 20000-30 10100-00 00 00 .31020-12 117030-00 .33110-30 .17000-00 100 00 07020-12 10200-00 03070-30 .10320-00 105 cc 117300-11 .10020-00 100700-30 .10000-00 110 00 .30000-11 .10000-00 00030-30 .10000-00 115 00 .70000-11 .10020-00 .00010-30 .10000-00 120.00 13010-10 .10030-00 10210-37 .10100-00 120 00 21000-10 10110-00 .11030-37 .17200-00 130 00 .31010-10 113220-00 13000-37 .10000-00 13! oo 00000-10 11310-00 10300-37 .10700-00 100 00 00000-10 .03230-10 .10000-37 .10220-00 100.00 .70000-10 .73230-10 .10000-37 .10700-00 100 00 00000-10 .00000-10 .10020-37 10030-00 100 00 10070-00 .30070-10 .21000-37 10070-00 10° 00 12130-00 .20000-10 ,22000-37 10000-00 100 00 13370-0! .13000-10 .22000-37 .10770-00 170 00 .10320-00 .02010-11 .23370-37 .10000-00 170 00 10010-00 .10000-11 .23720-37 ,10070-00 100 00 10110-00 .17200-30 .23000-37 .10110-00 100 00 10010-00 .10000-11 .23720-37 .10070-00 100 00 10320-00 .02010-11 .23370-37 .10000-00 100 00 .13370-00 .13000-10 .22000-37 .10770-00 200 00 .12130-00 .20000-10 .22000-37 ‘10000-00 200 00 .10070-00 .30070-10 .21000-37 .10070-00 210 00 .00000-10 .00000-10 .10020-37 .10030-00 210.00 .70000-10 .73230-10 ,10000-37 .10700-00 220.00 .00000-10 .03230-10 .10000-37 .10220-00 220 00 .00000-10 .11310-00 .10300-37 110700-00 230.00 .31010-10 .13220-00 .13000-37 .10000-00 230 00 .21000-10 .10110-00 .11030-37 .17200-00 200 00 13010-10 .10030-00 .10210-37 .10100-00 200 00 .70000-11 .10020-00 .00010-30 .10000-00 200.00 .30000-11 .10000-00 100030-30 .10000-00 200 00 117300-11 .10020-00 .00700-30 .10000-00 200 00 07020-12 10200-00 .03070-30 .10320-00 205 00 .31020-12 .17030-00 .33110-30 .17000-00 270.00 130730-12 .10000-00 20000-30 .10100-00 270,00 .00000-12 .10000-00 .17030-30 .10120-00 200.00 00070-12 .12010-00 .12700-30 .12010-00 200.00 .11030-11 .11210-00 .00010-30 .11320-00 200.00 .11000-11 .02020-10 .00000-30 .00000-10 200.00 .12000-11 .70000-10 .30000-30 .72100-10 300.00 .11700-11 .07000-10 .20000-30 .00000-10 300.00 .00020-12 .01020-10 .10300-30 .02010-10 310.00 .71330-12 .01230-10 .10100-30 .01000-10 310.00 .72020-12 .20210-10 .03010-00 .20030-10 320.00 .00000-12 .10700-10 .00010-00 .10300-10 320.00 .37220-12 20100-10 .20700-00 .20030-10 330.00 .22000-12 .17000-10 .13000-00 .10170-10 330.00 .31220-12 .00010-11 .02110-01 .00730-11 300.00 .33200-12 .30100-11 .01000-01 .30000-11 300.00 .10200-12 .00200-11 .31000-01 .01720-11 300.00 .22220-13 .10720-10 .70100-02 .10700-10 300 00 .10000-12 .07030-11 .10200-01 .00200-11 300.00 .20000-12 .22010-30 .20000-01 .20000-12 TABLE 'Hl DEC IO 15 20 23 30 3S ‘0 ‘5 SO 55 ‘0 7° 73 to 85 IO ’5 I00 105 IIO I15 I20 I25 13¢ 135 I10 I05 150 I55 I60 I55 I70 I75 IIO ‘I5 I90 1.5 200 205 2I0 2'5 220 225 230 23‘ 240 208 3.0 285 260 255 370 27I 2.0 2.3 2.0 III 300 303 310 III 320 323‘ 330 3'0‘ 360‘ 8-21 : Probe near a c Incident field (Fig. FREQUENCY I ISOOI‘IO 00 00 00 00 00 00 00 00 00 00 OO 00 00 CO 00 OO 00 00 00 00 00 00 00 00 00 00 OO 00 00 00 0° 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ,OO 00 00 00 00 ,00 ,OO 00 00 00 LOAD cunneuv so ton rn: 00(300 00(300 00¢)00 00(300 001300 00(300 00(300 001,00 00(>00 00¢)00 00¢)00 00¢>00 00¢!00 001,00 0130 170 Y 1 3.3.6) 'IELO I 2 0° LOAO CUIIIN? $0 FOR C 00(300 00(300 OOC>00 00¢)00 00(i00 001300 00¢)00 001300 00‘300 00(300 00(300 00¢>00 00(300 001300 0013 indrical biolo (2 gical body. ,0 deg.) V/m,f-I.SGH2. INCL! U 0 00 LOAD CUIIII? SO POI YE IJCII‘ I075!‘ IOOOI° TOOOI' I77OI' .SIICI' $32.!- 72.6!- IO2IE' I320!- 232‘!- JOIII' CI‘?!‘ 3.69!- .032!- IISSI' IIIII° ICIII- JIIOI' cots!- OIO)!’ I323E° 7700!‘ O2I§E' I000!- .125!!- 1030!- I00!!- ,I77SI' .IOJTI' 2087!- .2220!- ,2333l- ,IIZJI' .2000!- .2530!- 2‘04!- .2‘30!’ alOOE° .2423!- .2333!‘ 2220!- .20.?!- III)?!- IIVTOI' 1.05!- .ICJO!’ .IIOOI' .IOOOI' .IZIII- ,77001' 3323!“ OIOJI° 6°C.!- ,IIOII' .2010!- .IIIII' .1133!- ,OOOII' .OIC.I° .IOC7I' .JIIII- .232Cl° .IizOl' .IOZII- .7238!- SSIII' .34..!- .17731' .7000!° .OOOOI' .IOVII' .IJIO!‘ I) II II II 13 I3 13 I: I2 I2 d‘u‘“ d‘d-‘ 0“..- 10 10 IO 10 IO ‘0 10 10 IO 10 '0 IO I0 10 d.“‘ duo-add I. I, I) LOAD CUIIEI? SO VOYAL ISOCI'II ,IO7II'13 .OOOOI-IC .7000l-Il .I7TII'IJ .I‘OCI-Il ,OJZIl-IJ 7ZOCI-IJ I021l-12 .15231-12 232Cl'12 ,SOIII-IZ .I’S7l-I2 ,OII’E-IZ .III2E-I2 .ISJSl-I .IIIII'I .III‘I'I OIIOI'I COOII°I ‘aadd IIOJI' .C323!' 1700!’ ’21‘!‘ IOOOE- o‘a—c 1|2SSE-I0 .IIJOI'IO .IOOOI‘IO I77OI'IO .IOJTB-IO .IOIVI'IO .2220l-IO .ZIIJl-IO ,lell'IO .2..OI°IO .ZOJOI-IO IOOII°IO .ZOJOE-IO OIIOE'IO 3C23I'IO .21332-10 .222OE'IO .IOIVE-IO .IOJ7I-IO .177§I°IO .IIOOI’IO .IIIOE-IO AIZOOI°10 ‘IOOII-IO .OziOI'II .VTOOI'II .OOZII'II .OIOJI-II .OOICI'II .JIOOE°II .IIICI'I .ICIII'I .IISOI'I .IOIZI-I .IO.II°I .OOOTI-IZ .QQIII°12 .ZJZIl-IZ .IOIOI-II .IORII-IZ .7208I-13 .IIZOI-IJ .I‘OII‘IJ .177IE-13 ,YOOOI-I‘ .IDOII-Il IOTBI-Il .IICCI°13 171 TABLE B-22 : Prope near a cylindrical biolo ical bod . kggidegthéfld = (2,30 deg.) V m,f=1.56az. lg. . . 3|30U3~CV 8 13003010 '13LD I 2 00 INGL3 3 30 00 PH] ll LOAD CUII3NT 30 LOAD CUIIINT 30 LOAD 3033337 30 LOAD CUIR3NT 30 D36 '03 PM! FOR I FOR T3 TOTAL 0 00 32333-13 0 10233-13 .32303-13 3 00 23733-13 .33203-12 .30333-13 .33333-12 10 00 12003-13 17723-11 .30323-13 17333-11 13 00 32333-1! .27203-11 32303-16 .27303-11 20 00 11033-13 .27033-11 .13313-13 .27333-11 23 00 23323-13 20333-11 .23233-13 .20303-11 30 00 33133-13 .10313-11 .33333-13 .13733-11 35 00 33353-13 13333-11 33333-13 .20003-11 IO 00 32333-13 .33333-11 73333-13 .33733-11 05 00 .37033-13 .33133-11 .11‘33'12 .30333-11 30 00 31313-13 33223-11 .17333-12 .33333-11 SS 00 .33213-13 .70303-11 23333-12 .73333-11 30 00 .33373-13 .72333-11 .37133-12 73333-11 35 00 37333-13 30313-11 32273-12 .33213-11 70 00 33033-13 33213-11 72333-12 .10303'10 73 00 .33333-13 12213-10 .10013-11 .13233-10 30 00 23373-13 10333-10 13333-11 .13733-10 33 00 23723-13 .13333-10 .13103-11 .17073-10 30 00 23703-13 13173-10 .23333-11 .13333-10 33 00 30033-13 13033-10 .30333-11 .13333-10 100 00 33333-13 13333-10 .33273-11 .20333-10 105 00 13133-12 .17373-10 ,37323-11 .22373-10 I10 00 23313-12 .17323-10 37733-11 23333-10 115 00 .30333-12 .17323-10 .33123-11 .23033-10 I20 00 .73133-12 .13333-10 .31323-11 23313-10 12S 00 11333-11 13003-10 .33123-11 .23373-10 130 00 ,13103-11 .13173-10 10723-10 .23303-10 135 00 .21333-11 11303-10 12003-10 23033-10 1‘0 00 27733-11 33373-11 .13323-10 .23333-10 105 00 30433-11 77133-11 .14333-10 23333-10 130 00 31303-11 .33333-11 13333-10 23733-10 155 00 37313-11 33333-11 .13333-10 .23303-10 130 00 33333-11 .23333-11 .17303-10 .23733-10 135 00 33003-11 13333-11 .13133-10 .23733-10 170 00 .32333-11 .73133-12 13373-10 .23713-10 17S 00 .33233-11 .13323-12 .13333-10 .23333-10 130 00 33033-11 .27333-37 .13033-10 .23333-10 133 00 33233-11 .13323-12 13333-10 .23333-10 130 00 .32333-11 .73133-12 .13373-10 .23713-10 135 00 33003-11 .13333-11 13133-10 .23733-10 200 00 .33333-11 .23333-11 .17303-10 .23733-10 205 00 47313-11 33333-11 .13333-10 .23303-10 210 00 .31303-11 .33333-11 13333-10 .23733-10 215 00 .33633-11 .77133-11 13333-10 .23333-10 220 00 .27733-11 .30373-11 .13323-10 .23333-10 223 00 .21333-11 .11303-10 12033-10 .23333-10 230 00 13133-11 .13173-10 10723-10 .23303-10 233 00 11333-11 13003-10 .33123-11 .23373-10 200 00 .73133°12 .13333-10 31323-11 .23313-10 203 00 .30333-12 .17323-10 .33123-11 .23033-10 230 00 23313-12 .17323-10 .37733-11 .23333-10 233 00 .13133-12 .17373-10 .37323-11 .22073-10 230 00 33333-13 .13333-10 33273-11 .20333-10 233 00 .30033-13 .13033-10 .30333-11 .13333-10 270 00 .247‘3-13 .13173-10 .23333-11 .13333-10 273 00 .23723-13 .13333-10 .13103-11 .17373-10 230 00 .23373-13 .13333-10 .13333-11 .13733-10 233 00 .33333-13 .12213-10 .10013-11 .13233-10 230 00 .33033-13 .33213-11 .72333-12 .10303-10 233 00 .37333-13 .30313-11 .32273-12 .33213-11 300 00 .33373-13 .72333-11 .37133-12 73333-11 303.00 .33213'13 .70303-11 .23333-12 73333-11 310 00 .31313-13 .33223-11 .17333-12 .33333-11 313 00 .37033-13 .33133-11 .11333-12 .33333-11 320.00 .32333-13 .33333-11 .73333-13 .33733-11 323.00 .33333'13 .13333-11 33333-13 .20303-11 330.00 .33133-13 .13313-11 .33333-13 .13733-11 333.00 .23323-13 .20333-11 .23233-13 .20333-11 300.00 .11033-13 .27333-11 .13313-13 .27333‘11 333.00 .32333-13 .27203-11 .32303-13 .27303-11 330.00 .12003-13 .17723-11 .33323-10 .17333-11 333.00 .23733-13 .33203-12 .30333-13 .33333'12 330.00 .32333-13 .33023-33 .10233-13 .32303-13 172 Prope near a cylindrical biolo ical bodn. Incident field - (2,60 deg.) V m,f=1.SG 2. (F19. 3.3.6) TABLE 8-23 : 333003331 I .13003-10 313LD ! 2 00 AROL3 1 30 00 PM] 1" LOAD CURRENT 30 LOAD CURR3NT SC LOAD CURR3UT 30 LOAD CURRENT 30 DEC 'OR 3“] 303 R 30R 73 TOTAL 0 00 37073-13 0 .33133-13 .10033-12 3 00 77203-13 13333-11 23333-13 .17333-11 10 00 .33003-13 .33173-11 13373-13 .33333-11 1S 00 12733-13 .31303-11 .17303-13 .31733-11 20 00 .33133-13 .32333-11 33373-13 .32713-11 23 00 33733-13 .31133-11 .37333-13 .32133-11 30 00 .13333-12 .33723-11 .13323-13 .33213-11 35 00 13333-12 .33033-11 13213-13 .33733-11 3C 00 12333-12 10373-10 23333-13 10323-10 35 00 .11123-12 .13333-10 .33133-13 13103-10 30.00 12373-12 .13373-10 .33113-13 20033-10 55 00 .13333-12 .21233-10 .33273-13 21303-10 30 00 .20313-12 21733-10 .12333-12 .22033-10 SS 00 .20333-12 23033-10 .17323-12 .23373-10 70 00 .13313-12 23333-10 .23233-12 .23373-10 73 00 11303-12 .33333-10 .33333-12 .37033-10 30 00 .33303-13 33033-10 .33233-12 .33333-10 33 00 73133-13 .33323-10 .30333-12 37333-10 90 00 .73233-13 33323-10 .73333-12 33333-10 33 00 10333-12 33333-10 .10123-11 .30333-10 1°C 00 21003-12 .30373-10 .12733-11 .32333-10 103 00 33333-12 .32723-10 .13313-11 .33733-10 110 00 33233-12 .33773-10 .13233-11 .33333-10 115 00 .13133-11 32373-10 .23033-11 .33703-10 120 00 .23733-11 33733-10 27113-11 .33333-10 I23 00 33773-11 .33333-10 .31373-11 .31313-10 130 00 33333-11 .33303-10 .33733-11 .37313-10 133 00 .33733-11 .33313-10 30123-11 .33333-10 130 00 .33233-11 .23333-10 33333-11 31233-10 13$ 00 10333-10 .23133-10 .33333-11 .33333-10 130 00 .12333-10 17333-10 .32173-11 .33303-10 I33 00 ,13373-10 .13033-10 .33333-11 33023-10 130 00 13133-10 33733-11 .33323-11 .30333-10 133 00 17703-10 .33333-11 30333-11 .23733-10 170 00 .13333-10 .22333-11 .32233-11 .27333-10 173 00 13333-10 33773-12 33233-11 .23373-10 130 00 .13323-10 .32233-37 .33333-11 .23133-10 133 00 13333-10 33773-12 .33233-11 23373-10 130 00 .13333-10 .22333-11 .32233-11 .27333-10 133 00 .17703-10 .33333-11 .30333-11 .23733-10 200 00 .13133-10 .33733-11 .33323-11 .30333-10 203 00 .13373-10 .13033-10 .33333-11 .33023-10 210 00 .12333-10 .17333-10 .32173-11 .33303-10 213 00 .10333-10 .23133-10 .33333-11 .33333-10 220 00 .33233-11 .23333-10 .33333-11 31233-10 223.00 .33733-11 .33313-10 30123-11 33333-10 230 00 .33333-11 .33303-10 .33733-11 37313-10 233 00 .33773-11 33333-10 .31373-11 .31313-10 230 00 .23733-11 .33733-10 .27113-11 .33333-10 233 00 .13133-11 .32373-10 .23033-11 .33703-10 230 00 .33233-12 .33773-10 .13233-11 .33333-10 233 00 .33333-12 .32723-10 .13313-11 33733-10 230 00 .21003-12 .30373-10 .12733-11 .32333-10 233 00 .10333-12 .33333-10 .10123-11 .30333-10 270 00 .73233-13 .33323-10 .73333-12 .33333-10 273 00 .73133-13 .33323-10 .30333-12 .37333-10 230 00 .33303-13 .33033-10 .33233-12 33333-10 233 00 11303-12 .33333-10 .33333-12 .37033-10 230 00 .13313-12 .23333-10 .23233-12 .23373-10 233 00 .20333-12 .23033-10 .17323-12 .23373-10 300 00 .20313-12 .21733-10 .12333-12 .22033-10 303.00 .13333-12 .21233-10 .33273-13 .21303-10 310 00 .12373-12 .13373-10 .33113-13 .20033-10 313.00 .11123-12 .13333-10 .33133-13 .13103-10 320.00 .12333-12 .10373-10 .23333-13 .10323-10 323.00 .13333-12 .33033-11 .13213-13 .33733-11 330.00 .13333-12 .33723-11 .13323'13 .33213-11 333.00 .33733-13 31133-11 .37333-13 .32133-11 330 00 .33133-13 32333-11 .33373-13 .32713-11 333.00 .12733-13 31303-11 .17303-13 .31733-11 330.00 .33003-13 .33173-11 .13373-13 .33333-11 333 00 .77203-13 .13333-11 .23333-13 .17333-11 330.00 .37073-13 .10323-33 .33133-13 .10033-12 TABLE PHI OED 30 33 30 33 70 100 103 110 113 120 123 130 135 130 133 130 133 130 135 170 173 130 133 130 133 200 203 210 213 220 223 230‘ 233 230 233 230 233 230‘ 233 270 273 230 233 230 233 300 303 310V 313 320 330. 333 330 333 B-Zh PIIOUENCV In LOAD content so POI PNI .oo 12932-12 00 .10233-12 00 .33003-13 0c 16233-13 oo 33233-13 00 11373-12 oo .13073-12 oo 13733-12 00 17133-12 00 .13323-12 oo 18733-12 oo 22333-12 oo 27:33-12 00 .27133-12 oo .22023-12 oo 115733-12 oo 11333-12 oo 100135-13 loo .38073-13 oo .13733-12 00 23003-12 oo ,COSIE-12 oo 11733-11 oo .20233-11 oo .31633-11 oo 3637E-11 00 .33373-11 oo .3330l-11 00 11113-10 00 13733-10 00 .13323-10 oo 1917E-10 oc .21373-10 oo .23003-10 oo 23133-10 00 23103-10 oo 23433-10 00 .23103-10 co .2514l-1o .oo ,23303-10 00 .21373-10 00 .13173-10 00 .13323-10 oo .13732-10 .oo .11113-10 .oo .33303-11 oo .33873-11 oo .33373-11 oo .31333-11 oo .20233-11 loo .11733-11 oo .30333-12 oo .23003-12 oo 13733-12 ,oo .33372-13 .oo .33333-13 .oo .11333-12 .oo .13733-12 oo .22023-12 loo .27133-12 .oo .27333-12 .oo .22333-12 oo .13733-12 oo .13323-12 loo .17133-12 .oo .13733-12 oo .13073-12 .oo .11373-12 .oo .33233-13 .oo .13333-13 .oo .33003-13 .oo .10233-12 .00 .12333-12 : Probe near Incident fl (Fig. 3.3.6 1 13003010 173 3 cy fld FI3LO 3 in ( l 2 00 LOAD CURR3RT 30 FOR R .22033- .70333- .10333- .10333- ,31373- .33333- .77323- .13323- .21273- .23333- .23323- .23023- .32123- .33233- 133333- 137333- .33303- .70303- .33333- .32333- .37333- .30333- .23333- .17333- ,33333- .30033- .11373- 717333- .30333- .37333- .33213- .32333- .33333- .33333- .70303- .71703- .70303- .37333- .33303- .33333- .32333- .37333-10 .33333- .33233- .32123- .23323- .23333- .21273- .13323- 10 10 10 10 10 10 10 10 37333-10 10 10 10 10 71703- 70303- 33333- 10 10 10 10 10 33213- 10 10 10 11 11 11373- 73703-12 .10373-33 .73703- .30033- .33333- 12 11 23333- 10 10 10 10 10 10 10 23023- .70333-11 22033-11 .13773-33 dr 2. AROL3 1 ic 90 l bi deg C ) lo ical bodzIé V m,f=l.SG 3O 00 LOAD CURR3RT 30 FOR 73 .21323-31 .13733-31 .32303-32 .10333-31 27713-31 ,33313-31 .33133-31 711333-30 .13333-30 .23333-30 .33233-30 .33333-30 .77303-30 .10333-33 .13133-33 .20333-33 .23233-33 .37333-33 .33233-33 .33213-33 .73333-33 .33733-33 12023-33 13333-33 13333-33 .13333-33 .22323-33 .23033-33 .27723-33 30233-33 .32333-33 .33323-33 .37333-33 .33333-33 .33313-33 .33723-33 .33313-33 .33333-33 .37333-33 .33323-33 .33333-33 .32333-33 .30233-33 .27723-33 .23033-33 .22323-33 .13333-33 .13333-33 .13333-33 .12023-33 .33733-33 .73333-33 .33213-33 .33233-33 .37333-33 .23233-33 .20333-33 .13133-33 .10333-33 .77303-30 .33333-30 .33233-30 .23333-30 .13333-30 .11333-30 33133-31 .33313-31 .27713-31 .10333-31 .32303-32 .13733-31 .21323-31 LDAO CURRERY 30 707AL 12333- .23113- .71373- 110303- 111023- .32723- .31333' .73303- 13333- .21323- .23333- .23333- .23233- .32333- .33303- .33013- .37303- 32333- .33733- ,33033- .33113- 70303- .72373- .72323- .33303- 33333- 133123- .33333- .33033- 33333- 30313- 33323- 133133- .30273- 23133- 23333- .23333- .23333- .23133- .30273- .33133- .33323- .30313- 33333- .33033- 133333- .33123- .33333- .33303- .72323- .72373- .70303- .33113- .33033- .33733- .32333- .37303- .33013- .33303- .32333- .23233- .23333- .23333- .21323- .13333- .73303' .31333- .32723- .11023’ .10303- .71373- .23113- .12333- 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 174 TABLE B-Z : Probe res onse vs. separation betweep the probe 5 p 180 deg. (Fug. 3.3.7) and the body along phi = 'REOUENCV = 21‘03‘10 FIELD I 2 OO ANGLE 1 05.00 'Hl 81.6 00 1 1n n LOAD CURIENY 10 L010 cu111~7 10 L010 cunl1u7 10 LOAO 1011117 10 101 PH) 101 1 101 11 TOTAL 0 0000 27111-11 11131-31 21111-11 12711-11 0010 13211-10 17321-31 12701-10 21111-10 0010 37531-10 11221-31 37211-10 .71121-10 0120 70711-10 ,10711-31 71321-10 11211-01 0110 10701-09 72211-37 10152-01 21111-0! 0200 11021-01 11111-37 11211-01 121271-01 0210 11111-09 11101-37 .11771-01 .33211-01 0210 17731-01 10711-31 111001-01 131731-01 0320 17111-01 17111-31 17711-01 31371-01 0310 11101-01 11131-31 11201-01 .32301-01 0100 13111-01 11211-37 13121-01 27011-01 0110 10311-01 .37111-37 10221-01 20171-01 0110 70:11-10 .11101-37 11331-10 13171-01 0520 11211-10 .71311-37 .31011-10 110301-10 0110 .20111-10 11311-37 11131-10 31111-10 0100 11311-10 .10111-31 110111-10 .21111-10 0110 11101-10 10711-31 11111-10 21711-10 0110 .21211-10 .10121-31 31311-10 10101-10 0720 52111-1C 11211-3” 55111-10 10111-09 0710 10111-10 71731-37 11111-10 11111-01 0100 10111-01 12711-37 11211-01 22121-01 0110 .13111-01 .11101-37 13111-01 21111-01 0110 11111-09 30111-37 11101-01 21111-01 0920 11111-01 11111-37 11111-01 30121-01 0110 11211-01 12711-37 11211-01 .21111-01 1000 12111-01 11771-37 12311-01 .21131-01 1010 .10111-01 11771-37 11171-10 20031-01 1010 71171-10 .23711-37 71301-10 11121-01 1120 11131-10 111371-37 11131-10 11711-10 1110 121121-10 11771-37 .27111-10 17111-10 1200 11771-10 .11211-37 17111-10 .31111-10 1210 .17101-10 ,11171-37 .11131-10 .31131-10 1210 121101-10 111211-37 .21111-10 11111-10 1320 11311-10 .70111-37 17121-10 12211-10 1310 17011-10 ,17221-37 71121-10 13171-01 1100 11211-10 11121-37 11011-10 11731-01 1110 11211-01 .12171-37 .11721-01 .23001-01 1110 .12131-01 13711-37 13111-01 .21171-01 1520 13111-01 31011-37 .13171-01 .27111-01 .1110 13211-01 .21011-37 13211-01 121111-01 1100 12071-01 23171-37 11111-01 23131-01 1110 10111-09 21111-37 11171-10 .20011-01 1110 .71311-10 23311-37 71211-10 11171-01 1720 .11711-10 27311-37 .12111-1c 10111-01 1710 37131-10 33211-37 31311-10 {71171-10 1100 21111-10 .31111-37 23211-10 11121-10 1110 .21231-10 11111-37 21101-10 12:31-10 1110 21311-10 .11711-37 21011-10 .11311-10 1120 131121-10 11211-37 12711-10 .12111-10 1110 .11211-10 11111-37 .12701-10 .12011-01 175 ' be B-26 : Probe response vs. separat10n between the pro TABLE and the body along ph1 = 135 deg. (F19.3.3.7) '020U2NCV 3 20502010 '12LD I 2 00 ANCL2 I 00 00 2H) 8135.00 5 IN M LOAD CUII2N7 00 L000 CURRINT 00 LOAD CURI2NT $0 LOAD CUII2NT $0 '00 2H! '00 I 200 T2 TOYAL 0 0000 22522-11 07002-10 .10012-11 01302-10 0000 07702-1‘ 01002-10 77002-11 03022-10 0000 10972-10 72202-10 .22002-10 10012-00 0120 .20502-10 101002-10 00002-10 ,12722-00 0100 32702-10 01002-10 170072-10 110002-00 0200 00372-10 00302-10 ,00072-10 110002-00 0200 00222-10 .30702-10 12022-00 721012-00 020C 72032-10 22012-10 10772-00 120332-09 0320 02002-10 17172-10 10302-00 20002-00 0300 00202-10 10002-10 .17202-00 .27072-00 00°C 01332-10 .13002-10 117222-00 .27702-00 0000 00772-10 10272-10 10302-00 .20702-00 0000 01802-10 .10002-10 10702-00 20022-00 052C 71202-10 .20072-10 12002-00 22002-00 0500 00102-10 20002-10 .10002-00 .10002-00 0000 03032-10 30002-10 70002-10 ‘0022-00 0000 30102-10 00002-10 .00702-10 .12172-00 0000 10102-10 00002-10 .31002-10 .00072-10 0720 03022-11 07002-10 10002-10 70002-10 0700 00202-11 00002-10 13232-10 00312-10 0000 00252-11 07002-10 10002-10 07002-10 0000 07002-11 00302-10 25002-10 .00012-10 0000 10022-10 01002-10 02122-10 10002-00 0920 20072-10 37072-10 02302-10 .12012-00 0060 00002-10 33232-10 00302-10 10002-00 1000 03012-10 20002-10 .10002-00 10032-00 1000 05022-10 20002-10 12332-00 .21032-00 1000 70372-10 23102-10 13002-09 .23302-00 112C 70002-10 21002-10 10102-00 20302-00 1100 00722-10 21072-10 10002-00 .20332-00 1200 77002-10 23272-10 113232-00 .23312-00 1200 70252-10 20002-10 .11012-00 .21002-00 1200 59902-10 20032-70 00002-10 10022-00 1320 07002-10 31002-10 ,70102-10 10002-00 1300 .30202-10 30002-10 700002-10 12012-00 1000 .23032-10 37732-10 .01102-10 .10202-00 1000 10202-10 .30732-10 .20002-10 .02012-10 1000 02502-11 00002-10 .20002-10 .00052-10 1520 01002-11 00002-10 .20272-10 .07202-10 1000 02332-11 30012-10 .20302-10 70002-10 1000 10112-10 30102-10 30172-10 00032-10 1000 23002-10 35702-10 .00202-10 .11312-00 1000 33002-10 33102-10 72002-10 13002-00 1720 00002-10 30002-10 01202-10 10732-00 1700 00002-10 20102-10 10702-00 .10332-00 1000 05352-10 720032-10 12002-00 .21102-00 1000 71232-10 20022-10 12712-00 22372-00 1000 73022-10 20202-10 ,12702-00 .22002-00 1020 71002-10 20072-10 12202-00 122012-09 1000 00302-10 27212-10 11102-00 20012-00 176 Probe response vs. separation between the probe TABLE . . and the body along phn = 90 deg. (Fag. 3.3.7) B-27 : FIEOUENCV 3 20502010 VIELO 3 2 00 AHCLO l 00 00 PM] I 00 00 5 IN N LOAD CURQENT 50 LOAD CUIRONT 50 LOAO 00200"? 50 LOAD 00002“? 00 FOR PH] 200 0 FOR 70 TOTAL 0 0000 10772-11 .00102-10 .21070-12 .00302-10 0000 00102-12 03202-10 .11202-11 00050-10 0000 .17272-12 00002-10 .33000-11 .03002-10 0120 12032-12 .07052-10 .00102-11 .00002-10 0100 20752-12 .00002-10 11000-10 07352-10 0200 30712-12 .00002-10 .17312-10 .10172-00 0200 50002-12 .02002-10 20210-10 10720-00 0200 70102-12 .00722-10 .32112-10 .11300-00 0320 10200-11 .70000-10 00002-10 12002-00 0300 12072-11 ,70072-10 .00012-10 .12002-00 0000 10072-11 .70002-10 00000-10 .13002-00 0000 10700-11 .72202-10 70002-10 10002-00 0000 10732-11 .00712-10 .01070-10 .10320-00 .0520 20072-11 .07072-10 .02102-10 10122-00 .0000 .22202-11 .00302-10 .10230-00 .10000-00 0000 23052-11 .01702-10 .11100-00 .17002-00 .0000 .25202-11 .00202-10 .12072-00 ,10202-00 0000 20012-11 00030-10 .12000-00 .10702-00 0720 27012-11 00712-10 13002-00 10232-00 0700 .20000-11 .52002-10 13070-00 .10052-00 0000 20072-11 .01022-10 10302-00 .10702-00 000C 30702-11 00302-10 .10002-00 .10002-00 0000 31552-11 .00732-10 10002-00 .10730-00 0920 32272-11 00500-10 .10202-00 110012-09 0000 32010-11 .00002-10 13002-00 ,10170-00 1000 33000-11 00002-10 13322-00 10702-00 1000 30002-11 01002-10 412030-00 10132-00 1000 30002-11 03002-10 11000-00 ,17002'00 1120 30002-11 00030-10 10072-00 10712-00 1100 ,30200-11 00002-10 .00000-10 .10002-00 1200 35002-11 00072-10 00110-10 10072-00 1200 30000-11 .01302-10 .77002-10 10202-00 1200 30172-11 03730-10 00002-10 13022-00 1320 .30032-11 00022-10 .00000-10 12002-00 1300 ,30002-11 00100-10 ,07002-10 .11002-00 .1000 .30072-11 .70172-10 .30502-10 .11300-00 1000 37002-11 71000-10 .32002-10 .10002-00 1000 37230-11 .73322-‘0 .27010-10 10002-00 1520 .37302-11 ,70300-10 .20130-10 ,10232-00 1500 37022-11 .70102-10 .22072-10 10132-00 1000 .37002-11 .70020-10 .22002-10 10102-00 1000 37702-11 .70302-10 .20032-10 .10302-00 1000 .37020-11 .70012-10 .20300-10 10700-00 1720 .37000-11 70122-10 .33030-10 .11100-00 1700 .37000-11 73020-10 .00202‘10 11710-00 1000 37000-11 71002-10 00002-10 12302-00 1000 .37072-11 .70000-10 .00002-10 .13052-00 .1000 .37002-11 .00302-10 .00732-10 13702-00 .1020 37022-11 .00000-10 70002-10 .10000-00 1000 37072-11 .00772-10 .00002-10 10200-00 APPENDIX C Computer pro ram and the print outs for the back scattered electric fie d from a cylindrical body of varying radius, illuminated by the plane EM waves. 177 n nonnnnn ('3 75 80 999 178 ***********A****************************************************** THIS PROGRAM COMPUTES SQUARE OF THE MAGNITUDE AND PHASE OF BACK SCATTERED FIELD FROM CYLINDER OF COMPLEX PERMITTIVITY. IT ALSO PRINTS OUT THE PARAMETERS ” ” AND "P” , DEFINED IN THE TEXT. THE CY LINDER IS ILLUMINATED BY PL NE WAVE, ”A" IS RADIUS OF CYLINDER AND “R” IS POINT OF OBSERVATION IN METERS. CONDUCTIVITY SIGMA, SOURCE FRE UENCY AND RELATIVE PERMITTIVITY OF CYLINDER ARE RE UIRED AS FOR ATTED INPUT DATA. THIS PROGRAM NEEDS SUBROUTINE ”C MBES“ . *xkxz‘ :*:n a”:i xakx:x:x*)*********1******x:fiflfikfikkkfl:+x******+***xfl+ PROGRAM HEARTI (INPUT, OUTPUT, TAPE IO IINPUT, TAPE 20 8 OUTPUT) DIMENSION BJRE(7) .BJIM( ), YRE(AI), YIM(AI) COMPLEX BODY, (WKé N, HNKL, RIES, TERMN ,AA ,PC P|=A. 0*ATAN . 905M GM FREQ DIELEC . II. “A 5. i) E A I VELITE=3.O OMEOA=2. OxPI* WKO=0MEGA/VE DELCTR=DIELE : CUUM BODY=CMPLX(DELCTR, -(SIGMA/0MEGA)) s ROMG= OMEGA*R2 =CSQRT(S R0MG*FREEMUNBODY) wRITE (207) SIGMA, FRE ,DIELEC FORMAT (lHI, x, IAHCONOU TlVITY =,F6.3,3X,IIHFREQUENCY =,EII.A. nr-x -CHnO' pawn no: 0 *3x, IAHPERMIT IVITY = ,FS 2.//) WRITEIZO, 75) FORMAT( X,3HKOA,IOX.18HFIELD MAGNITUDE SQ, 5x, iZHPHASE IN DEG, *5X,lAHREAL ART Q,5x, IAHIM MAG PART P, //) DO 9 I-l,12 DO 9 J=I,5 WKO =WKO*R WKOA=WKO*A PI=S RT(2. O/(PI*WKOR)) P2=W OR+E3.' .O*PI/h. O) PC= CMPLX O 2) SERIES= CMPL VCND\&D -&»XC) GO TO 8O CALL COMBES (WKOR, O. O, O. O, O. O, N, BJRE, BJIM, YRE, YIM) HNKL=CMPLX(BJRE(N),-YRE(N )) *P| $ERSN=(BNNHNKL*COS(QI))/(PITCEXP(PC)) SERIES=SERIES+TERMN CONTINUE x-REAL(SERIES) Y= AIMAG($ERIES) lav/x PHASERsATAN(Z) PHASEA=PHASERII80 O/PI AMPLI-(X**2+Y*x2)*(Pl* Xl-EZ. .O/WKOA *x Yl= 2 O/WKOA *Y WRITE (206 II WKOA, AMPLI, PHASEA x1, Yl FORMAT PiIingh ,EII. A, I2x, EII. A, 6x, EII. A, 8x, EII. A) 3 II UE O I E SUBROUTINE COEFBN (N, DIMENSION BJRE(z%)CgJ COMPLEX WK WKA ,H,H|I,DERHAN,D,E,COMPX IO 20 *J, BN, AAC 179 PI=A. 0*ATANII. 0) WKOA=WKO*A WKA=WK*A REWKA=REAL(WKA) AMWKA= AIMAG(WKA) Cl=WK/WKO QsFLOATIN-Ig IF(CABS WKA ARGUl=REWKA- ARGU2=ARGUI+ o) I )- CBl=CSQRT(2. .9 c ,8 O EI/ 0 (30 0*Pl/h. 0) /2. ) Pl* KA)) O RGUI),-SIN(ARGUI)*TANH(AMWKA)) SI AR U2), -S|N(ARGU2)*TANH(AMWKA)) CALL COMBES WKA, |AMWKA, O. O, O. O, N, BJRE, BJIM, YRE, YIM) =CMPLX(BJRE ), BJ (N )) l=CMPLX(BJR RE(N ’+I), BJIM(N+I)) ARTI= *B/WKA RBES= ARTl-BII =Cl*DERBES/B LL COMBES (WKOA (R/WKOA) - (BJRE( =c PLx(BJRE(N).- i=CMPLX(BJRE(N+ SHAN=(H *H/WKOA) c c BII=c3IxCMPL B=caIcCMPLx( GO TO l0 L 5 9' 2 I o /( N (C A OS G RE N ,O. ,O. o, 0.0,N,BJRE,BJIM,YRE,YIM) N+ /BJRE (N )) YR (N)) I) -YRE(N+I)) —-'O [Tl—.2. ERHAN BJRE(N)/H) ?éXI- c)/(xI- D) ILN=I. 062 IO AA=QaPI/2. 0 AAC= CMPLX(O. COMPXJ= —CEXE 180 TABLE C-I : Back scattered field from a con¢uctin$ cylinder, coefficients Q and P vs. k.a FIg. A. .1 CONDUCTIVIYY II! .00 FREQUENCY l .JOOOI¢10 'ERHITTIVIYY I I 00 duo-nu... 400.00 OMWU" '5... .UUUU UNNNN ”-‘da OJJQJ Nut-0‘... KO: FIILD HAGNXYUDE SO 'HASE IN DIG IIAL PART 0 IMAG fill? P 20 .iOO‘E~OJ OOCOIOOZ .‘3072001 - 00208601 40 2082l-03 4008:002 .38771001 - JIoclocI .50 OIYIE-O3 3.23!¢O2 .32312001 -.2372!¢01 so .suszz-oa 3:02:00: .JOIOEOOI - 10.02001 00 .030‘E-03 .JOIIIOOZ .QOOIEOOI -.!IIO!OOI 20 .IaIzc-oz .20001002 aaoocooz - ICO7E°OI co 1IIIE°O2 zlaIlooz _2VJCIOOI - 1332(001 so It‘ll-02 .2l82E002 IIVIlOOI - 1237:001 so .zzttl-oz 2:50:00: 2.27100! -.I|OOE001 oo .2IOZI-02 .22C2loo: 2sII£001 - IOIVEOOI 20 .30242-02 .2‘l91002 .25‘II001 - 1000100! no JITII-Oz 2°30E002 2522EOO' -.l47IIOOO so .assac-oz Ilaotooz alttEoOI -.3001looo no OASIl-oz Iooceooz .207JIOO‘ -,css|!ooo oo 40006-02 ICISEOOZ 2IIZE¢OI - IITZEOOO 20 .IIIGI-oz IVIJE~02 IOJCIOOI - vlzilooc co CISIE-OZ 172.1002 2l1ll001 -.7|20!000 so IleE-oz 1071:002 2002:001 - 7241:000 lo 70331-02 1830l002 ZIIIEOOI -.tOIIEOOO oo .OIIJE-OZ ‘306l002 .2376EOOI - 87531000 20 aazzz-oz Itascooz 238lI001 -,Isallooo a0 IIIot-O2 1607:002 ZJSCIOOI ~.IJJO!OOO 6c IOIJl-OI 1l72!.c2 ZJIIEOOI -.CI5SIOOO so .Itizl-OI Iasltooz 233CI00! - soaazooo OO 110£l-0I Ilotlooz 2326IOO! o.5024£ooo 20 Izvit-OI .13702002 2:15:00! - lIVClooo no 13871-01 13O7IOO2 .ZBIOIOO! -.IIJA!¢OO so ICSOE‘OI 13201002 2103:001 - Iaozlooo so 15526-0! 1200(002 .2206l00‘ - 82771000 00 Isaoe-OI .Izvolooa 2:00:00! -.I'IIE¢OC 2o .17472-01 1:07:00: .22.!!001 -.s0II£ooo lo IOAOE-Ol IzzlEOOZ .221IIOOI - OICJEOOO so IOSIE-OI 3203:002 .22722001 - ll‘JIOOO so 20616-0! 1183:902 2237I00! -.OTCIE°OO oo 2I129-0I .IIoalooz .2202EO0I - Ccsllooo 20 22055-01 11.32002 2237:00I ~.0572looo .ao .240Iz-01 1127:002 .2253l¢01 - QIOOEOOO so zszoE-OI IIIotooz .22OII001 -.4I11!ooo so 2‘IIE'OI IOQSEOOZ .2IIIIOOI — 0335:000 oo 27SIE-01 10732002 22.01001 - 02836000 20 2|.JE-01 Iosazooz .2236!001 - OIOIE‘OO ac .JOZJl-OI 1047:002 .ZIJJEOOI - aIzvlooo so .SIIOE-OI iOJJEOOZ .2220!‘0I - OOIJEOOO so .32lIt-OI .IOIOIOOZ .2226I901 ~.lo¢2!000 oo .3‘206-01 .Iooclooz .2222l001 -.3|42£ooo 20 .357OI-OI .IIJOIOOI 22'01001 -.allilooo no .JVIQI-OI .IOO61001 .22‘3l061 - assocooo so ,38811-01 ICICEOOI .IZIJIOOI -.J777£¢oo to .AOIOE-OI .0807100I .22101001 -.372Il¢oo oo .aIsze-OI 04843001 .22081001 -.:¢70Iooo 20 703171-01 .03405001 .2203190\ -.JI!|IOOO so OC1§I-OI .IZJ1IOOI .2202EOOI -.3$IIIOOO IO CIItE-OI .OIIJEOO‘ .IZOOIOOI -.JSJT£¢oo so OTIIl-Ol .IO:2!¢01 21.7!001 -.3693looo oo .OIISl-OI .IOIOIOO1 .ZIOIIOOI -.adlilooo 20 .313al-01 .IISOIOO! .21031601 - SOIOEOOO no .IJOIE-ot .Ovttloov .ZIIIEOOi -.3370Eooo so .BOCOI~OI Iliil‘bi .218IIOOI '.3331!°OO .00 .I057t-Oi .nscvt001 .21.‘£001 -.3204!000 00 3837I°OI .Ill‘EOOI .2IIAEOOI ~.3287l¢00 d.c.-no- ”an..- JOOOO I’M“. OD... .UUUU UNUM” ”did- .4444 TABLE CONDUCTIVITY KOA .20 ‘0 80 .00 00 20 ‘0 ‘0 .80 00 20 IO 50 00 20 00 IO 00 .20 60 00 00 00 20 00 80 IO 00 2O 00 $0 80 00 2O 00 $0 .80 00 .20 .00 60 .00 ,20 40 00 00 C-2 : FIELD MAGNI?UDE 30 .IOIOE'Oi .JCZJE-Ol 10IOI-03 .23050'03 .3007I'03 .007II-03 .05050°03 .1127E'02 .i‘33E‘02 17003-02 .21302-02 25202‘02 29525.02 3C04E-02 .JIOSE-02 .03000'02 lilSE-O? SSOJE-OZ IIOOE'02 0720E-02 73010'02 .IOSOE'O? I7TSI°02 I$i0lc02 102IE-0I 110.!‘01 ,IIOII'OI 1270E'01 130.!‘0! i000E'01 .10‘0E-01 .IBC‘E’O‘ I7CSE'01 1.001'01 i053l-01 .IOSIE'OI 2172E‘0i .2205K'0! 200iE*01 .2521E'01 .ZICZI-OI .27076'01 .ZUOSE‘OI .30250'01 .3100l‘01 .lzlnl-OI .3033E'01 .3IVII-OI .37IIE-OI .Jllst-OI .OOIIl-OI IIOIl-OI .‘323l-01 .aOOII-cI .QUI2£°OI .0000I‘01 .‘I7ZI°01 .IiliI-OI .0313!°0‘ 0‘00I'01 Back scattere coefficients Q and P vs. koa J81 .JOOOIOIO PHASE II DEC .20101002 .23301002 .2220l902 .20742002 .10030‘02 1030.002 .‘I730002 .1010I002 .1701E002 .1700I002 .iIS‘I'OI 10072002 i500l°02 10102002 1074(902 .‘IJIEOO2 13070002 1302E002 .13300002 1200E002 .12700‘02 .12023002 .1210E002 ,IIOZIOOZ IIIIIOOZ .1140£.02 i125E902 .1105I002 100§E002 1007l‘02 .IOQIIOOZ .10332‘02 .10101902 i001i¢02 .0000!¢01 0717160! .03702901 .IOICEOOI 03170901 .IIOIIOOI .0074!’0\ .0000l001 .00472001 .07303901 .00302‘01 .3332!901 .OOSOEOOI .03302001 .IZQCIOOI .IVCIIOOI .IOIOIOOI .10838001 .7000l001 .70101001 .71011001 .7000200! .7000I001 .70i7l901 .7000!‘01 .73772001 PllfllTTlVlTV IIIL PAR? .10430001 .151SIOOI .1700I001 .1007E001 .3002E001 .21200001 .2IIAIOOI .21811001 .IIIIEOOI 2205:001 .2200E901 .2zoue.0i 2200200! .22002001 .22041001 .2202Eooi .22OOEOOI .2‘072001 ZIIOIOOI 2I02300I 2‘0!!°0i .2116£.OI .2100!001 .2IIIEOOI .2170l001 .217Il901 217IIOO| .2172IOOI .2I7OE¢OI .21‘12001 721000001 2‘030001 .2VCIIOOI .2’00E¢01 .210BE¢01 .21002001 .21SCE001 .2!§2E¢0‘ .2151I901 .ZIIIEOOI .21IVEOOI .2146EOOI .21CCEOOI .ZIOIIOOI .23411001 .2IIOIOO1 .21301001 .21372001 2‘302901 .2130l001 .21303901 .2132000! .IIIII001 .21301901 .21201901 .21201001 .2127I601 .2120I001 .2120E90‘ .2‘201001 d field from a CY; 0 I9. 0.00 Indricai A.I.I) XMAS POI? .30102000 0001l000 .7220E000 .73722000 .74771600 10002000 .1330looo .71721000 .000'IOOO .01701000 .00002000 .0301E000 01002900 CIVIEOOO .07073‘00 .0030I000 .0072E000 .‘JZSEOOO .Ill‘EOOO .0000I000 .00323‘00 .00i01000 0700(000 IIOSIOOO .00050’00 IliIIOOO 0320l000 .0200I000 01005000 ,60002000 0011I¢00 30‘1I000 .3070E900 .301‘2000 .3750I000 JCIIEOOO .30302900 3001E‘00 .3020E000 .JIVIEOOO .ICSOIOOO .altalooo .33302000 .azoazooo .stzlooo .3211IO00 ,SIVIEOOO .JISJEOOO .3000l900 .30302000 .30203000 .20002900 .20072000 .20202000 .ZIOOIOOO .20008000 .ZISCIOOO .ZIOSIOOO .27773000 .27002000 bWDd)/o 182 TABLE C-3 : Back scattered field from a c lindrical biological body vs. koa at 3. GHz. (Fig. h.l.2) CONDUCTIVITV : 2 200 FIIOUENCV : .30000010 PERMITTIVITY s00 00 non 'XELD MAGNJYUDE 00 vans: ll 0E0 IIAL PART 0 Inn: 0001 20 1031E-03 .2000£¢02 .0011!001 .30020001 00 00012-00 20102002 .10701001 72001000 so 12010-03 10010002 .10070001 .07310000 00 11120-0: .32000002 .12102001 70330000 I 00 10700-0: 00000902 .7310E¢00 13120601 1 2o 1000E-03 012§E002 .10002600 .12032001 I no 23000-03 .70100002 .32110o00 11000601 I so .20056-03 0110£002 .07012000 .001I£¢00 1 no .20530-03 .20700002 .01010000 .00320000 2 00 .30000-03 .35100001 .00370000 .00200-01 2 20 3000l-03 10708.02 0727(000 .31322000 2 40 37000-0: 02070002 .0000£000 .00020000 2 0o 2000E~03 00000002 .2003!.00 70010000 2 80 02008-03 00100002 .11tSl-01 .00702900 3 oo .00000-03 .07070002 .20700000 .72000000 3 20 00070003 00000602 .02070600 .02000000 3 00 01070.0: .21020002 .00100000 .20730000 3 00 502JE-03 1001:001 .7003!000 .1003l-01 3 00 ITOIE-03 .20002002 .0202!¢00 .20700000 0 00 .00000-0: .0101t¢02 00000000 .00700000 0 20 .02020-03 10000002 .2103E000 .01000000 0 00 0870E-03 .00002002 ,IJISE-01 .03000000 0 so 0071E-03 03000002 .20200000 .00700000 0 00 VIIJI-OJ .00000902 .0070E000 .30302000 5 oo .10310-03 .17000002 07200900 .11000000 5 20 7720E-03 00102001 .50322000 .01OSI-01 s 00 .00230-03 .20000002 .00320000 .27000000 5 00 0310t-03 0107E002 .SOOOIOOO .00001000 5 so .0000E-0: .70000002 .1001£¢00 .03000000 0 00 0000!-03 .02012002 .70202-0‘ .IOOOEOOO 0 2c 01012-03 00000002 .27000600 .00000000 0 0o 0073I-03 .3000!002 .02032600 .31071000 0 0o 07000-03 13110002 .00000000 .11700000 6 00 .1006£°02 .00000001 .00020000 .07032-01 7 oc .10350-02 .32020002 .02370000 .21330000 7 2o .1000l-02 .00700002 .21000000 01100000 7 4c 1111E-02 .70302002 .00000-01 .00000000 7 00 11010-0: 70000902 .00000001 .07700000 7 00 1170c-o2 .00070902 .27130000 .30130000 0 oo 1200E-02 32710002 .30000000 .20010600 0 2c .12200-02 .07000-01 .00220600 .70070-01 0 00 1200l-02 .13216902 .0010l000 .10002000 0.00 .12000-02 .30170002 .20000000 .21013000 0 0o .13170-02 .00130002 .2321!¢00 .30030000 0 00 .13010-02 .02osn.oz .01002-01 .00200000 0 20 13701-02 .70002002 1100F‘00 .42721900 0 00 .10000-02 .02010002 .20030600 .30000000 0 00 .10352-02 .20001002 .3700!000 .21020000 0 00 10002-02 .01002001 .02501600 .00071-01 10 00 .10002-02 .1000Io02 .00501000 .12200000 10.20 .10200-02 30702002 .32200000 .20070000 10 00 .10030-02 .0270l¢02 .10000000 .20000000 10 00 .1002l.02 .00000002 .20000-01 .01000000 10.00 .10120'02 .71370002 .13020000 .2000£¢00 11.00 .10010-02 .00020002 .20010000 .3022l.00 11.20 .10710-02 .20000002 .20100000 .17220000 11 00 .11000-02 .20000601 .20000000 .17000-01 11.00 .11300-02 .20000002 30000000 .12710000 11.00 .17000-02 .03200002 .20800600 .20100000 12.00 .17000-02 .00200002 .10000000 .20200000 183 TABLE C-h : Back scattered field from a cylindrical Fi biological body vs. koa 0t l0.0GHz. g. A.l.3) COIDUCYIVITV 010.200 722002.0' I .10002011 PICIIYTIVIYV O20.00 K02 'llt. HIS-17000 00 PI... I. 220 2020 '22? 0 3". '22? P 20.00 .III2I-02 .00022002 .10002000 .10200000 20.00 .11072'02 -.72202002 °.72102'0$ .20020000 21.00 .10000'02 °.|0002002 °.20000000 .00200'0‘ 27.00 .12100'02 .01022002 -.00022900 -.!0002000 20.00 .t2002'02 °.01000002 .22“2°01 '.20002900 20.00 .I2002-02 '.220IIO02 .22000000 -.10100000 20.01 .12720°02 .22002002 .20000900 .‘2000000 20.01 .I200I-02 -.00700002 °.0$200'02 .20202000 20.01 .1200I°02 ‘.2‘022002 ‘.2000IO00 .‘2222000 20.02 .12I00°02 .20102002 '.21212900 °.10202900 21.02 .‘2222'02 .00722002 -.2!00I’0‘ “.22002000 2i.02 .12000'02 °.27002002 .10022900 -.‘020IO00 22.02 .12000'02 .20122002 .21020000 .20200-01 22.02 .10200'02 .17000002 .00i20°01 .22722000 22.02 .10022002 -.00722002 °.10012000 .10220000 22.02 .10000'02 .12002002 '.22000000 -.00002-01 20.02 .10022-02 .00000002 -.70|02-01 °.21022000 20.00 .00172'02 °.02002002 .12722000 0.17000000 20.0. .‘0220-02 .0020200' .22220000 .10100s01 20.00 .10272-02 .02702002 .10002000 .12000000 20.00 .10070-02 '.00222002 '.11102000 .10700000 20.00 .‘0702-02 '.i0000901 0.21702000 .00770°02 27.00 .‘0000‘02 .00202902 -.t2022000 -.100'IO00 27.00 .10422-02 '.0000IO02 .07222-0! -.10702000 20.00 .00702°02 '.000|2001 .21212900 °.22202'00 20.00 .1700I°02 .00702002 .10‘12000 .‘01‘0000 20.00 .i7222'02 '.22722902 '.00002'01 .20020900 20.00 .17022-02 -.10222902 0.20212000 .00202-01 00.07 .17002'02 .01102002 °.'072IO00 -.12702000 00.07 .17002'02 '.0‘$2IO02 .23022'01 .20002000 APPENDIX D Computer prodram and the print outs for the back scattered electric fie d from a spherical body of varying radius, Illuminated by the plane EM waves. 184 n nnnnnnnn n I0 I00 N A5x, IAHREAL PAR OF E,5x IAH AG PART OF E5x, 22HSCAT- -CROSS- SE AAREA. //) 185 PAAAA************************************************************* THIS PROGRAM COMPUTES SQUARE OF THE MAGNITUDE AND PHASE OF THE SCAT TERED FIELD FROM SPHERE OF COMPLEX PERMITTIVITY. IT ALSO PRINTS OUT THE BACK SCATTERING CROSS SECTION NORMALIZED BY CROSS SECTION OF THE SPHERE. THE SPHERE IS ILLUMINATED BY PLANE WAVE. “A'I IS RADIUS OF THE SPHERE AND ”R“ IS POINT OF OBSERVATION IN METERS. CONDUCTI VITY OF THE SPHERE SIGMA, FREQUENCY OF PLANE WAVE AND RELATIVE PERMITTIVITY OF THE SPHERE ARE RE UIRED AS FORMATTED INPUT DATA. THIS PROGRAM NEEDS SUBROUTINE ” C MBES ”. W:1:::kx*k :P:' *3:***++*+*P*++***i*1******k*f*x++*+***x*k******m***mfl PROGRAM HEARTZ élNPUT, ,OUTPUT, TAPE IO =INPUT, TAPE 20=0UTPUT) DIMENSION BJRE BJ|M(7g) ,YRE(AI) ,Y|M(Al) COMPLEX BODY, WK, ERIES COM XJ, AN, TERMI, DN, CN, HNKLI, HNKL2, DHNKL, ='=TERM3, BRAKET, SUM, ARGUI, ARGUZ, HNKLII, TERMZ, ARGU}, BODYI PI=A. O=' 'ATAN (I.O R= O C LE TY =,F6.3,3X,IIHFREQUENCY =,EII.A, wK0= OMEGA/ DELCTR= DIE cuum BODY= CMPLX TR,-(SIGMA/0MEGA)) BODYl= BODY VACUUM wR0MG= OMEGAAAz EESRRR (SQROMGAEREENUABODY) wK0R= KOAR wRITE( 0,7 ) FORMAT( 5x, HKOA, on, IBHF ELD MAGNITUDE sq, 5x, IZHPHASE I X I Z 8 FR IT xV LC DEG, 0 BY 00 9 I=I,I2 00 99 J=I ,5 NK0A=NK0AA SERIES=CMPLX(O. 0.0.0) 00 999 Nw=l .30 N=Nw+I 8: -FLOAT (N I) I:$QRT(PIAwK0R/2.0 0) =§Q+l. .)A$QRT(PI/(2. OANKOR)) ABSIWKOR) 50.) GOT I0 LL COMBESN (NKOR, 0. 0, o. 5, 0. O,N,BJRE,BJIM,YRE,Y|M) =CIABJRE =cerJRE N B =CIABJRE N+l) B I=Bz— B3 HNKLI=CI*CMPLXE HNKL2=CIACNPLX 0HNKL=(cz/CI)AH 00 TO I00 ccc2=Q +l. fl; -8§RI/§IANK0R/2. 0) XI=cc BI=SIN(XI) |N(Xl)+ COS(XIg (Xl+(P|/ 20)) XI) ) 2 O BJREéN) 'YRE( BJRE N+I),-YRE)(N+I)) NKLI- HNKLZ BDI=(ccz/NK0R)AS ARGUl-CMPLXEO .0, ARGU2=CMPLX 0. 0, HNKLI=CEXP(ARGUI HNKLII=CEXP(ARGU 0HNKL=(ccz/NK0R) COEFFs API/z. ARGU3- MPLX(0. 0, c ANI=((2. 0A )+ 0) COMPXJ-CEX (ARé U3 Bi 0 L ) WHN KLl+HNKLIl OEF F) U{IQ Q*(Q+l.0)) AN=ANl/COMPXJ TERMlsAN*CMPLX(B 8 CALL CNDN (WK, NK A TERN2=ANA0NAHNK A , D i’( I) B?D;l,N,CN,DN) . 186 TERM3= ANACNAOHNKL BRAKET-TERM2+TERM3ACMPLX(0.0 I.0) C *xx:‘::n Afi:XAAxfl:*Auk:xkflx:*************x**************:*:+******** C TERMI SHOUD BE ADDED TO “BRAKET” TO GET THE TOTAL FIELD AT ”R”. C HOWEVER. SCATTERING CROSS SECTION IN THAT CASE WILL BE DIFFERENT C FROM PRINT OUT RESULTS. C :'::'::'::'::‘: :2: ‘:::"< :':: :".<: :‘Pc: :'::' ::'::' :‘::P: ‘P :::' ink: ~P :‘x :'::‘: .'::'::‘::'::‘::'::’::‘::'::'::’::‘::‘::'::':: :'::': :‘z:': :‘c:"::: :‘c: '::I::'::' ::P:': :P:': :': :': C2=(-I. )*2'=NW C =Qfi(Q+] ) SUM=CE CA*BRAKET SERIE =SERIES+SUM 999 CONTINUE X=REAL(SERIES)*(-I.) Y=AIMAG(SERIES)*(-I.) Z=Y/X AMPLI=(X**2+Y**2)/(A.O*(WKOR**2)) PHASER=ATAN(Z PHASEA=PHASERAI80.0/PI AMP=(L.0*(R**2))/(A*fi2) AMP2= AMP AMPLI wRITE (20, II)NKOA, AMPL|,PHA SE ,Y P2 II FORMAT 3x, F6.2,IDX, EII.A,12X ”A 8X,EII.A,8X,EII.A,8X.EII.A) A= A+(I (PI=100.)) 99 CONTIN NRITE( III FORMAT 9 CONTIN STOP ENO SUBROUTINE CNO DIMENSION BJRE COMPLEX wK,wKA AAURCI,AUR02,EP PI=A.0AATAN(I. NKA=NKAA NKOA= wKOAA EPCILN=CSQRT(BODY) REwKA= REAL(wKA) AEMNKA= AIMAG(WKA) =FLDAT EN- I cI=CS RT PIAwKA/z. 0) C3: 2-§*Pl/2. REWKA Cg:-AEM C EXP C5)+EXP -C53)/2.0 C585 RT PI*WKOA 2.0 C =S RT PI/ 2. .O:WKOA;; C 8C RTEPI (2 0*WKA I (C BS WKA) 0.0) GO TO CALL COMBES(REWKA, A MWKA, W3,0 N, BJRE, BJIM, YRE, YIM) SBFWKA=CI*CMPLX(BJRE(N) ,BJI (N) gBFSA?C2*C9*CMPLX(BJRE (N) BJIM (N))- CI*CMPLX(BJRE(N+I), BJIM(N+I)) 0 ) YIM(AI ) , A 02, HNKL, HNKLI, DHNKL,C9, ON (1"):- M on nro‘n 0 G F F c ) 0 A LX(FI,F2) F S I D F D KA= DI+D s KA=C6ACMPL ABS(wK0A) GD 93 .5,0. 00 N, JRE, BJIM, YRE, YIM) ABJRE(N+I) )YREINI)+1 N I=S 2=T I=C 2A0 =TANH( 2=C SBF BFW F ( ALL BF X( I I .G C COMBES (WKO S NKO=C7AB RE(N OSBEK0=C2AC ABJR HNKL=C7ACMPLX