.1. v 2.... .41 grid... itnzévufimulqu . . 3.1.... v.3. _ . . . . .1: .3... .3fl47:1.n%5:v31115~51.fi$9?9 fl. u 3.39. 11.41; . , . , . ,.... . . a 1 i.» 3...“. 5).Na1)afii...3.s P..W\G.!I.:. lit. . a I , ,gl, inI. o. .r.(..vt\.3..5~ .. . . . . . o. . . .. I \.‘s a 2 «113%. 1.3.5 Ila! . S... .... fink»... 18mm. .5... .112. .. .. «u... ...x 53.5..57J’L.(£3¢i ‘22.).pskdx V3. Alfiulynutfirqwfiflx $8..le :08...» , , . l. ). Vi... 0: at; . \.«.\.¥x\<1i\\.\.u . .1. .. 3G V.. .. 4.5.9933}... gt: 1...... 53mg E \ g .l. '\QD.’ .v u}: . . ..... .§§&1%.§ ., ‘09... , K r u! s.) u... 1...... a \3. 30.5.53”... . 12.41: ,3). 1.... ......3m»............... 2 13.4.... (2. .. l ‘1‘ v .. -. 1.... . . . x: .I x. .2... x . . a s... . "nit: . If .3: Nil... 21’ Ni . . Hf... . . - LL32 .. - burs... .s m... 4... . .14....) .. .2... 1.. .._...,.-......i?... RRP. I... {awn {g 3.: 3%.?) ) Eov....n$ Nagaiuvdkdflfil . , ,3. . . . . 9‘215 .13 . \ b.‘ . )1 .64)\5153l... . “N... 7...... immumfi .. . Hats... 9... 1%..-.) .S [mantra .'\ . .‘ 81.1 .. -\ 72(81):)... 1. .11.;1(..$.i.. 7L3! “Ill-J. IOU iii-133$... 115.11: 1‘1: \siylil . . .‘(elliilli .. .ul.n.2.\.i T. 3...!) \dfl: 6.3.13... .35.... a .6.)4....!lx1u..s.mfl.. ....c.....;.~..1..h:i:.. . .. t .. .30.. 1...... : . i . .. ... . H. I. i) . 183%.}: L i.) . {fl-53$ ‘ . 5 n). )5 .. JfihlzwudfizWIrix. . u IV 0 . . 1.}! \‘2‘ ’Jn.§ghnhnz§1§117 .Vgx... .. . I‘ll: .1 :3“ as“!!! \l\:\1.\.)ih)|v 1‘13... . . “'0’. “0(9). 13‘ 5‘... D 31"... 3‘. $1 .. ~ 4 . a... 13).)... win! 1310 . 2.! 11.1.1.1}...533131Ix3tn . .L .1 ll: 1 )2. Y. is“ . . . 1|.l‘i‘g x. 1 () 1.53;...1s $§1§txlgif l. 3 11...... 5.6.... . . . iii}... .131).-\§.m.\ 22).”.N1}? 3 \ 1111142....)‘5 3i 1. 111.- . . 1.3.1.. .13“... +13 9:53.32: fiziéigiéxi. L .32.... 3311.7. . ... . 1 .. .lfi’l. ) . I 5 \1|\ g5; 1N4}: . g2}... . 3 . I! . .113... 11.11.... V ragfig .12.): :31. .v Ill-.7331? 2:3 igl‘t‘an; QJHLI-xlai. .112. . kin... \\Q ‘15 . .. 711;.ch ..‘.\ 1).... . _. 132:!) 1. 15.5132!" 13.3. 7 ~;)1..l.t. . s1 {III-3.3.1.32...) is. J. 112...): z. , a? . V... . V .22." [I . on. . . $1.35.; .11121221WLIEJ...‘ 2.1! $2.11.} 1.. . . t .1 L .- 2 .1. 3.1... 11!! )2. 34¢. a. J . 1.71“! . 0 12.13 5. eat an... . as}... a: I... GALKIJIEJImiisg. wage!!!) not}; 1.3.1.3.. .32 $319 -39.... rfizsis. .........r....... Exitfiguhn. Jul? :9}... mi}... u... 1.. @3135}... 3??!31.....s{n..... 1.080.331 i,- .. I (“H v1.3 1.. .. .1 .4 l . L. l .. l. ... P.) 1 ..V\ {51... .N. Tux}. .111 gfizwvnfi .icrgxxl. ”33:91. . 3g \ . 11' . . I! 3.53;)... . . 3.1. a... 13:18:". A .. fin. .71 .. t '{thnmnflflu’ V v! V a...) . T1 gab”. 575)}.1'1119} 1411. “gift... .53.??? \. '7. .3: 4‘! . V . K‘s-’13}! a to (I. . V . . £11??? .14.. ....fi..nu§.§£¥ fininghfiw. 3......» .......J..l......21 13.... .53.. y. . . .39).... ‘ I. ‘I - iii; ii‘v‘3hl: ‘{;b a... .17.! 3.15.... . 7 H41! .. .5. fi§.21.r}.. 1.... ..:?fi(.....1!§3nunn..utfia. ~n§afianazwafi In... §§.§.l-w .. 2%....1i: . 1...”. _ A I! mm m“ n ‘ . 51.11. LI giftt ‘ it! . . \v x If"... . .. . .uhuflf‘z‘u .. 34.1.44...) . 1...! 0H1 Lang.“ :0... .' 5.0.11.4...vlttuthflu (in... «z.....h(|..!i.bltx. . 5.1.9.. .3.“ .15... . L... Lt, EV I... t . ~h A". . \{Al‘lflvntfinnlxdfr‘l It 1.; . t .10? 53......» 55.31.... Hana £5.11}.-. . .5. A: .. . iii‘la-Lf .‘l‘t‘L’ 7.: . .3; . {(11% fifLLI....|. .z... - . -. . .- - . . . .ttzt..shhm.§m. hi..f.£ .s...fsn..iwei.fidunou.4 5.. “(£31,749 . . V. . ,}.?......L.:..V. . farmlrnk... , ..1.-.-...........,.....i.}i.. .I ; .. é. . . V.. 2 . I .... .- . . .. as...) .1 -23 2.3.1... . . 53E... .3. .1. ‘ifiti‘égvfi I3 . . ; . . . .. . . £5.1tvvixyzé......o.r.l..rf.£.:-....h..3..:§t...nn- r ‘ .I, . . IL..- . . . ... . V .1? r . . I . . . . .2.%.LEE£;IE. 2.9.1.2».-. 1., . . : . . .. S..- .z!t...?..?.4l.rz..t i.-..... .(.,. . f - . myMm;lilyujmwnmylu{will}! LIBRARY Michigan Sm: University «.4 . I rurqm This is to certify that the thesis entitled THEORETICAL AND EXPERIMENTAL STUDY OF THE PROXIMITY EFFECTS OF THIN—WIRE ANTENNA IN PRESENCE OF BIOLOGICAL BODIES presented by Khalid Karimullah has been accepted towards fulfillment of the requirements for Ph.D ELECTRICAL ENGG. degree in KM 5/: Major professor Date July 26, 1979. 0-7639 OVERDUE FINES ARE 25¢ PER DAY PER ITEM '\ Return to book drop to remove n this checkout from your record. MSU THEORETICAL AND EXPERIMENTAL STUDY OF THE PROXIMITY EFFECTS OF THIN-WIRE ANTENNA IN PRESENCE OF BIOLOGICAL BODIES By Khalid Karimullah A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering ABSTRACT THEORETICAL AND EXPERIMENTAL STUDY OF THE PROXIMITY EFFECTS OF THIN-WIRE ANTENNA IN PRESENCE OF BIOLOGICAL BODIES. by Khalid Karimullah This research has been conducted to achieve an in—depth knowledge of the electromagnetic coupling caused by placing a biological body in the vicinity of a radiating antenna. The thesis presents a numerical solution to the above mentioned problem and quantifies the current distribution on the antenna and the induced electric fields inside the biological body. This study is necessitated due to the widespread use of high power transmitters, CB radios, etc., where the operator of such a device is exposed to a possible radiation hazard. A detailed analysis investigating the problem of electromagnetic coupling between an antenna and a biological body in the near zone- of the antenna has been carried out in the introductory chapters. A.basic theoretical approach assuming a.thin-wire, center-fed linear dipole antenna as the radiating source has been adopted which leads to the coupled integral equations. Using the method of moments, these equations are transformed into a system of consistent simultaneous equations which are then solved on a computer. In addition, elaborate instructions for using the computer program are also provided. Experiments have been conducted using a plexiglass container of suitable dimensions filled with saline solution to represent the biological body. Perturbation of input impedance from its free-space value is plotted as a function of distance of separation between antenna and the body and is found to be in good agreement with theoretical values. Also current distribution along the length of the antenna and the electric fields induced inside the biological body are in good agreement. Comparison of fields induced inside a body from a radiating antenna with those from a plane wave with intensity of 10 mW/cm2 shows that use of high powered transmitters could prove hazardous. ACKNOWLEDGEMENTS I offer my most grateful thanks to many persons who helped me in this project. Special thanks are extended to Dr. Kun4Mu Chen for his sincere guidance and counsel , under whose supervision this research was conducted. I am equally thankful to Dr. D. P. Nyquist for his invaluable suggestions and guidance. I thank Dr. D.K. Reinhard and J.H. Shapiro, the other members of my guidance committee, for their c00peration. Thanks are extended to the Division of Engineering Research and the Department of Electrical Engineering and System Science_at Michigan State University for the financial assistance rendered during the Doctoral program. I must sincerely thank Ms. Joanna Gruber of the Diary Science Department at Michigan State University for her prompt typing services. I am also thankful to Enid Maitland and Mary Bentley who were extremely cooperative in providing me with the typing facility at the office. Last but not the least, I am indebted to my wife Cynthia for helping me in the preparation of the rough draft of my dissertation and I appre— ciate her patience, understanding and encouragement during the graduate program. TABLE OF CONTENTS List of Tables. List of Figures . . . . . . . . . . . . . . . . . . I. INTRODUCTION . . . . . . . II. THE STUDY OF FIELDS IN A BIOLOGICAL BODY EXPOSED T0 NEAR-ZONE FIELDS OF ANTENNA . 2.1 Introduction . 2.2 Theoretical Development . . . . . . . 2.3 Coupled-Integral-Equations . . . . . 2.4 Radiation Fields Maintained by the Antenna-Body System . . . . . . . III. NUMERICAL ANALYSIS . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . 3.2 Pulse Function Expansion and Point Matching. 3.3 Computer Program . . . . . . IV. FREQUENCY SCALING . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . 4.2 Frequency Scaling . . . . . . . . . . . 4.3 Frequency Dependence of Electrical Parameters. V. EXPERIMENTAL VERIFICATION OF THEORETICAL RESULTS. 5.1 Introduction . . . . . . . . . . . . . . . 5.2 The Antenna—Body System . 5.3 Input Impedance Measurement. . 5.3.1 Experimental Setup . . . . . . . . . . 5.3.2 Method of Measurement of Load Impedance . . . . . . . . . . . . 5.3.3 Free—Space Impedance Measurement. 5.3.4 Input Impedance in Presence of the Body. . . . . . ii vi 18 23 23 24 31 36 36 36 40 46 46 47 49 49 51 53 4e VI. VII. 5.4 5.5 Measurement of Current Distribution. . . . . . . 5.4.1 Experimental Setup. . . . . . . . . . . . 5.4.2 Free—Space Current Distribution . . . . . 5.4.3 Current Distribution in Presence of Body. . . . . . . . . . . . . . . . . Measurement of Induced Electric Fields Inside the Body . . . . . . . . . . . . . . . . . . . . 5.5.1 Experimental Setup. . . . . . . . . . . 5.5.2 Free—Space Field Measurement. . . . . . . 5.5.3 Induced Electric Field Measurement. . . . Sources of Errors. . . . . . . . . . . 5.6.1 Errors in.Impedance Measurement . . . . . 5.6.2 Errors in Measurement of Current Distribution. . . . . . . . . . . . . . . 5.6.3 Errors in Electric Field Measurements Inside the Body . . . . . . . . . . . . . THEORETICAL STUDY OF VARIOUS MODELS OF ANTENNA- BODY SYSTEM . . . . . . . . . . . . . . . . . . . . . 6.1 6.2 6.3 6.4 6.5 Introduction . . . . . . . . . . .-. . . . . . . Antenna-Body System Operating at 80 MHz. . . . . Antenna-Body System Operating at 27 MHz. . . . . 6.3.1 Test of Numerical Ability of Our Program. Antenna—Body System with Operating Frequency of 90 MHz . . . . . . . . . . . . . . . . Problem of Arbitrarily Shaped Thin—wire Antennas . . . . . . . . . . . . . . . . . . . A USER'S GUIDE TO COMPUTER PROGRAM . . . . . . . . . 7.1 7.3 7.4 7.5 Introduction . . . . . . . . . . . . . . . . . Formulation of the Problem . . . . . . . . . . 7.2.1 Description of Program "FIELDS” . . . . . Data Structure and Input Variables . . . . . . . Example . . . . . . . . . . . . . . . . . . . . Free—space Program "ZFREE" . . . . . . . . . . Printout of Results . . . . . . . . . . . . . 61 61 66 66 7O 72 72 77 77 77 78 80 80 91 94 98 101 102 102 102 108 110 115 116 118 iv LISTINGS OF PROGRAMS FIELDS AND ZFREE . . . . . . . . . . . 126 VIII. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . 144 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . 146 6.3 LIST OF TABLES Dependence of impedances and dissipated and radiated powers upon dipole location 2 (geometry dimensions and parameters specified in Fig. 6.1). Z.n = input impedance of antenna Z = perturbation to antenna impedance due to proxigity effect, Z = free—space antenna impedance and Zin = Z0 + ZP.o 88 Dependence of impedances and dissipated and radiated powers upon dipole location x (geometry, dimensions and parameters are specified in Fig. 6.1). Z. = Z . 1 . o + Z (Z = free—space impedance, Z = perturba ion duepto Body proximity effect and Z? is input impedance in of the antenna), 89 Dependence of impedance and dissipated and radiated powers upon dipole location xo (geometry, dimensions and parameters specified in Fig. 6.1). Z. = Z + Z (Z = free—space impedance, Z = perturbaEIon dge top body proximity effect and Zinpis input impedance of the antenna). 90 Data in FILE no. 3. This data corresponds to the example problem of section 7.4. 117 2.1 5.3 5.4 LIST OF FIGURES A thin-wire antenna coupled to a biological body of volume V . This situation is also defined as antenna— body system. 8 A thin—wire linear centerfed dipole antenna coupled to a biological body of volume Vb. 15 Coordinate system chosen to define the far-zone radiation field pattern. 19 Representation_of the system of equations defined by = y, where A is the matrix of coefficients. 30 Illustration of frequency scaling. 37 Static—dielectric—constant es versus normality of saline solution, 42 Relaxation time parameter r (secs)vershs normality of saline solution. 4 Ionic conductivity of the saline solution OiVS. percentage of NaCl in distilled water by wt. 44 Geometrical arrangement of experimental setup (b) and corresponding theoretical model (a) used in the computer aided numerical solution. 48 6 Experimental setup for measurement of the input impedance of the antenna by using vector voltmeter. 50 Input conductance of the antenna as a function of k h, where h is the height of the antenna. 54 Input susceptance of the antenna as a function of k0 h, where h is the height of the antenna. 55 Perturbation (Z = +jX ) in input impedance versus the spacing 2(209 betgeen tfie antenna and the body. = input impedance of the antenna due t8 coupIingZo and ZZZ = the free-space impedance. 57 vi 5.15 Perturbation (Z = R + jX ) in input impedance versus the spacing (z betgeen the antenna and the body. 0 . . . Z = Zi - ZO, Z.n = input impedance of the antenna due tB coupIing and 20 is the free-space impedance. Perturbation (Z = R + jX ) in input impedance versus the spacing (z betgeen tge antenna and the body. 0 . . Z = Zi 20’ Z n = the input impedance of the antenna dge to Phe coupling and 20 is the free—space impedance. Perturbation (Z = R + jX ) in input impedance versus the spacing (20? betgeen tge antenna and the body. Z = Z. - Z , Z. =the input impedance of the antenna dge tolEouplIng dad Zo = the free-space impedance. Experimental setup for measurement of the current distribution along the antenna. Free-space current distribution on the antenna of height h = 0.25 l . Theoretical and experimental values have been normaIized by their respective maximum values. Free—space current distribution of the antenna of height h = 0.385 10. Theoretical and experimental values have been normalized by their respective maximum values. Free—space current distribution on the antenna of height h = 0.445 A0. Theoretical and experimental values have been normalized by their respective maximum values. Current distribution on the antenna in presence of a biological body. Theoretical and experimental values have been normalized by their respective free—space maximum values. Current distribution on the antenna coupled to a bio— logical body. Theoretical and experimental values have been normalized by their respective free-space maximum values. Current distribution on the antenna coupled to a bio— logical body. Theoretical and experimental values have been normalized by their respective free—space values. Experimental setup for the measurement of electric field inside the biological body. 58 59 60 62 63 64 65 67 68 69 71 6.3 6.4 viii Free—space electric field distribution at points in space corresponding to the central location of body cells. Free-space electric field distribution at the locations specified in the Fig. 5.17. Distribution of induced electric fields inside the biological body of Fig. 5.1 when irradiated by the impressed field from the antenna of height h = 0.25 lo at 600 MHz. Distribution of induced electric fields inside the biological body as shown in (a). The antenna is of height h = 0.25 lo and the spacing between the antenna and the body is 4.5 cms. Geometrical arrangement of the human body model and the radiating antenna to which it is coupled. Current on antenna in presence of body compared to that in free—space where antenna is driven by identical input voltages. Geometry, dimensions and parameters are specified in Fig. 6.1. [E] field (V/m) induced in human body model by an input current of 1.0 Amp when the antenna is placed very close to the body at neck level. Refer to Fig. 6.1 for other constants of the system. Induced body field and antenna current for antenna of near anti—resonant length in proximity to human body (geometry, dimensions and parameters are specified in Fig. 6.1). Radiation field pattern maintained by dipole antenna coupled to the human body model in H—plane of the dipole (geometry, dimensions and parameters are same as in Fig. 6.1). Distribution of induced electric fields and the power density (SAR) at the central location of each cell of the body for an isolated antenna—body system. Antenna is driven by an input power of 1 W. Distribution of induced electric fields and the power density (SAR) at the central location of each cell of the body for an antenna—body system over infinite ground plane. Antenna is driven by an input power of l W. 73 74 75 76 81 83 84 86 87 92 93 7.2 7.3 7.4 ix Distribution of the induced electric fields and SAR at the central location of each cell of the body irradiated by a plane EM wave of 27 MHz frequency and intensity 10 mW/cmz. Distribution of the induced electric fields inside a cylindrical model of man in direct contact with the ground and located in the immediate vicinity of a grounded quarter-wave monopole antenna. Distribution of the induced electric fields inside a cylindrical model of man insulated from the ground and located in the immediate vicinity of a grounded quarter-wave monopole antenna. Distribution of the induced electric fields inside the realistic model of a man located in the immediate vicinity of a grounded quarter-wave monopole antenna. Values are based on input power of 1.0 W and spacing of 20 cm between the dipole and the antenna. Distribution of the dissipated power density (SAR) inside the realistic model of man located in the immediate vicinity of a grounded quarter—wave monopole antenna. Values are based on input power of 1.0 W and spacing of 20 cm between the dipole and antenna. Transformation of the physical system of an antenna and a biological body into a computer model for program FIELDS. Illustration of (a) two quadrant vertical plane symmetry (2—QUAD VPS) and (b) two quadrant horizontal plane symmetry (2—QUAD HPS), Illustration of four quadrant symmetry (4—QUAD SYM). Theoretical model of the system given in the example of section 7.4. 95 96 97 99 100 104 106 107 114 CHAPTER 1 INTRODUCTION In recent years the interaction between high frequency electro- magnetic fields and biological bodies has been extensively investigated. These studies were motivated by the potential biological hazards associated with such electromagnetic radiations, (1,2). Chen et.al., (3,4) have determined the internal electromagnetic fields induced in biological bodies of arbitrary shapes excited by a plane electromagnetic wave. Also extending this technique to any known impressed electric field was a simple matter. The results of their work provided the information necessary for a realistic assessment of potential radiation hazards. As an immediate consequence of this study scientists were alerted to another related situation which could prove a potential danger. Modern technological developments in the field of high frequency trans- mission/reception of electromagnetic waves have led to CB radios, back pack transmitters, portable transmitters, etc., which have given new dimensions to wireless communications. However, these devices have also exposed their operators to a situation which could be dangerous to health if high power transmitters are used for long range communications. This problem attracted considerable attention and the main objective was to determine the induced electromagnetic field inside the body of an operator who is using such a device. An approach to this problem was adopted by Nyquist et.a1. (5) who obtained the impressed fields that excite the biological body, by a "known" current distribution on the antenna. It is worthwhile to mention that the presence of a biological body in the vicinity of an antenna will perturb the current distribution from its "free-space" distribution and.hence by this approach, substantial inaccuracies are imminent. Broadly speaking the fundamental aspect of this thesis is to develop a method by Virtue of which, unknown currents on the antenna can be determined numerically by computer aided analysis. Once the induced electric fields are obtained, a comparison with those obtained when the body is illuminated by a plane wave, with electric field intensity equal to the maximum intensity allowed by the federal radia- tion safety standard, can be made. Theory for solving this problem has been developed for arbitrary shaped,thin—wire antennas, however, the research is concentrated at center—fed linear dipole antennas (or base—fed monopole antennas over infinitely extending ground plane). Since a biological body is usually a heterogeneous finite body with an irregular shape, the determination of the internal electromagnetic fields becomes a formidable task. For mathematical simplicity, a body with simple geometry will be considered (even though the computer program can successfully deal with the problem of spatially dependent electrical parameters of the body, uniform conductivity and permittivity have been used in all experiments and theoretical models). The theoretical development for calculating the fields induced in the body and the currents on the antenna is given in Chapter II. This chapter also gives a short description of Hallen's integral equation in "free—space", which helps in determining the free—space impedance and current distribution of the antenna; and also radiation—zone fields generated by the antenna-body system are determined. In Chapter III, method of moments, which is a transformation that converts the system of integral equations into a set of simultaneous linear equations, is discussed. Elements of the matrix of coefficients representing the system are explained in detail and the corresponding subroutines that evaluate these coefficients are identified. A numerical test of accuracies of the integration process carried out in the sub— routines is also explained. In Chapter IV a basic derivation is given for determining a linearly scaled version of the biological bodies whose true dimensions are large and impractical for laboratory experiments. Properties of saline solution along with the graphs used to obtain a desired effective conductivity are reproduced. Chapter V is devoted to the theoretical and experimental results on the induced electric fields inside the body and the currents maintained on the antenna. It includes explanation of the experimental techniques used to measure impedance, current distribution on the antenna and the electric fields inside the biological body. A short account on possible sources of errors, that may have been encountered during the experiment, is also given. Chapter VI discusses the practical importance and the outcome of this research. A realistic model (uniform biological body resembling a human body placed in the vicinity of an antenna) is investigated and commented. A brief account on solving a problem where arbitrary shaped, thin—wire antennas are involved is given. Chapter VII provides a complete description of the computer program. Definition of input variables, construction of data files and the instruc- tions for its use are given in detail. In addition, an illustrative example is worked out to give the user a better understanding of the computer program. Suggested modifications which a user may want to make are also mentioned. A listing of the computer program which gives the free—space impedance and current distribution is also given in this chapter. CHAPTER II THE STUDY OF FIELDS IN A BIOLOGICAL BODY EXPOSED T0 NEAR-ZONE FIELDS 0F ANTENNA 2.1 Introduction. In the beginning of the first chapter it was mentioned that potential radiation hazards may be encountered when working with highjwwerCB radios, back-pack antennas etc. Simulation of the exact situation created by such antennas is difficult and solution for fields/ currents is a complicated task especially when the current on the antenna is not known. It is for this reason the study was restricted to a situation as shown in Fig. 2.1. Consideration of arbitrarily shaped, thin-wire antennas was an appropriate choice for most practical purposes. At a later stage it was necessary to specialize this situation to a linear dipole antenna to achieve greater mathematical simplicity and system as depicted in Fig. 2.2 was adopted. This approach could also successfully represent the case of a base-fed monopole antenna over a ground plane of infinite extent uSing the image technique. The following major topics are to be covered. (a) The quantification of current distribution and input impedance of the antenna in proximity of a biological body. (b) Determination of free—space current distribution and input impedance of the antenna. (c) Quantification of electromagnetic (EM) fields induced inside the biological body when it is in the vicinity of the antenna. (d) The total power deposition inside the biological body under the exposure of EM radiation from antenna. (e) The EM fields generated in the far-zone by the antenna— body coupled system. 2.2 Theoretical Development. When a biological body, such as a human body, is illuminated by an EM radiation, EM fields are induced inside the body and an EM wave is scattered by the body into space. Obviously these EM fiEldS are dependent on the physiological parameter and geometry, frequency and polarization of the exciting EM radiation. The total field in the space containing the body and antenna is therefore different from the field that would be present in the absence of the body. Field, current etc. associated with the antenna in the absence of the body are termed as free—space quantities . Since currents and charges on the surface of the antenna are always maintained in such a way as to satisfy the boundary conditions there; the current and charge distributions on this surface are expected to be perturbed from their free—space values in the presence of a biological body in its vicinity. The perturbation however, is dep- endent upon the distance of separation between the two "sources" namely, the primary source antenna and the secondary source, excited biological body. The phenomenon underlying the cause of these perturbations is called "coupling". Coupling may be strong or weak depending upon the separation distance between the two sources. It is apparent in the forementioned discussion that EM fields induced inside the body and the current on the antenna are both unknown quantities, and as such, it is necessary to determine them simultaneously. This paragraph gives a brief description of the theoretical analysis of the problem at hand. Firstly a tensor integral equation for fields inside the body is derived. The derivation is quite general in that, an arbitrarily-shaped,thin-wire antenna is used as an exciting source as shown in Fig. 2.1. Secondly, Hallen's integral equation is derived for a special case of centerfed linear dipole antenna as shown in Fig. 2.2. Our analysis is therefore aimed at solving the system excited by a thin- wire linear dipole antenna. These two equations together are referred to as coupled-integral—equations (CIEs) throughout this analysis and in the following chapters. Next, method of moments (using pulse functions) is utilized to transform the CIEs into a system of simultaneous equations. These equations yield a matrix bf coefficients which is square with non-zero diagonal entries. Gauss's elimination process is used to solve this system once the matrix elements have been computed. The solution yields the current on antenna, input impedance of antenna, EM fields inside the body and the power deposition in the body. Lastly,radiation- zone fields of the antenna—body system are computed. 2.3 Coupled—Integral-Equations. In this section we aim to derive the coupled-integral-equations that were mentioned briefly in the previous section. It is emphasized that time-harmonic analysis is being adopted and a time dependency of the form exp(jwt) is being assumed. We will first derive a tensor integral equation for a general case. Input Fig. 2.1 A.thin—wire antenna coupled to a biological body of volume V .This situation is also defined as antenna— body sysIem. (a) Tensor integral equation: +—> We consider a localized current source with current density J(r) existing in free-space and occupying a volume V. Maxwell's (curl) equations can be written for such a system in the following form v x Em = guinea?) (2.1) v x fie») = 3G) + jweofié), (2.2) Using the continuity equation V°3(f) + jwp(f) = O,which gives the relationship between the current density 3(P) and the free charge density p(f) we get v - t6?) = :2— vim. (2.3) o . For a system of equations as given above, a solution for the electric field is obtained by using tensor Green's function. Derivation of this equation,which enables one to write the electric field in terms of a tensor integral expression has been carried out elsewhere (61(16). Electric field is given as + ++ . + an ._. m. I new war?» dv'-—->——g§;€'1 ‘2") O V 10 for all points P interior to volume V. The symbol P.V. denotes the principal value of the integral meaning that the integral is carried out by excluding a small volume surrounding the field point first and then letting this small volume approach zero (7). For_points exterior to V, the field is represented by the tensor integral only. In above 9 O O I is the identity tensor ‘2 is the tensor Green's function -qu0 4n Ci $1 :1} ll ff + :VZ] IIII'I exp(-jko|?-¥'|) (2.5) r-r 0 where k0 = w Viggg , P and P' are field point and source point radius vectors respectively. We now examine the system depicted in Fig. 2.1. In this system, EM field is originated by a current density 33(P) in the antenna of volume Va‘ It is termed as "incident-field”. This field excites conduction and polarization currents inside the biological body of volume Vb which in turn produces an EM field of its own. The field produced exclusively by these secondary sources is termed as "scattered- field". The problem would have been relatively simple had it been possible to assume- 336;) as an independent known quantity. But due to the coupling this simplified assumption can not be used; and therefore both the primary and secondary sources are unknown. Total EM field {E(P), H(;)} is the sum of the incident and the scattered field at all points in space. For this field to be a valid 11 solution to Maxwell's equations it must satisfy the following v x E?) = -jwuofi(‘r*) (2.6) v x fiat) = 3%?) + o(?) E(?) + mama?) (2.7) -> -> where C(r) and E(r) are varying and discontinuous functions of space. This situation will therefore be a very complicated one if an attempt a ++ . . 1 . is made to solve for the E(r) field u51ng tensor-Green s-function +-> approach. Also V'E(r) is not a simple expression when related to the free charge density. The method of superposition gives a convienient way out of this situation. We introduce two EM fields as follows. Ea?) r Impressed EM fields from the ANTENNA. +3 -+ H (r) Eb?) ‘ +1) : Scattered EM fields from the BIOLOGICAL BODY. H (r) By superposition EG) = E86) + EbG) ' (2.8) +a+ fi(¥) = H (r) + $6). (2.9) 12 Electric field Ea(f) is assumed to be produced exclusively by the current density 33(P) in antenna. Therefore the following expressions are true . v x FR?) = -jwuofia(¥) (2.10) v x fiad’) = 3%?) + jweoiaé) (2.11) v - tad?) = 6%— v-3a(?). (2.12) 0 Similarly, we can write a set of equations for {Eb(f), Hb(f)} with a condition that equations (2.6) and (2.7) are satisfied identically. v x EN?) = -jwuofib(¥) (2.13) v x EN?) = 3eq(‘r’) + jweoEbG) (2.14) v - PM?) = 3?:— v-ieqd’), (2.15) 0 Adding (2-10) and (2-13); and using (2.8) and (2.9); the expression for curl of total electric field in (2.6) is satisfied trivially. Next, using (2.11) and (2.14); and again using (2.8) and (2.9); the expression for curl of total magnetic field in (2.7) is satisfied with 3eq(?) = a?) E6) where a?) 9 0(3) + jw[s(_f)-to] is called 13 the complex conductivity, a parameter which completely determines the conduction and polarization currents induced in the biological body. A comparison of the set of equations (2.10), (2.11) and (2.12), and (2.13), (2.14), and (2.15) with the set (2.1), (2.2), and (2.3), Ea G) and Eb 6) directly. Since we are assuming the antenna a perfect conductor,points will enable us to write down the expressions for inside the antenna will not be included in the following analysis, therefore the expression (2.16) below is valid for all points outside the antenna. Therefore Eh?) =J 336') -‘5(?,¥')dv'. (2.16) Va Also, ->b + + -+ -> -> 3 it)? E (r) = P.V. 3 (r') - G(r,r')dv'- 41—; (2.17) Vb eq Jweo for all points P inside the body's volume V Total electric field b' will be given by the following expression (in which thin-wire approxi— mation has been used) using equation (2.8) E6) =1 1(s')§'.‘6(¥,z')ds'+p.v.J jeér")fG(-f,_f')dv' ant V b —3 (3?) I j3me (2.18) 14 + for all points r in Vb' Other quantities are as before and I(s) is the current on the antenna. (b) Hallen's Integral Equation: Before we attempt to derive the Hallen's integral equation it will be necessary to specialize the general situation of Fig. 2.1, therefore we now analyze the system shown in Fig. 2.2. Furthermore the antenna conductor is assumed to be perfect so that the electric field interior to the antenna is zero. Using the boundary condition for the tangential component of electric fields along the entire length of the antenna we get, for -h:x:h E:(x).+ E:(x) = —V06(x) (2.19) where V0 is the impressed voltage (input of the antenna is situated at the origin). Subscript ”x" signifies the tangential component and it is the + I l same as x — component of electric field. The electric field produced exclusively by the antenna satisfies the relation (on the surface of antenna) -> -+ Ea(x) = -V¢a(x) - ija(x) ¢a(x) = scalar potential 14 + for all points r in Vb. Other quantities are as before and I(s) is the current on the antenna. (b) Hallen's Integral Equation: Before we attempt to derive the Hallen's integral equation it will be necessary to specialize the general situation of Fig. 2.1, therefore we now analyze the system shown in Fig. 2.2. Furthermore the antenna conductor is assumed to be perfect so that the electric field interior to the antenna is zero. Using the boundary condition for the tangential component of electric fields along the entire length of the antenna we get, for —h:x:h E:(x).+ E:(x) = -V06(x) (2.19) where V0 is the impressed voltage (input of the antenna is situated at the origin). Subscript "x" signifies the tangential component and it is the same as I — component of electric field. The electric field produced exclusively by the antenna satisfies the relation (on the surface of antenna) + Ea(X) = -V¢a(X) - ija(X) ¢a(x) = scalar potential 15 Input “J Fig. 2.2 A thin-wire linear centerfed dipole antenna coupled to a biological body of volume Vb. l6 .+ Aa(x) = vector potential therefore, 34> (X) a ‘__ a _. Ex(x) — 3x 3 ax(x). (2.20) For points on the surface or outside the antenna a good approximation is to assume the current flowing along the antenna axis. Then h u Aax(x) = 2% L1 I(x')Ka(x,x')dx' (2.21) Ka(x,x') = -% exp(-jkoR), R = [(x-x')2+a2]l/2 where "a" is the radius of the antenna conductor. This is a valid approximation only for the cases where EM field outside the antenna isreq- uired. Starting from the basic expression for ¢a(x) in integral form, using continuity and boundary condition I(h) = I(—h) = 0, it is easy to arrive at the following expression for _3 4ne w .3x 0 h Q (x) J' I(x')K (x,x')dx' (2.22) a a . -h using (2.21), (2.22) in equation (2.20) and substituting these in equation (2.19) and after some algebra we can arrive at the following differential equation. l7 2 —j4'nk F 2 b —3ax§—X) + k0 F(x) = —n ° [V06(_x)+EX(x)] (2.23) where h F(x) = J I(x') Ka(x,x')dx' and no = Vuo/Eo . --h At this point we state without proof that for a differential equation of the form 2 3 ——12’- + 12y = g(x). 3x a solution, using :the Lagrange variational method,can be obtained as, y = Cl sin Ax + C2 cos 1x +% g(u) sin A(x—u)du. o By inspection of equation (2.23) we arrive at the desired Hallen's integral formulation for the current distribution on antenna in the ' presence of a biological body. The equation is, h J I(x')K (x,x')dx' + A cos k x + B sin k x —h a o o x + j? J E:(u) sin ko(x-u)du = -j:—TT V0 sin kolx o o . (2.24) o 18 The free-space Hallen's integral equation is exactly like the one in (2.24) above except the contributing term due to body effects is zero, that is E:(u) = O in (2.24) above. Also reproducing equations (2.18) with the length vetor g replaced by I as shown in Fig. 2.2, and some rearranging, we have for +‘V rinb [1 +53%] 136?) -P.V. [16?) ET?) °*E(}’,¥')dv' 0 Vb h " -> + = J' I(x') sz(r,r')dx'. (2.25) -h Equations (2.24) and (2.25) together are referred to as coupled—integral- enuations (CIEs) and these will be solved numerically on a computer. In Chapter III a detailed analysis of the numerical methods used for the computer solution is given. 2.4 Radiation field maintained by antenna-body system. In this section we aim at obtaining the radiation pattern of the EM system which is formed by the antenna and the irradiated body. The far-zone field pattern is greatly dependent on the separating distance between the body and the antenna. The situation is similar to an antenna with a parasitic element. For the system under consideration, we have two sources, namely l9 Biological Body Fig. 2.3 (Zoordinate system chosen to define the far-zone radiation field pattern. 20 the current I(x) on the antenna and current density 3eq(?) = T(;) E(P) where r(f) is the complex conductivity as defined previously and {E(P) is the total electric field inside the body. The coordinate system is chosen as given in Fig. 2.3. The electric field expression is given as E6?) = -j n k JR?) . fi+ 5737—] c (?,¥')dv' (2.26) o o k 2 o v o + +, exp (-jkoR) -> +, G0(r,r) " T— 9 R - lr-r I: no " JUO/Eo. One approach will be to solve for the above integral numerically since the current on the antenna and the induced fields inside the body are obtained (at least at a sufficient number of points) once the CIEs are numerically solved. A much simpler formula can however be derived (5) using radiation-zone field approximation. This approximation requires + +' +. . _ +' . that koR>>l and r>>r , where r is the field p01nt and r is the source point. An outline of the derivation of this formula follows. + +! - .ko . A VGo(r,r ) — “IZFR exp(-JkOR)r (2.27) also J(?)~v— J(+')—E’—+J(:')-§—+J(—r")-3—' (2 28) - x r 8x y‘ 3y z 32 ' 21 Next, 2 __3__ VC (+ + I ) 1 “k0 3x 0 r,r — 4wR . a-R “ exp(-JkoR) (53-h . (2.29) Using (2.27), (2.28) and (2.29) above one can easily arrive at the following expression; -rk 2 o 4flR Whom 9d,?) exp (~jkoR) (9369)). and consequently using (2.26) and defining I(F') = er(P') + 616(P‘) + 6J (I') ¢ we get exp(-JkoR) 1 4nR dv. (2.30) E a —j noko J. [5Je(?') + 61¢(P')] v Invoking the far zone approximation and using binomial expansion to approximate R.we get, , + +, Since r >> I . Nexttransferring J and J into linear combinations of JK , Jy and J2 9 ¢ 22 r = O O '. " ”*1 E ——_41rr exp( Jkor)J [9{Jx(r ) cos 6 cos ¢ V + Jy(?') cos 6 sin ¢ - Jz(¥') sin 8} + d{-Jx(r') sin ¢ + Jy(?') cos ¢}] exp'{-jko (x' sin 6 cos ¢ + y' sin 6 sin ¢ + 2' cos 6)}dv' , (2.31) Equation (2.31) gives the radiation—zone electric field. Volume Integration is carried out over all sources thus, for antenna 3(¥')dv ' will reduce to I(x')Kx' and for body 3(1'") = Ema") where r' is inside Vb. CHAPTER III NUMERICAL ANALYSIS 3.1 Introduction. The integrals obtained for the electric field E(;) at any point inside the biological body and the current distribution on the antenna are, in general, very difficult to evaluate. A simple way to obtain an approximate solution is to require that equation (2.24) and (2.25) be satisfied at certain discrete points in the region of interest. This procedure is called point matching. In the moment method, the total volume of the biological body is partitioned into N subvolumes B or "cells"; and the antenna length into NA partitions or "segments". We must have NA an odd integer because we are interested in knowing the current at the central segment, which will be frequently referred to as the input segment. It is worthwhile to mention that method of moments is a generalized technique and the method outlined above is a special case which utilizes ”pulse—function-expansion" to approximate the unknown fields/currents . The cells in the body are assumed to be regular cubes. electrically small and in each cell electrical parameters and unknown fields are assumed to be constant. Similarly the current in each segment of the antenna is assumed to be constant. Also recalling from past experience, it has been found that the cell edge should be smaller than one tenth of the wavelength of radiation inside the biological body. This requirement can however, be 23 24 relaxed in some cases. An upper limit on the size of the antenna segment is Ao/4O where 10 is the free-space wavelength. Information supporting this choice is also experimental. Finally, point matching is done at the central coordinate of each cell and segment. 3.2 Pulse Function Expansion and Point Matching. At this point we introduce a new notation to replace the conven— tional rectangular coordinate system variables x,y,z. x1 = x yl-Y 21:2 The pulse function approximation for current distribution on the antenna is NA 1,x1 in (Axl)L I(x ) = E I p (x ). p (x ) = (3.1) 1 1 l l l 1 . l=l 0 otherwise . The pulse function expansion for the electric field inside the body is 52%?) = z'finpn<¥), pn<¥> = n=l (3.2) NB [ l,r in (AV)n 0 otherwise . In equations (3.1) and (3.2) above, 0 0 th It is the current in the l segment of the antenna, th (Ax represents the span of l segment of the antenna, 1)l (AV)n represents the volume enclosed by nth cell of the body, and E? is the total electric field in the nth cell of the body. 25 +>++ The matrix representation of tensor Green's function G(r,r') can be conventiently written in terms of the new notation for coordinates. For simplicity, arguments are not specified in the matrix expression. n¢ = G G G (3.3) where the matrix elements have been evaluated by Livesay and Chen (8). -j mu (oz 6 G = . k exp(-jd){ —l-ja) xpxq 4fla3 o pq 2 l + - ' - ' 3-0 +3'a —- (xp x p) (xq x q)( J ) R2} A -> -> a = kOR and R = 'r-r'l (3.4) 6 = 1, if p = q, otherwise zero. PG The pulse function expansion for the current is then used in the L.H.S. term of equation (2.24) to yield a sum of integrals over each segment. This gives l h NA a-+ I x' K x ,x' dx I ( l) a( 1 l) l l n’ I Ka(Xl,X'l)dX'l a II M -h where 26 - 1 ' o h §_xl :_h and x l in (Axl)L. Also 1.x a. i a_ — x1 - 2 (Ax1)L L A L l a+ - x1 + 2 (Axl)l where x% is the central location of LFgegment. Next the pulse function expansion for the electric field will give us the following expression for field at ; outside the body produced by the currents and charges induced inside the body N B EN?) = 2: 1 E“ '("f + “+' ' +1 . (AV)n . . . +b This can be uSed to determine the tangential component of E at the + + _ surface of the antenna where r = x1 and -h §_xl j_h. This can be assumed for the surface of the antenna when thin-wire approximation is made or when the diameter of the antenna conductor is very small compared to the wavelength. To a first order approximation, this component is written as, b NB Ex (x1) = Z 1 n= "MUD n + + Tn(AV)n Ex Gx x (Xl,rn), where l p l p p l :n is the central coordinate of nth cell inside the body. The integrand of the 4th term in the L.H.S. of (2.25) can be written at some vector 27 _) location u on the antenna as 2 B + +n Integrand = ( (u,r ))sin ko(xl-u) I1 3 Z Tn(Av)n E: Gx X 1 p=1 P P l IIM A ..) where u = ux1 and represents the dummy variable introduced to perform }. the integration in the interval {0,x1 We are now in a position to transform the equation (2.24) into the ”sum-of—integral" form of Hallen's equation- It is L NA 1 a+ o l A Cos kox1 + B Sin koxl + E It Ka(xl,x 1)dxl l—Z L a- N x B 3 l +jfiz-Z Z T (Av) EnI G (3,?“) Sin k (x -u)du n n n X x x o 1 0 n=1 p=1 p o l = -jng-V Sin k Ix | (3.5) o o o l where currents in the outermost segments of the antenna have been assumed to be zero. Similarly the right hand side of equation (2.25) is transformed as follows by using pulse function expansion for the current on the antenna. It is I(x'l)xl~ G(r,x'l)dx'l = Z x {Z 11 G x(r,x'l)dx'l} p=1 P 1‘1 1 -h at where 28 .+ r is the field point inside the body, of the central coordinate of any cell, and xp represents the unit vectors for p = 1,2,3. Next, the L.H.S. of equation (2.25) is represented by the following expression (except for polarity) for the field point ?, P.V.I r(}")'€(¥') . E(¥,?v)de{1+—-T—Lr-l} E(E’) v B 3Jw€o 3 A NB 3 n +i+ T = Z x { 2 2 Ex (T P.V. Gx x (r,r')dv'-5 6++n(1+ n ))} p=1 p n=1 q=l q (Av)n p q pq rr j3w€o where 1 if p = q 1 if I = r .{ gm: pq 0 otherwise , rr 0 otherwise, and ;n is the central coordinate of nth cell. Tn will be the complex conductivity of the cell in which ;n lies. These two expressions replaced into equation (2.25) will yield the "sum-of—integral" form of tensor integral equation. Subscripted unit vector along with the summation over p = 1,2,3 yield a set of 3 scalar equations for each point. N a1 3 A A + + + Z x [ 2 IL Gx x (r,x'1)dx'l NB 3 n n=1 an. n I GxX (nr'mv' (Av) P q n Tn + - 5pq§+n (1 + ije )}1 = o (3.6) rr 0 29 where the component terms and variables have already been defined in previous pages. Equation (3.5) is point matched at the central location of each segment of the antenna. This is done by substituting {x11} in place 1 in that equation, thereby generating NA Since currents I1 = IN = 0 because of the boundary conditions, there A are exactly [NA + 3N3] terms in each of the NA equation (3.6) is point matched at the central location of each cell of field point x equations. equations. Similarly, of the body. This will be accomplished by substituting the central co-ordinates {;m} of each cell in place of field point ; of equation (3.6). This will generate 3NB equations (NB equations for each vector component) and each will contain (NA + 3NB) -2 terms, two terms less because the boundary condition I1 = INA = 0 is imposed. The two groups of equations thus developed by point matching, form a system of (3NB+NA) equations and the same number of unknowns. The matrix of coefficients is therefore square and since each equation has a distinct matching point, we expect the matrix to be full rank with a unique inverse. The matrix is depicted in Fig. 3.1. Submatrix AA is NA x NA matrix, submatrix AB is NA x 3NB matrix, submatrix BA is 3NBX‘NA. matrix, submatrix BB is 3NBx 3NB matrix. Since I1 = INA = 0 are already known the tOp and bottom current positions in.; are replaced by A and B, the unknown constants of Hallen's equation. .2H . i ,_ -Jfir-VO Sin kolxll, i- 1,2,..N 0 Vector yA has yi A 3N NA r-—“”‘——-\ I I A I A l I I I I B I I A I I I I l h- Fig. 3.1 30 Ax = y where A is the matrix of coefficients. Representation_of the system of equations defined by 31 3.3 Computer Program. This section is devoted to the explanation of the major subroutines that are used to evaluate the matrix developed in the preceeding section. Also included is a brief description of computing processes involved in computation of these elements, which will enable the reader to have an overall understanding of the computer program. In the computer program four subroutines are assigned to compute the elements of the coefficient matrix (one for each submatrix) and are named accordingly: for example, subroutine "MATAB" computes the elements of submatrix AB of Fig. 3.1. Another subroutine "CMATP" then solves the system of equations by Gauss's elimination process. Finally, sub- routine "RAD" is used to determine the normalized far-zone radiation fields using the discrete numerical data obtained from the solution of equations. This section deals only with the four subroutines that are used to evaluate matrix elements. Following is the computational assignment of each subroutine. SUBROUTINE NAME SUBMATRIX ELEMENT I COMPUTATION 8‘+ i t V l. MATAA (AA)il n, K.a(x1 ,xl)dx1 a— . _ . 1 ‘1 - l to NA Sin koxl or i l = l to NA cos koxl 32 SUBROUTINE SUBMATRIX COMPUTATION 'NAME. ELEMENTS i x 2 MATAB ( ) '4" (Av) 16 (I w)’ k (xi d ° AB ik JE—Tn n x x u,r Sln o l-u) u o o p 1 i = l to NA k = (p-1)NB+n where n = l to NB p = 1,2,3 3. MATBA (B ) A rl I = l to N A am r = (p-1)NB + m + +m + I Gx x (r ,xi)dx ' where m = l to N a p l 1 p = 1,2,3 4. MATBB (BB)rk r = (q-1)NB + m 4m +n T {r P.V. G x (r ,r )dv'- 5 a (1-I—-m——)} ( k = (p-l)NB +‘n Av)n xp q pq;n¥m 3J(”go where m,n = l to NB p,q = 1,2,3 The diagonal entries of the matrix of the entire system are the dia- gonal entries of submatrix A and B of Fig. 3.1. These entries A B correspond to the situation in which the field point lies in the same cell (segment) of the body (antenna) over which the integration has to 33 be performed. The diagonal elements of submatrix AA are obtained by the following approximation. Integrand = ex é-.kR) é-% 1/2 where R = {(xi-xi)2 + a2} = a? and the upper limit a'1L of Integrating between the lower limit x' + 1 th .. . .1 the L partition, whose central coordinate is x we get 1, (xll¥af) +-/lel—af)2 + a2} (A ) = log A ll e l l I 1 2 2 (x1 -a+) +,/{(xl —a+) + a } "a" being the radius of the antenna conductor. The diagonal elements of BB are obtained by an involved process which yields an analytic expression (8). The expression thus obtained is given by _ :2 . . _. _ l (BB)nn — 3 quoTnK1+Jkoan) exp( Jkoan) l}-—§ o T 3Jw€ o where 3(Av) a g ( n 1/3 n An ' Subroutines MATAA, MATAB and MATBA make use of Simpson's method for numerical integration. Subroutine MATBB processes volume integration over each cell of the body subdividing the cell into sufficiently small subdivisions and summing up the contribution from each subcell. Accuracy and the cost of computations are the factors which govern the choice of the number of subdivisions and has been discussed elsewhere (9). We shall now discuss the accuracy of the Simpson's integration processes that were used in the above mentioned subroutines: Our objective is to come up with an optimum number of subdivisions of the span of integration so that reasonable accuracy is achieved with min— imum computational cost. A separate computer program is written to determine the appropriate number of subdivisions to meet the prescribed accuracy limit. In this program the worst possible situation, meaning, that the case in which integrand's behavior is not smooth, is chosen for integration. An arbitrary number (usually 4) of subdivisions are used as a starting point and the integral evaluated. The number of subdivisions is doubled and the integral is reevaluated. This new value is compared with the previous value. If the percent difference is less than 0.1% the current number of subdivisions are accepted otherwise the process is repeated. This method was tested by evaluating the diagpmfl element by equation (3.7) and from the above process. The error was found to be less than 0.01%. The separate program for Simpson's integration is used, so that the user can test the accuracy before he actually starts solving the problem. Once the required number of 35 subdivisions are determined the corresponding adjustment can he made in the main program by changing just one card. Due to the simplicity of the test program its details have not been mentioned herein. In Chapter V the computed values of impedance and current distribution etc. have been found to agree reasonably well with the experiment and we are encouraged to assume a satisfactory convergence of the numerical techniques employed in this program. CHAPTER IV FREQUENCY SCALING 4.1 Introduction. This study is devised to understand the EM coupling effects inside a biological body. The practical aspect however, is to study EM inter- action between a human body and a radiating antenna. Theoretically there is no limitation on the size of body as long as the cells are sufficiently small compared to the wavelength; and the number of cells remain under the maximum that can be handled by the computer. As we approach the experimental aspect of this research we find that it would be almost impossible in many cases, to work with the actual dimensions.To illustrate this by an example, consider a system with operating fre— quency of 30 MHz (wavelength = 10m) and a body of height 1.7 meters with appropriate width and depth. Apart from the fact that the body would be large, a ground plane. that might be considered as being infinite in extent, would be practically impossible to realize for laboratory work. It is possible to cope with this problem by, what is called the "frequency scaling" discussed in the next section.The later part of the chapter deals with the conductivity and dielectric constant of salt solution since a plexiglass container filled with salt solution has been used to replicate biological systems. 4.2 Frequency Scaling. In order to achieve a geometrical configuration suitable for 36 37 ° I__I/ I wZUIE'I (00,036) Fig. 4.1. Illustration of frequency scaling. 38 laboratory purposes and yet retain identical situation as posed by the actual problem, it is necessary to transform the actual coordinate system into a scaled version, such that the field quantities and there— fore, the absorbed power remains the same. The following analysis will provide the answer to this problem. It is possible to replicate an EM field configuration in a scaled space by frequency scaling. Consider the actual system represented by unprimed coordinates and the scaled version by primed coordinates as shown in Fig. 4.1. For a scaling factor d as defined by f = d?‘ the Operator V in the unprimed system is related to the operator V' in the primed system by the relation . V = -V'. (4.1) In the actual (unprimed coordinate) system the vector Helmholtz equation for the configuration shown in Fig. 4.1, and for points interior to the body v x \7 x E6?) - wzuoEEG) = o (4.2) where _. '0' e = (€115) is the complex permittivity. The spatial dependence of E'is determined by that of o and e of the biological system. Using the relationship of V operators from (4.1) and substituting in equation (4.2) we get 39 v' x v' x Em?) - wzazpoE'ém?) = o (4.3) Let w' = am, 0' = a0 and E' = E, then V' x V' x Em?) - w'ZuOEE(a1-*') = o (4.4) _ oJ where e = (S -jap). Now equation (4.4) is exactly the vector Helmholtz equation that would be obtained in the primed coordinate system with w' and 0' as the angular frequency and conductivity respectively. This means that we can use the scaled version of the true problem with appropriate w' and 0' for our analysis. Later on the true field quantities may be obtained by using the fact that $56?) = [E(oE'H f’ = flu where E(df') will be the solution to equation (4.4). In the experiments performed in Chapter V it has been found apprOpriate to choose a suitable size of the container and work with 600 MHz frequency, since at that stage, we are primarily interested in comparing the theoretical and experimental results. 40 4.3 Frequency Dependence of Electrical Parameters. To carry out the experiments with salt solution it is necessary to know its electrical prOperties which are defined by the conductivity and permittivity. These quantities exhibit strong frequency dependence at frequencies above 1 GHz and hence it is essential to know the values of these parameters at the Operating frequency. The details of the molecular theory used to explain the frequency dependence is given in (10), (11), and (12). We have found it sufficient to incorporate the emperical results given by those sources and have used their experimental data to our advantage. Total or effective conductivity which determines the dissipation of energy in salt solution is composed of two parts, namely, the ionic conductivity and the dipolar or dielectric conductivity. Ionic con— ductiVitVis;.caused by a lateral flow of ions and is the dominant part of the total conductivity at frequencies below 300 MHz. At higher frequencies the dielectric conductivity, which is an apparent conductivity arising from viscous retardation of induced rotation of the modecular water dipole, also becomes a contributing part. In all such cases, total conductivity will be the sum of ionic and the dielectric conductivity. The method for determining the total conductivity and complex permittivity of salt solution is given below. Let 8w denote the complex permittivity of distilled water. If this quantity is defined by its real and imaginary parts as 8W = 6' -j€" N then, s' = s s' and s" = e s O I‘ O I' where 41 eS—4°9 ' = 8 r W + 4'9 (4'5) (ES-4°9)wr E" = ’ r l+(wr)2 (4.6) as and T are obtained from the Figs. 4.2 and 4.3. The former is called the static-dielectric-constant and the later is called relaxation time parameter. When salt is added to distilled water, sodium and chloride ions produce what is called the ionic conductivity. The real permittivity of salt solution remains the same as that of water. The complex permittivity s of salt solution is therefore a = e' -js -j——- : (4.7) Ci is the ionic conductivity and is obtained from Fig. 4.4. We can rewrite E, to identify the total conductivity explicitly in equation (4.7) as follows = I i, n s s - w (aims ). (4.8) Total conductivity at is identified by the expression in parenthesis. ... H _ H ot - q1 + we - oi + wsoe.r. (4.9) The frequency dependence of E' and at can be determined from equations 42 90 _ 80 —-——-> Normality N l 1 I l 30 ; Jr l I I ' 0 0.5 1.0 - 1.5 2.0 2.5 3.0 Fig. 4.2. Static-dielectric-constant ES versus normality of saline solution. 13 12 11 43 772.5 at 0°C 7' at 40°C 5 - 1 ' J 1. I 0 0.5 1.0 1.5 2.0 2.5 3.0 ——* Normality N Fig. 4.3. Relaxation time parameter 1-(secs) versus normality of saline solution. 44 (SE (S/m) 20°C . ( For other temperatures use 2.1% rise per degree C ) —-—>% NaCl in H O 2 I 1 L I 1 ' 1 I l 1.0 2.0 3.0 4.0 5.0 6.0 Fig.4.4. Ionic conductivity of the saline solution 0: vs. percentage of NaCl in distilled water by wt. 45 (4.5) and (4.9). Whenever conductivity is referred to, it is understood that we are referring to total conductivity at of the medium. Care must be taken to enter proper parameter into the computer program when working with such mediums. As a final remark, graphs shown in Figs. 4.2, 4.3 and 4.4 have been obtained by the experimental data given by Saxton and Lane (12). CHAPTER V EXPERIMENTAL VERIFICATION OF THEORETICAL RESULTS 5.1 Introduction. In this chapter experimental evidence to support the theoretical development given in Chapters II and III is given. The first step in this connection is to choose a suitable laboratory model. A monopole antenna over an infinite conducting ground plane is undoubtedly the best choice since not only the terminal zone effects are reduced but also feeding transmission lines do not interfere with the measuring apparatus. It must be kept in mind that this model when transformed to some actual situation by frequency scaling, must represent a realis- tic case. The model can not be too small because of practical diffi- culties encountered, especially when making electric field measurements inside the body. The model is of plexiglass and has a 2.0 - 2.5 mm thick copper plate base so that once filled with salt solution and sealed, it can be moved from point to point on the conducting plane. Use of copper plate however restricts us to the use of lower frequen- cies since at very high frequencies the plate thickness will become a source of disturbance. On the other hand use of lower frequencies will require a large ground plane which will become impractical for laboratory work. All these factors are to be kept in mind when.making a choice 46 of frequency, size of container and the conductivity. There are essentially three aspects-to be verified experimentally. Firstly, we attempt to verify the perturbation in the input impedance of the antenna from the free—space value; secondly, we want to verify the current distribution inside the body; thirdly, we want to verify the in- duced electric field distribution. In each of the above experiments performance of the apparatus is tested by first doing experiments in free-space and later on with the body. The three aspects above have been discussed in seperate sections however the antenna-body system, unless specified, is the same for all experiments and is discussed next. 5.2 The Antenna—Body System The antenna—body system chosen for the experimental verification of theoretical analysis is given in Fig. 5.1. The dimensions of the container are to be kept as (12.5 x 6.25 x 1.5625) cms. The operating frequency has been chosen to be 600 MHz giving a free-space wavelength of 50 cms. A 0.5 N sodium cholride solution has been used throughout these experiments. Using the graphs of Chapter IV, the conductivity is obtained as 4.4 S/m and the dielectric constant (real) of 71.00 at a temperature of 20° C. If this model is assumed to be a scaled version of an actual problem, then a scale factor of d = 10 gives a situation at least of the same order as that given by a radiating antenna of 60 MHz. The actual height of an operator is usually 1.7 m and conductivity at 60 MHz is approximately 0.7 S/m, assuming it is a homogeneous system. By the above system we get a height of 1.25 m and, a conductivity of 0.44 S/m which are of the same order of magnitude. 48 .cowunaow ascendans woman P nonnano ecu :a wow: Amy Hopos Hmofiumnomnu wcfipnonmmnnoo , can Anv anumm amusoefinmnxm mo unoEmwnmunm Hmofinumaomo .~.m .wfim - L _ \ I} All 8.: H w «m Em is Nb . 411.3 1:1 um: 000...." w \ LO A 3mw> mam v VIPI . > flvfil p . - WV IVVVV. i N . \ . e— an mmnm.o u m N . conusnom au mmom.s u e \4 a: mafiamm : Eu m~.o n 3 A 2 me 5 8.3 n a . m ll ILPI . I i r: Eu mmom.~ _ : oN . ma mwpm Hku Hwofinno some _ X x Lr X anumm HmquEHnmnxm Anv Howe: II. Hmowuwnowsy va “ _ _ 49 The computer model for this system is obtained by using image theory. The situation is shown in Fig. 5.1 and has a 4-quadrant symmetry. It is necessary to maintain this kind of symmetry while the experiments are being performed. Also the upper right quadrant is divided into 16 cells, each cell being 1.5625 cm. cube. The antenna height "h" is divided into 10 segments plus the input segment, for h < Ao/4 and into 20 segments plus the input segment for h > 10/4. Even thougha higher number of cells and segments could have been chosen this would have become an uneconomical choice. The results of theory and experiment have shown that these values do provide a satisfactory convergence of the solution. In all experiments, with the exception of final\part of section 5.5, the body model described above has been used. 5.3 Input Impedance Measurements. In this section experimental techniques used for the measurement of input impedance of the antenna are first discussed. Following this, is a brief discussion regarding the free-space impedance measurement, and then the experiment with the body, is explained. 5.3.1 Experimental Setup, The apparatus comprise of a microwave Cbcillator, E-H probe guide, vector voltmeter and anechoic chamber. The roof of the chamber contains sheet aluminum plate while other sides are completely covered by microwave absorbers which prevent back scattering. The antenna is formed by extending the central conductor of the 50 0 characteristic impedance co-axial waveguide (WG), which terminates at the ground plane VECTOR VOLTMETER OSCILLATOR OSCILLATOR E-H probe Guide 7 V I_I ANTENNA Anechoic Chamber BODY -n-- -- A B VECTOR VOLTMETER (a) (b) Fig. 5.2. Experimental setup for measurement of the inPUt impedance of the antenna by using vector voltmeter. 51 of the chamber. The schematic diagram is depicted in Fig. 5.2 (a). Extension of the central conductor is made by making a threaded hole along the axis of the conductor where a copper rod can be screwed into, to form the linear mon0pole antenna over ground plane. The vector voltmeter in conjunction with the E-H probe guide gives an extremely efficient method of impedance measurement. This meter is a very sensitive device which can measure the voltages at two input ports labeled "A" and "B" and simultaneously measures the phase of the signal at B with respect to A. Details of the E—H probe guide are given elsewhere (13). The probe guide is inserted between the WC system feeding the load and becomes a part of the 50 0 wave guide system. We will call the location along the WG at which the E and H field probes are located as probe-section. Signal proportional to the voltage at probe-section appears at the terminal marked B. Signal proportional to the current appears on the terminal marked A. The ratio of these two signals, their phase and the "calibration factor" of the E-H probe guide will give the impedance at the probe-section. Calibration factor Riis a complex number. It is a constant at a given frequency and is determined experimentally. Effects of probes' geometries, their sensitivities, etc. are contained implicitly in this constant. The impedance at the probe-section is transformed to the load point by using transmission line theory. A brief description of determining an unknown load impedance is given in the following paragraph. 5.3.2 Method of Measurement of Load Impedance- 1. Impedance at probe-section (Zp): Assume that the calibration factor R'is known and the following measurements recorded on the vector 52 Voltmeter. Va = Voltage amplitude recorded at port A (volts) Vb = Voltage amplitude recorded at port B (volts) Ob = Phase angle of B with respect to A recorded on the phase meter (degrees). Let V£ = VB I32 9 V5 is a real number. The impedance at the probe- section is V 2 = (i)'f<‘ohms. (5.1) p Va 2. Impedance at load point (ZL): Assuming that the electrical length from the probe-section to the load is known equal to L cms then ZL = ZC(Zp-jzctankL)/(ZC-jZp tankL) ohms (5.2) where k = %g, A = wavelength in the guide (cms) and Zc = Characteristic Impedance = 50 ohms. In (5.2) knowledge of tan kL is sufficient and electrical length L need not be computed exclusively. 3. Steps to determine an unknown Load impedance: (i) First we check the amplitude and phase measurement capability of the Vector Voltmeter. For this see Fig. 5.2(blgBy this 53 arrangement the amplitude measured at A and B must be equal and the phase difference should be zero. (ii) Determination of R} The end of the E-H probe guide marked LOAD is terminated by a 50 0 load. E-H probe guide is thus matched. Va’ V and 0b are recorded. Assuming that a perfect match exists, the b impedance Zp should be 50 0. Hence letting Zp = 50 0 in (5.1) we get V E = 50 (i)|:_@_b_ (5.3) V b (iii) Determination of tan kL: The E—H probe guide is placed in the system and a perfect short is made at the load end. (In case of the antenna as load, a c0pper plate was screwed at the end of the feeding WC and care was taken to ensure a perfect contact between the inner and outer conductor). Va’ Vb and Ob are recorded. Then .—P (5.4) tan kL where'Zp is obtained from (5.1) and must come out as a purely imaginary number in this case. (iv) Any unknown impedance at the load end can now be determined by recording Va’ V and Ob, computing Zp from (5.1) andtfiufilfinding Z b L from (5.2). 5.3.3 Free-space Impedance Measurement. Before doing measurements in presence of the body, it was necessary to test the performance of the entire System at the operating frequency of 600 MHz. This was accomplished by comparing the theoretical and —-14 I f = 600 MHz 12 a = 0.3125 cm _— \ k = phase const 0 —— 10 theory Conductance ° 0 odata points (milli—mhos) exp. Fig. 5.3. Input conductance of the antenna as a function of koh, where h is the height of antenna. 55 __}0 f = 600 MHz a = 0.3125 cm ‘-8 ko= phase const “'6 theory _4 o o 0 data points """-'exp. Susceptance (milli-mhos) --2 0.5 1.0 —“— l N ’- -0..— I Fig. 5.4. Input susceptance of the.antenna as a function of koh , where h is the height of antenna. 56 experimental input impedances of the antenna. By virtue of this process the extent of errors, if any occured due to the use of a finite ground plane, could be determined. The program ZFREE discussed in Chapter VII was employed to determine the theoretical input impedances of antennas of various heights. The graphs of Fig. 5.3 and 5.4 were obtained. There was a good agreement between the theory and experiment over a wide range of the heights of the antennas. Our next step was to measure the input impedance in presence of the saline container. 5.3.4 Input Impedance in Presence of the Body, The container was placed in front of the antenna at various locations and corresponding input impedances of the antenna were det- ermined. Care was taken to ensure that the system under consideration maintains a four quadrant symmetry as required by the computer model. Perturbations in the input impedance are plotted as a function of the spacing between the antenna and the container. The observations were made ndth four antennas of different heights and the spacing was varied from 3 cms. to about 60 cms in each case. The comparison between the theoretical and experimental results is shown in Fig. 5.5 to 5.8. Fairly good agreement is obtained at spacings beyond 10 cms which is a fifth of the wavelength. In the immediate neighborhood theoretical values may not be very accurate since the field distribution in that region is quite complicated and a rapidly varying function of the spacing. In this region the order of magnitude and the trend in variations are in agreement. A short account on the possible sources of errors is given at the end of this chapter. It is emphasized at 57 wumamImmnw man I o mccwucm wsu :meuwn A vaCHomaw w:u wsmnm> mucmnmaefl uDQCH CH A mosmuommn mncmucm cu c IIIIPII\\J 11:], oo om ow mane ow.oawm I w~.nN mace oo.Nwmm I em.mi o I N mam weaansou Om map mncwucm msu mo wunmvmmefi manna a x conumnnsunwm Ans . ___————— nxmAONv fixes E O I am . N a a a xm + m n NUqumewh Nficwufiw Cu Anomsu mucfioa sump o o o .me IIIII a mucmpmaefi aw .Avon wnu paw N v:0flumnuaunmm m coaumnnsunmm Amv I: ml o wEu mN.ou A mN~.o um: ooo 58 o momnwlmmnm mzu ma N van wCAHnnoo cu was wcsmusm msu mo monopoasfl page“ H o a accounw mnu :mmBuwn A vacfiomnm was mnwnm> mocwpmnEH named as A xn + m n NV aoflumnusunom mUGmuUmwu mfidmuflm Guava GOHumAfihauHmm ADV :8- .4 3- I. ONI o .a New ’ ‘ me o . K 9.50 Nana + was» A No . 4 1:58 .3 o ., c a maze 52” + T; u AS I x ( mucmvoaefi as .ou I :«N new N a a .hpon osu can as a: mocmumfimon mscmucw ou am nonumnnaunmm Amv Anomnu nonfioa sump o o o .walllll .ool .oql -ONI o c was coo n w m . Dog! monmvmaefi mownmuwmnm o a“ o a“ a on» ma N van mafiansoo us» On map wcamucm wsu mo mocmpmmefi unnafi mzu n .N . N I N n N o a a a .Apoa 0:» new unsound msu monsoon A NV wcfiuwam onu mamnm> monmvmnefi usanfi 5H A Na + m u NV aoaumnuaunon .A.m .wflm a a mocwuowmu mucousm ou x coeumLHSuuom Anv mucmumfimmn wcsmucm cu m coaumnnsunmm Amv ..OOMI {cowl knows» _IIIIIIII mucfioa mum—o o o a ECONI .53.. 98 III... ..ooHI .NI 0 AEUVoN _ i.OONI Aaov N o u o OH ..ood .. CON " _ ..ooN _ -. cos __ . _ _ 1.00m _. _ 4 cos _ _ , exp 0 o _ 1. 23o 93% I oaom u A s r o .753 i an o . so mm.mau a mmm.o u n _ , me o . n I . n 1 _ 5 N mew. o Nun A NV com um: ooo u m C _. a . oom €53 x a mosmpmaafi mommwlwmnm o :H o cw a can ma N van wswaaaoo was on was mccwucm m:u mo mocmpmaefi some“ mnu u .N . N I N u N o a a a .zpon osu paw mccoucw mnu cmmsumn A NV wcfiomnm ans msmnm> mocmpmnsw upon“ as A Na + m u NV sowumnnauuma .A.m .me a a mocwuowwn mucousm on x coaumnnnuumm Anv mocmumfimmn msnmucm on m nowuwnnsunmm Amv IVOOMI JdOOI NAHOUSU IIIIIIIIIII mucfioa mummy o o I L.OONI .63. 98 III... \J .03.. o AEUVON _ I.OONI AEUV N o n o On .ooA .. ooN _ _ .joom _ -1 cos ” .oom _ 4 cos axo o ‘ meno m.~qMH I o.mom n A NV r o .ooq :u o 1 Eu mN.mHu A mwm.o u me o . n I . n i s N mQN. o Nun A NV ocw as: com I h oom 60 monoponaw o :w o a“ a momnmlmmnm man u N paw mafiaaaou ou map macwuam ecu mo mocmpmnefi unasfi mcu . u N N I N u N o a a a .Awon can mucousm can monsoon A vanfiomam mfiu mnmno> wonwpmnsfi unnca n« A xn + m u NV nowumnnaunma .m.m .wflm moswuommu manmusm ou ax coaumnnsunmm Aav monwumfimmn msnmunw on AM noaumnnnunmm Amv 1+ 03.. I.omNI 110ml r .8? _ o _ . _ 62.. _ I. on _ _ .OOHI _ 1. 0A: _ _ .oml Anomnu . I; own mucfiom mump o c o _. o .98.IIIII _ _ L com . .om .J.omN nxm o meso 0A.ommm I am.Amm n A NV r u o - o I maso AA.moqfi I mm.fi¢m u: A NV a oofi Eo om.NNn A mq¢.o n : Luoom :58 x was cos I a 3:3 m 61 this point that E-H probe guide in conjunctionwith Vector voltmeter has proven to be the most reliable apparatus for such measurements. 5.4 Measurement of Current Distribution. In this section we are to determine the theoretical and experi- mental current distributions on the antenna. Current distribution on the antenna is best determined by using a magnetic field probe (H-probe). The signal sent to the measurement device is preportional to the magnetic field on the surface of the antenna and therefore, to the current at that location. 5.4.1 Experimental Setup In this experiment the apparatus comprise of the microwave Oscillator, the vector voltmeter and a specially designed antenna which carries the H-probe. The setup is shown in Fig. 5.9 (a) and the waveguide, the antenna and the H-probe are shown in Fig. 5.9 (b). The antenna is made out of a hollow conductor with a slot running along the entire length of its surface. The rod can be moved back and forth to get different antenna heights. The probe moves in the slot and it is kept from touching the antenna conductor by a plastic spacer. This spacer also keeps the probe at a fixed level from the surface of the antenna which is extremely important. An unstable probe will cause errors. The H-probe is a very delicate device and care should be taken when moving it back and forth. The adjustable shorting ring, even though moveable between the inner and outer conductor of the guide, maintains perfect contact with these Conductors and insures a perfect short. This ring is used for tuning purposes. The probe signal is 62 to Vector Voltmeter VECTOR VOLTMETER A Bl !, attenuator OSCILLATOR —-> tuner Antenna . l Driving probe _ Input arrangement .qF_FJ Antenna Body ‘F_J Antenna ::> Anechoic chamber (a) (b) Fig. 5.9. Experimental setup for measurement of the current distribution along the antenna. 63 h = 12.5 cm = 0.25 A0 f = 600 MHz theory ' O 0 data points the antenna "" "' "' experiment 00 C: O H W C O .H 4.) N U O H 0 j \\ “‘ 0.5 1.0 II(X)I Fig. 5.10. Free—space current distribution on the antenna of height h = 0.25 A .'Theoretical and experimental values have been normaIized by their respective maximum values. 66 taken to the vector voltmeter at port—B and a reference signal after being attenuated, is applied to port A. The attenuator is a pre- cautionary measure. 5.4.2 Free-space Current Distribution. As in the previous experiments it was found essential to compare the theory and experiment regarding current distribution on the antenna. These measurements were made with three different lengths of the antenna. The theoretical distributions were determined from ZFREE. The results are shown in Fig. 5.10 to 5.12 and agree quite well. The values given in these figures are normalized values I(x)/Imax. \5.4.3 Current Distribution in Presence of Body. Our next step was to determine the current distribution on the antenna when the container is placed in its near—zone. The body was placed at a distance of 4.0 cms and the currents recorded for each of the three cases. The graphs for these are given in Fig. 5.13 to 5.15. The free—space current distribution has been redrawn to show the marked difference in the current distribution on the antenna in free-space and when a volume conductor is placed in its near-zone. The current values have been normalized with the maximum value of the corresponding free- space distribution. In this way even though the role of input impedance perturbation is emphasized, the curves are spread apart and easily discernable. The theoretical andexperimental results are in very good agreement. A brief discussion on the sources of errors that may have been encountered is given in the last section of this chapter. 67 .+__. .———y h = 12 5 cm I 2o ! Ks “‘ \ O \ \ h \ \ \o \\\ \\ \\ \\ \\\ \3. \ \ \ ‘\ \. \ h = 0.25 x0 ‘\ \ f = 600 MHz \V \. z = 4.0cm m \ a c o 4.) a m .2 Free-space X: 44 no a o H w n o .H 4.) m U o H theory a o a data points — - - — experiment 1 \X\\ I O 0.5 I I I Fig. 5.13. Current distribution on the antenna in presence of a biological body. Theoretical and experimental values have been normalized by their respective free-space maximum values. 70 5.5 Measurement of Induced Electric Fields Inside the Body, In this part of the experiment we attempt to verify the induced electric field distribution inside the biological model. A few changes have to be incorporated in the container before it can be used for this experiment. Firstly salt solution is replaced by a synthetic thick jelly like substance called phantom matter. This is prepared by mixing the synthetic powder of a specified prOportion into the saline solution. Next.two slots are cut on one face of the container so that the fields at the central location of each cell (Ref. Fig.‘5.1) can be probed. Antenna of height h = Ao/4 has been used throughout this experiment. 5.5.1 Experimental Setup. The schematic diagram of the experimental setup is shown in Fig. 5.l6(a). Details of the basic construction of the probe has been discussed in (17) and are not included here. The basic requirements for such a probe include: 1. relatively small size; 2. sufficient sensitivity; 3. polarization independence; 4. minimum interference due to the lead lines and; 5. no direct contact with the biological substance. The polarization problem is not of a major concern since the horizontal components (y,z) of the induced electric fields are anticipated to be small as compared to the vertical (x) component.In- terference from the lead lines has been minimized as an improvement over the design of (9). This has been accomplished by inserting six resistor symmetrically and in series with the probe. The probe designed in this manner is found to havea high signal to noise ratio-,- and as evident in the following experiments, its performance at 600 MHz carrier frequency has been extremely satisfactory. The probe is shown in 71 on» spawns pawww owuuomac mo unmamunmmme was now naumw kuamEanmnxm moons enmnmum noumwmmn Anv nofimmflamcmuu .seon Hmoawoaoas Amv nonsmno owocomn< m 3 w > .on.m .wnm MOH a I- .1 II J. o In I- 6 7 o -I L- o .I. I. . L o u- L- .. co me n W oq 0N 0H b So m.N~ u 5 o o o mucfioa pump as m.q "on .38.: was 86 u w 77 and the computer model of 32 cells in first quadrant was realized. Height of antenna, operating frequenCy and conductivity of the model were kept the same as before. Results obtained were not in total agreement. The reasons given in the next section, have ascertained that the model chosen in this case was not a reliable experimental choice. The results are given in Fig. 5.20, and are presented merely to emphasize the major drawback in choosing a body of smaller dimensions. 5.6 Sources of errors. 5.6.1 Errors in Impedance Measurements. As evident from the theoretical and experimental results of Fig. 5.3 and 5.4, experimental errors are practically non-existing. There are three basic errors that may be encountered during such measurements. These are the terminal zone capacitance effect, the effect of dielectric support and the effect due to finite ground plane. From the tables given in (14) for co-axial waveguide and for b/a = 2.3, where b is the radius of the outer conductor and a is the radius of the inner conductor, we get terminal zone capacitance of 0.048 pico-farad. The:susceptance due to this capacitance will be 0.180 milli4MHxs at 600 MHz, which is negligible. Effects of the other two types are minimal. 5.6.2 Errors in Measurement of Current Distribution. The major source of error is the unstability of the H—probe during its movement inside the antenna rod. A perfect H—probe must extend out equally at all positions along the length of the antenna. This will provide a constant multiplier for the probe due to its gemoetrical shape 78 and thus the induced voltage will be proportional to the current distribution on the antenna and independent of the location along its length. Extreme care was taken to meet this requirement and the results of Section 5.4 show that the H—probe has worked satisfactorily. 5.6.3 Errors in Electric Fields Measurement Inside the Body. Electric field probe has been designed to meet the requirements as mentioned in the beginning of Section 5.5. However the major source of error is not in the design of the probe but it is dependent upon the location of the probe. A detailed analysis of this problem has been carried out by Smith (15). A summary of the results are given below. (i) The error in response is decreased if the load admittance is very small compared to the input admittance of the probe. (ii) An increase in the attenuation constant of the medium surr- ounding the probe will increase the error when probe is near the surface. (iii) The error is further reduced by the use of insulated probe such that the permittivity of the medium Em and that of the insulation 61 satisfy the condition Gin/6].. >> 1. (iv) The error is reduced by the use of probe with short receiving conductors. In the experiment all requirements except the one in (ii) above have been met by the design of Fig. 5.16 (b). In this way the main sources of errors are the noise collected by the transmission line connecting the probe to the measurement apparatus and the nearness of the interface from the probe. The later may have been a dominant error 79 in case of the 32 cell model of Fig. 5.20 where the size of each cell was (l‘x l x 1) cm. During the experiment the transmission line from the probe was surrounded by microwave absorbers and thus the conductors of the lines were shielded from the electromagnetic fields in the surrounding space. CHAPTER’VI THEORETICAL STUDY OF VARIOUS MODELS OF ANTENNA’BODY SYSTEM 6.1 Introduction This chapter is devoted to theoretical studies based on the results obtained from the computer program. In Chapter V, theoretical results have been verified by the experiments and a high degree of confidence in the accuracy of this method has been established. The container model chosen in the previous chapter is merely a model for laboratory work and as such does not resemble a realistic situation. In this chapter we have formulated computer models of situations involving biological bodies of the size of a human adult and studied the various electro- magnetic effects due to the coupling phenomena. The study is broken into three main categories each has a signifi- cance of its own. Work has been done with operating frequencies that are being used by various transmitter sets that have their operator in the near-zone of the radiating antenna. Situations given in the follow- ing study are not an exact representation of the true ones encountered by the operators, but their practical significance can not be over- looked.' The results of this study conclude that radiation from the antenna is a potential radiation hazard especially when high power transmitters are used for communication. Effects of the presence of a biOlogical body in the near-zone of the antenna upon the radiation pattern are given in this chapter. Furthermore, the effects on field 80 81 .cmaanoo ma uw guess Cu mccmucm wcfiuwfipmu ecu new Hmon Anon swan: wsu mo unmEmwnmnnm HwownumEomo A.o .me i, I_ 2T \r . A some :6 n \ 3 I I VG . 8.8 9.0 \ E... see -b . \ > ti, 2: -6} ~39: E IN) \A a . um: ow n m V\ . \ oN \ \ \ . £ \ .\ \ t \ . 3 Aon.o%.oxv.un mocmnwwmn VA 82 distribution inside the body of an operator and the power absorbed when he is in direct contact with the ground are compared to the case when he is isolated from the ground. 6.2 Antenna-Body System Operating At 80 MHz. This system is shown in Fig. 6.1. The shape of the body has the basic look of a human adult. Permittivity and conductivity of this model are assumed uniform within the entire volume. This system rea- lizes a situation of an isolated system with a radiating dipole antenna and a biological body in its near—zone. The system has a symmetry about the vertical plane passing through the axis of the body and this reduces the number of unknowns of this system. The number of cells chosen to model the adult frame is 56. Using the symmetry of the problem the effective number of cells is only 28 i.e. electric fields in only the right half of the body need to be determined ( see Chapter VII). For economical reasons, a trade off has to be made between the shape of the body and the number of cells. Since in this case the program has to be utilized many times we have found it satisfactory to choose the model of Fig. 6.1, even though its weight is not realistic. The dielectric constant (real) at 80 MHz is taken as 80.00 and the conductivity at the same frequency, as 0.84 S/m. The current distri- bution on the antenna can not be assumed symmetric in general, however, as proven in the following paragraph, it is nearly so for antennas of height h s Ao/4. The first case is an antenna of height 0.125 10. The current distribution on the antenna and the electric fields induced in the body are given in Fig. 6.2 (b) and 6.3 (a) respectively. These 83 .A.© .wfim :H pmfiwfiuwam mum mnmuwamnmn new meowmcmawp .Anumaoou .mmwwuao> wanna Havauampw An cm>finp ma manoucm mumss momnmtmmnw cw umnu ou ponmafioo Anon mo mocmmmna aw mssmunm no unmanao o Ewoo.o u A o o EUONuN Eu o.ou.A o 0 Eu cm H x A mNA.o u L Aav _H_pwmfiHmENo: ax muA // .A uommmm Avon oomnmlomnm sl- euuenue sq: BuoIe uorqeoot 0 So can N .N.6 .mne O 0 So «m. x A mN.o . e Ame 5' 1 \ \\ \\ \. \ \\ \. \. \ .\ .\ \. \_ \ \_ \ \ \ \ .H_pomwam5no: \ _ m.n t o.a_ m.o A i w A A / / / x / / // // uowmmo Avon \ // l/ // // momnmImmnm I’ll euuaque sun SuoIe uorneoot .Emumkm msu mo musmumnoo umnuo Now A.0.wwm ou momma .Hm>mH xom: um >000 can on mmoau hum> pooman ma unsound can mess 05¢ 0.A mo ucmunsu wanna an %n Hmpoa Avon amen: ca pmonpca AE\>V pamfim_m_ .m.0 .wfim Al. 84 nohmA xomn nmzma unonN nmmma xomn umhma uconm wow. 24 m3. N3. NN.N oo.N . . Eu 0N uoN NNN Neg Am.A 50 0.0 no» oN.m so am -ox mmN. mam. . NNe. no N Nm.s New. mN.N m6.N om.m NN.e moo. Nam. NN.N wo.n No.N mm.m Nm.m 6m.s cam. An N mi.N ma.i an N 66 m Nm.m 6m.s NN.N mN.N 6m.N NN.N aw N on N 6s.m sw.e No.N ow.N se.n Ni.m . . . Nm.m we N NN s iN N as: om I N um: em I o . I o nNN. u e . 6N.N A mN o I Ne.m Nm.s A NN m Any A60 85 electric field values are based on 1 amp-current input and the center of the antenna is located at neck-level‘(xo=34 cm) spaced at 20 cms from the body. Next the current distribution and the electric fields are specified for h = 0.25 10 in Figs. 6.2(a) and 6.3(b) respectively. Even though non—symmetric current on the antenna has been anticipated, these results have shown that to a first approximation, current may be assumed symmetric. This information supports the assumption made by Nyquist et. al.(5) who assumed a known current distribution for ellectrically short dipoles or monopoles for such a case. An interesting observation was made by using h = 0.382 X0 which is close to the anti-resonant length. The antenna was centered at t0p of the head (xo =0.cm) at a spacing of 20 cms in between the two. Other parameters were kept the same as in previous cases. The current distri- bution for this case was non-symmetric. This evidence is illustrated in Fig. 6.4. Other results of this study are given in Fig. 6.5 and the Tables 6.1, 6.2 and 6.3. The far-zone radiation fields in the H-plane are quite different from the free—space case. Moreover these curves are dependent on the level along the vertical axis. The radiation fields are greatly perturbed from their free-space distribution when the antenna is placed around the center of the body. Table 6.1 shows the effects of placing the body at various locations along the horizontal axis. The ratio of the power dissipated to the power input (Pd/Pin) goes on reducing as we move the body away from the antenna. Table 6.2 gives an interesting piece of information. The ratio Pd/Pin changes as the body is moved vertically. The maximum is attained when the antenna is positioned at the neck level. This effect does not seem to 86 f = 80 MHz h = 0.382 Ace anti—resonant height x = 0.0 cm 0 yo= 0.0 cm 2 = 20 cm 0 front layer back layer 6.48 2.67 _____n .______ 10.2 2.95 10.6 8.26 5.08 4.19 10.7 12.9 7.52 5.09 12.0 13.3 8.70 5.14 13.6 8.93 8.70 5.14 13.5 ,+_ 7.76 I EIin V/m 11.1 6.04 7.7 4.03 4.44 2.35 .____4. (a)l§ Ifield induced in human body by an input current of 1.0 Amp when placed near an antenna. free-space 0,2 0.4 /’ normalisedll body effect (b) Current distribution on antenna in presence of body and in free space when h is near anti-reso -nant length. Fig. 6.4. Induced body field and antenna current for antenna of near anti-resonant length in proximity to human body (geometry, dimensions and parameters are specified in in Fig. 6.1). 87 .A H.0 .wam =« no 05mm mum Qumumemnwn paw chchmEHv .huumEomw v waonfiv mnu mo caudal: CH A0005 Anon amen; any on voanpoo unsound maonap An wmcwmosawa unwound pamwm sowumfipmm .m.0 .me 000 Doc 0 00m _ — _ _ _ _ A000 u 90 mamAaI: =H_nm_mo mmaam> _ _ _ _ _ _ o00H o>fiumAmu usmmonnwn omenno moose To 0o 0 o E m0.0 u x . A mNA.0 u c u 0 o o I oi a:.o-ux.AmN.ouenm 00m n.01 o o .o E AA.0I u x A mNA.0 u a n < < COO oONA m com 88 a 0 :a o . . N + N u N was monmwoaefl unsound mommmlmmum u N .uommmm mufiEAxonm Ou 0:0 consumasfi mnnmuam ou noaumnnau Inmau No resound mo moampmaefi uansfi nsHN .AA.0 .wfim ca pmfimaumnm mnmumamuma pan w60HmamEHp Anumaommv N mogumooa onnfip com: mnmzon pmumfipmn 0cm pmumawmmav new wmonmpmmsfi mo moampsmmmo .A.0 mgmwa 30m: NNo. wNo. fiwq.m mo~.o me.m m.omqh I wm.w~ NN.qfi + aw.0I o.o Hm>wH \ vmm: 0N0. NNo. owm.w cm~.0 Nm.w N.Nm¢n I cc.m~ NM.Mm + mq.~ o.NHI vmm: m>onm a« v u w u v a a a o m\ m m\ m 2.3 m :3 m a3v Hm Ann—50v HN Amy—50v N AEUV N .UOA o o a o ENTNI K .8 o.OI\fl . 95 o; INN ‘mNNéI; o o 2: I I} :6 o.oN I N No.13.n I 2.3 I N Na: cm I N . mccwuam m u o moan mafia usa: mfi CHN vam uumwmw mufiE«xoua hcon ou mac aoaumauauuma "AN A a N u a m cN O 90 .wocmwmaafio momamlmmum n N v N + N u N .A fi.c .wam ca cmfimaomam mumumEmuma van maowwamafiv .muumEomwv x coaumooa maoafiw con: muoaoa vmumfivmu cam vmumafimmac cam wocmvwmafi mo mucmvcmamn .m.o mqmmH mqo. Hmo. cm.m~ om.~ «c.0N em.mNn + mm.mm oo.cw I ac.NMI o.onm u u a :«m\vm m\vm ABV m .A3vwm szcwn Amazovch Awesov N Aacvox .muoq o c o E mm.m n K mE< o.~ n HH Eu 0.0 u % mm: ow n m o oofi I m\: N.Nmfl + em.mw I N Eu o.oN IoN 0‘ mN.o I a 91 exist for the quarter-wave dipole whose results are tabulated in Table 6.3. 6.3 Antenna—Body System Operating at 27 MHz. This system is fairly simple in its appearance and does not quite resemble a human frame. However its size and its weight (68 kg) are those of an average adult. This model was used to compare the power dissipated inside the body exposed to the radiation from a CB radio antenna or a similar device, to the power dissipated when exposed to lOmW/cm2 plane wave radiation. The body model is shown in Fig. 6.6. It consists of 68 cells, however fields are to be determined in the cells forming the right half of the model. The antenna is of height h = 0.25 A0. The height of the human body model is 170 cm, and uniform permittivity and conductivity has been assumed inside the body. Fig. 6.6 defines an isolated system with symmetry about the vertical plane, as in the model of section 6.2. Other relevant data are given in the figure. Fig. 6.7 depicts the case of this body being illuminated by radiation from a monopole antenna above infinite ground plane. In Fig. 6.8 the same body has been illuminated by 10 mW/cm2 plane wave, the maximum .value set by the Radiation Safety Standards. In the first case the total power dissipated inside the body, when the antenna is fed by 1 watt , is 6.44 mW. In the second case the power dissipated is 0.084 W, more than ten times increase over the previous case. In both cases spacing between the antenna and the body has been kept as 20 cms. In the third case with 10 mW/cm2 indident wave intensity, the power dissipated is 11.14 watts. Comparing it with the grounded system, antenna input power of about 140 watts will dissipate the same amount of 10 le- cmgé \. Power absorbed in -—*\- the body = 6.44 W \I .25 l .20 I~ 02 ' 01 \ ' I' \4 .35 I .26 \\ .04 [.02 \~| .50 {.35 T\ T. —.02 ~.| .57 .42 )L—h ]~ .10 l°°5 I ~.J\ .65 |.48 2a -—5 :.: l \ .13 [.07 \L .73 [.54 |~\:.16 [.08 \-l ..79 '.58 T\ .19 1.10 x, .84 .61 ~ 1~ .22 {.11 20--———a4 ‘ cm \‘L .85 I.62 N, .23 1.12' l I Y \4. .84 .61 l \..22 !.11 \‘L .79 i.58 |\\ .19 l.10 .1 .73 1.5 \ __ _. ‘L\\ .1 [.08 \’ 3 +. 1‘ .65 1.48: [E] in V/m --top number | \‘ 13 {-07 SAR 1 W/ 3 -b cc h \‘K *‘57 |‘---"42 n m 0 om num er '\ .10 I .05 \L .50] .35, l\ .04 ! .02 ‘~1\ .35 ..26 J I .04 1.02. .25 [.20 . 2 1'01 Fig 6.6. 1.7 m _L f - 27 MHz h - 2.77 m =1 o/4 CT- 0.62 S/m Er" 113.00 h/a - 100 P - 1.0 W in Zin - 77.12 + le ohms Distribution of induced elictric fields and the power density( SAR ) at the central location of each cell of the body for an isolated antenna-body system. Antenna is driven by an input power of 1 W. Power absorbed in the body = 6.44 mW 2a [El in V/m --top number SAR in W/m3 -bottom number Fig 6.6. ‘D -h 92 10 r.— CID—A \ --k— \ \I .25 g .20 ‘I\ .02 ..01 ‘4 .35 l .26 \ 04 L.02 \' .50|.35 Tx 041402 \I 15.113512. T .10'.05 \ .65!.48 +\ .13 [.07 ‘\4~ .73 [.54 '\:.16 [.08 \l ..79 L58 ‘T-ii9 1.10 \ .84 .61 20 _.:\ .22 :.11 cm \* .85 I.62 l‘ .23 I.12 Y \t .84 '.61 \ .22 [.11 l I \* .79 [.58 l\ .19 ,.10 ~ .73 1.5 \ .._._ __ 'L\ .1 l.08 \' i ‘k Ail-if! I \ 13 5.07 \1. .57.in2 1\ .10,.05 ‘1 2.511112 l\ .04 ! .02 \L .35 I .26 I I .04..02. .25i.20 . 21.01 T 1.7 m _L f - 27 MHz 11 - 2.77 m -1 0/4 (T- 0.62 S/m er- 113.00 h/a - 100 P - 1.0 W in Zin - 77.12 +j10 ohms Distribution of induced elictric fields and the power density( SAR ) at the central location of each cell of the body for an isolated antenna-body system. Antenna is driven by an input power of 1 W. W ..---- « .._..._- ».-. um: 4--.... - -..__-._..______.__._m_-- , _ . 93 :1; “T" I 1 ( I Power absorbed in the body = 0.084 W E? b r 0 °‘/ -#—mL—+-7;~QWL a} 1| 7 O f g 27 MHZ 2.77 m ' 40/4 C" 0.62 S/m 113.00 100 P 8 1.0 W 55+fl8mm fip—l / O O m H F” 0‘ 0‘ D‘ I I O 7 6775 Nook- + |E|in V/m --top number ./ ..a N ‘1—4 O :3‘ \ {D II / O u: SAR in W/m3-bottom number Db OH MN N g P' :3 U l / / oxen / 0000 X l .71 - h NHl—‘OH CPD 4. “I l H NO O -— n—c-I—c-d—cn—I—n— 'N . / 2a 1.7 m NH (.045 l N H' 4‘ 0‘ —-/— .— x v v / tor—IN I—‘O—‘I OH OHOH O. .0 O. O. O O 1'" NO I—‘\D \O\l CD O‘b Nb NH |Ehm -I Ivy—- / / N N \l O J: E.» Cal / L» .l / NHN I—- bmb O\ / \Ob -#-¢—+—+—k— \ \0 L” N H 0 U1 \0 \ \ 20 cm L \_ \ \ \\ \\\\\ \ \\ \ \\\\\\ N NINNN N _—q~—_—r-.-—-dd—- MN N \lO 0‘ MN H OUI \O \C\‘\\\\C\)\\§\ Fig. 6.7. Distribution of induced electric fields and the power ‘ 'density( SAR ) at the central location of each cell of the body for an antenna-body system over infinite ground plane. Antenna is driven by an input power of 1 W. 94 2 . power in the body as will a plane wave of 10 mW/cm . By this study we are able to conclude that unrestricted use of high power transmitter may prove hazardous. A similar result is derived in the next section where a more realistic situation is presented. 6.3.1 Test of Numerical Ability of Our Program. A test was made at this stage to determine the computational ability of the program FIELDS given in Chapter VII. The body under study is placed at a distance of 100 meters from the antenna which is nearly ten times the wavelength. This case is the same as the isolated system of Fig. 6.6 except for the spacing between antenna and the body. We have thus created a situation in which antenna and the body, to a first approximation, can be considered uncoupled. The body can there- fore be considered as being irradiated by a far-zone EM field of the antenna with known current distribtuion (free-space). Far-zone electric fields from an antenna of height h = 0.25 10 are given by jn I <0) ——ng:—— exp(-jkor) F(e) (6.1) CDH where F(0) = cos (g-cos 6)/sin 0 and 6 is the inclination from the vertical. In the region of space formed by the body; and by the manner in which the antenna and body are located; electric field can be con- sidered of constant amplitude, transverse and vertically polarized in 0 = 900 plane. Also 274.6 V/m are produced by a current of 457.67 amps. using equation (6.1) for 6 = 900. Therefore, the power dissipated in the body spaced 100 m from the antenna when the antenna is driven by 457.67 amps.of current, must be approximately equal to 11.14 watts 95 _\_x<.. Power absorbed in l 10 9 8 the body = 11.14 W \\b. 31. 30 f = 27 MHz \ I 15. 15. := 0.62 S/m 4. 73. 68. = 113.00 I\ r \\k 19. 18 \ 116 107 \l ,23- 22. I. 159 144 -» \’ 25_~ .232 I Eil = 274.6 V/m I‘\ 198 178 \ 27. 26. TN 229 205 \L 29. 27 l \ 3 226 = 2 \ 29. 28. Pin 10 mW/Cm L 268 238 I \ 1.7 In \I\ 30. 28 l \ 273 .242 \k 29. 28. _> I \ 268 238 [Elin V/m ---top number \\L 29. 27. SAR in W/m3-—bottom number |\-253 226 \ 27. 26. 1‘\ 229 205 \l 25. 24. I\ 198 178 \l 23. 22. I“ 159 144 \L 19. 18. I\"1m 107 \k 15 15. l \,73. 68. 10. 9.8 31. 3 . I Fig. 6.8. Distribution of the induced electric fields and SAR at the central location of each cell of the body irradiated 2 by a plane EM wave of 27 MHz frequency and intensity IOmW/cm. 96 Total absorbed power \ in the body = 0.049 W \ \ . ~ 1 0.2m \ 2a \ 0.2 HIF__ I “L \ "‘“ + . I I \ IEIJLn W111 \l 395 I 194 h= 2.77m ‘ IN ___I____ I \l .593I .289 7 I T\ --—l——— I \l .789: .367 I T\ - I I -—l'-_- I \I .963I .431 I I l\'--hnu. L6m | \l 1.11II .478 I I *\_-- I ""- l N l 1 23: .515 I IN ______ l I l I NI 1.31l .541 1 I I\ -—_l'——— I 1.35 .554 III(O)I \L I I ground f=27MHz o‘= 0.62 S/m Input power P15 1.0 w EI.= 113.00 Input impedance = 32.0 + j6.6 ohms h/a = 100 Fig. 6.9. Distribution of the induced electric fields inside a cylindrical model of man in direct contact with the ground and located in the immediate vicinity of a grounded quarter- wave monopole antenna. 97 Total absorbed power in the body = 0.005 W 0.2 m I 0.2 I m; 2a"" __.:N<_.- -> . I ‘1‘ "'17 1 IElin V/m N I 213 I 157 ‘IN __ I___I I l \.l 272 I .136 I F\_--I ....... = I h 2'77 m I N\l 340 l 169 I\\I—_-._ - _- ‘ I l' ‘ \I 377 I .198 16 m I I\_.._l ___ ‘ I .385 I .210 l ‘\L l I l\--—l--~ I \1 .357 I .197 I I‘\-__;|.__ ‘ \l .292 ' .167 | \N\I I | I ""1"“3 I insulator ;. '189 I '013 I .I.. t: I .I | :3" '8.0: I .II(0)I -..I.:.. I ground f = 27 M32 O'= 0.62 S/m Input power Pin: 1.0 w 6": 113.00 1 for body input impedance= 41.2 + j13.8 ohms CT‘ 0.0 S/m h/a = 100 E = 3.0 for insulator r Fig. 6.10. Distribution of the induced electric fields inside a cylindrical model of man insulated from the ground and located in the immediate vicinity of a grounded quarter—wave monopole antenna. 98 dissipation caused by plane wave of 10 m'W/cm2 intensity. Program FIELDS is used to determine the former while the latter has been determined by using Guru's program (9). The program FIELUSgave 0.55632 x 10.4 W with l amp.input current. 457.67 amps.input current will therfore dissipate (457.67)2 x 0.55632 x 10-4 = 11.65 W in the body. This value is also close to the 12 watts predicted by Massoudi et.al. (18) for a body of similar dimensions. Effects of isolation from ground are shown by using a different model and working with the same frequency. This situation is shown in Fig. 6.9 and Fig. 6.10. The dissipated power in the body, when it is in direct contact with,ground, is nearly ten times higher than the case when it is isolated from the ground by an insulator. By this evidence an operator of a transmitter should feel much safer when he is wearing shoes that are preventing him from a direct contact with the ground. 6.1I Antenna-Body System With Operating Frequency of 90 MHz. The human body model chosen in this case is the best representation so far of the true situation. The height of the model is 1.7 m and the weight is l793b6g An antenna ofheight h = 0.25 10 has been used for this study. The effective number of cells are the cells in which induced electric fields have to be determined from the use of computer program. In this way there are 47 cells, and unlike the previous cases, all of them are not of the same size. The objective here is to study the induced electric fields inside the body, the power density and the total dissipated power at 90 MHz. The conductivity is 0.85 S/m and the dielectric constant is 75.00 at 90 MHz. The coupling problem based on quarter—wave monopole over infinite ground plane is formulated and the 99 Front layer ' Back layer .22 .15 .30 .22 "'JZIL..86 "]::L__...85 -" .89 "'2 .89 .43 .22 .22 .26 .21 .53 .30 .30 .43 .34 .55 .34 .46 .59 .43 .55 .40 L21; -72 -57 .53 4 74 .53 .49 ""‘ -8 - .49 ““"1' 1 1 0 .1 1.0 . - 1.7 m 1 -38 .08 m 'L“”‘T' I 3.8 I 5.5 I 7.0 "'"""" + 8.3 IEI in V/m I 9.5 __i_ I 10- 0.1 m fi- 11. ' I“ 11. V /QC/70//0//OC/ Fig. 6.11. f = 90 MHz A = 3.33 m o h = A/4 o G-= 0.85 S/m €i= 76.00 r zin415.83 + j9.720 ohms Distribution of the induced electric fields inside the realistic model of a man located in the immediate vicinity of a grounded quarterdwave monopole antenna. Values are based on input power of 1.0 W and the dipole and the antenna. spacing of 20 cm between 100 Front layer ' Back layer Ir_x____. --1 .02 .01 .04 .02 ‘ ' 0.32 ::3::L-v'°-31 0.34 - 0.34 .08 .02 .02 .03 .02 .12 .04 .04 .08 .05 f = 90 MHz .13 ~05 ;33. .15 .08 A = 3.33 m .11 0 x .13 .07 -"' .22 .14 h = o/4 :13. O'= 0.85 S/m .12 .10 .30 .23 .10 I 6?: 76.00 .50 .42 .06 .08 m .51 .45 Zin= 15 33 + 39-72 ohms 1.7 m . . L__.__I_. I . 6.0 I I____. Is. I l -—-—-' 21. ___—I . Total power absorbed I 29' in the body = 0.5216 W _____, SAR in W/m3 38. ___—I—L ' 45 0.1 m I 51. I I IflI II J 53. /QC/70(/0//OC/ Fig. 6.12. Distribution of the dissipated power density( SAR ) inside the realistic model of man located in the immediate vicinity of a grounded quarter-wave monopole antenna. Values are based on input power of 1.0 W and spacing'of 20 cm between the dipole and antennae 101 results are given in Fig. 6.11 and 6.12. The spacing between the antenna and the body has been kept at 20 cms. Absorbed power is now 0.5216Iaatts. Exposure to IOmW/cm2 plane wave dissipate 14.2 watts in the body, thus, the input power to the antenna must be kept below 30 Watts for safe Operation. 6.5 Problem of Arbitrarily ShapedrThin-wire Antennas. A brief outline is given to explain the problem of antenna-body system of Fig. 2.1. In this case equation (2.18) remains the same. However equation (2.19) which is written exclusively for linear antenna directed along the X-axis, is now written in its generalized form 6 . 133(3) +6 . 1313(3) = -Vod(s) Integrals for Ea and Eb are given in equations (2.16) and (2.17) respectively. In principle , a numerical solution to this problem using pulse function expansion and point matching is possible. However difficulties may arise in modeling an approximate delta function and coping with the size of the resultant matrix; since in this case the currents on the antenna are not uni-directional. Feasibility of this method is questionable. This problem does have considerable practical significance and a wider range of problems could be handled once this problem is solved. CHAPTER VII A USER'S GUIDE TO COMPUTER PROGRAM 7.1 Introduction. This chapter explains the computer program "FIELDS” that provides a numerical solution to the coupled—integral-equations given in equations (2.24) and (2.25) of Chapter II. A major part of this chapter has been devoted to explain in detail, the formulation of a given problem. In this formulation, the antenna-body system as given by the existing situtation of the problem is reduced to a theoretical computer model; this can later be used on the computer to quantify the electric fields in the body and the current distribution on the antenna. In addition to the listing of the program, an example has been worked out to help the user understand the sequential order of data files and the results on printout. A listing of the program "ZFREE", which determines the free-space current distribution and the input impedance of an antenna has also been provided. The listing of FIELDS is valid for the problem given in the example and therefore a brief description of the alteration for implementation of other problems is also given. 7.2 Formulation Of The Problem. This program finds its true application to problems dealing with linear antennas. More specifically, problems involving interaction of 102 103 a center-fed,linear dipole antenna with some simple biological systems can be solved successfully. By using image method in EM theory the problems involving base-fed monopole antennas over a conducting plane of infinite extent can also be solved. The very first step in the numerical formulation of the problem is to visualize a theoretical model of the system which accurately represents the actual physical problem that needs to be solved. This model is obtained as follows. The body is carefully divided into (imaginary) cubic cells not necessarily of the same size. The size of the cells should be sufficiently small. One approximation requires that the edge of the largest cube should not exceed(l/10?uwhere A is the wavelength of the radiation inside the body. However, in many cases this requirement can be relaxed. The coordinate system is ' chosen such that the origin is the feed-point of the antenna and the x-axis lies along the antenna axis. Finally the antenna is assumed to be partitioned into an appropriate number of equal segments. Problems involving monopole antenna over ground plane are first transformed into equivalent dipole arrangement using method of images. See Fig. 7.1. The maximum size of the coefficient matrix the program can handle is limited by the capacity of the computer system. This restriction imposes an upper limit on the number of cells in the body and the number of partitions on the antenna. This also means that the size of body will have to be smaller as frequency gets larger. "Symmetry of 104 “_A.M_A- - Computer model .\\\‘ \\\\\ \§\\\ .\\\\ \ . \ X X 11 ‘I Given problem h -—' 11 Computer model I biological body I h I I .‘I _.__. .___, F? input segment . 1:; I antenna I III (a) Dipole System X X Given problem h I 5 biological -- 4 h body ‘— 3 . 2 /\ _ , ’ 4--/-—\—\—\\\ \\\\\\\\\\\\\\\\\ mp“ - 1 segment 5 ground \ x t I :> t t N a (b) Monopole system Fig. 7.1. Transformation of the physical system of an antenna and a biological body into a computer model for program FIELDS. 105 the system" will help us cope with this problem to a great degree. A system will have a "2-quadrant vertical plane symmetry" (Z-QUAD VPS) if in the model, a plane passing through the x-axis divides the body in halves one being the mirror image of the other. Again a system will have a "2—quadrant horizontal plane symmetry" (2-QUAD HPS) if the y-z plane divides the body in similar way as above. A system with both types of symmetry existing is said to have a ”4—quadrant symmetry" (4-QUAD SYM). Figs. 7.2 and 7.3 demonstrate these definitions more clearly. In case of 2-QUAD VFS the field in cells forming the right half of the body need to be determined; in case of 2-QUAD HPS the fields in cells forming the upper half of the body need only to be determined; and in case of A—QUAD SYM fields in cells forming the upper right quadrant need to be determined. Furthermore in case of 4-QUAD SYM or Z-QUAD'HPS the current distribution is symmetric and hence currents in the segments forming the upper half of the antenna and the input— segment of the antenna need only to be determined. Once the unknowns have been found, the fields in other cells (shaded in Fig. 7.2/3) can be obtained by the field relationships as given in those figures. The order in which the antenna segments are numbered is extremely important i.e. segments are numbered starting from bottom most segment in which current is to be determined, and ending at the top segment. )b/AO is a suitable upper limit on the length of a segment, A0 being the free-space wavelength. Referring to Fig. 7.2/3 the fields/(currents) in unshaded input segment input segment Fig 7.2. EI 106 K/ \ 7 "'1'" I _ 6 Nb’ 5 4...... ' 5 4 Y 3 (a) 2-QUAD VPS 2 t_L k) 1 41» E m 4 V W4 ‘— 3 §g§g a Nb= 4 Q: A at E' 1 Y .,<. [EI- Illustration of (a) two quadrant vertical plane symmetry (b) 2-QUAD HPS NF] -54.. [71 -‘< (Z-QUAD VPS) and (b) two quadrant horizontal plane symmetry (2-QUAD HPS). 107 g 7- input segment v 19’ Fig. 7.3. I 1 «————699fi%6%4/ Illustration of EII 4-QUAD EI SYM E' = -E E" = E EIII = _E four quadrant E; = —Ez E; =42: Eé" *E symmetry (4-QUAD SYM). 108 cells/(segments) are to be solved only by the execution of computer program thereby reducing the size of matrix. The size of matrix is . _ . . + + given by the expre331on (3Nb Na) x (3Nb Na) where Nb and Na are the "effective number of cells" in body and "effective number of segments" on antenna. In case of symmetry, N will be the number of b unshaded cells and Na will be the number of unshaded segments on the antenna. The next step in numerical formulation of the program is the specification of the location of each cell of the body. This location is specified by its central coordinates. The body may not be homogeneous and hence the electrical parameters of all cells may not be alike. These parameters are therefore specified for each cell too. The central coordinates of antenna segments are obtained by the program itself (once the height h and Na are specified) and the right hand side of the system of equations is automatically computed. The program assumes input voltage to antenna as 1 volt (peak value) at the central segment or input segment. 7.2.1 Description omerogram. The computer program is coded in FORTRAN - IV and can be compiled on any FTN compiler. The main program is symbolically named FIELDS. It has a number of subroutines for the numerical evaluation of induced fields in the biological body, unknown antenna current and the radia- tion pattern in the far-zone. The coefficient matrix obtained by the 109 system of equations generated by the coupled-integral-equations (2.24) and (2.25) is shown below. IIMATAAII IIMATABII "MATBA" "MATBB" IICMATPII "PAD" is a subroutine that computes the elements of matrix A. is a subroutine that computes the elements of matrix B. is a subroutine that computes the elements of matrix C. is a subroutine that computes the elements of matrix D. is a subroutine that solves the system of equations by Gauss's — elimination process to determine the unknown fields induced in the body and the currents on the antenna. is a subroutine that computes the far zone radiation fields produced by the antenna and 900 plane (see Fig. 2.3) body currents at ¢ 10°. at intervals of A6 llO Input to the program contains numerical information about the frequency, antenna height, cell location, electrical parameters etc. as well as logical information to enable the program to make decisions with respect to symmetry conditions. These will be discussed in the following section in details. A listing of the entire program is provided in the end of the chapter. The listing for subroutines appears in the order they are called by the main program. 7.3 Data Structure and Input Variables. The data deck is composed of three files. The first two files have one card. The third file has exactly Nb cards where Nb is the "effective number" of body cells. These files are read by the program, the data being thereby transferred to its corresponding variable names or array names. We will adopt a convention as follows: "for any variable name ‘xxx, (xxx) will represent the data stored under that name, needless to mention that this data will be provided by the user". We will now discuss the data files in detail. The example given in the next section will clarify any ambiguity that may be encountered in this section. Data File No. l FIELD ALLOCATED Col. 1 & 2 Col. 3 & 4 Col. 5 & 6 Col. 7 & 8 Col. 9 & 10 C01. ll NDIV NA NB 111 This file has one card. FORMAT VARIABLE CODE NAME IZ NDIV 12 NA 12 NB 12 ‘NQD I2 NSYM Il CRNT Specifies the number of subdivisions an edge of each cell will undergo in integration process in subprogram "MATBB". A suitable choice is (NDIV)=02. (NA) will be equal to the total number of segments on antenna iiftusymmetric current distribution is anticipated and it must be an "odd integer". (NA) will be one less than the effective number of segments Na on antenna in case current distribution on the antenna is considered symmetric. (NB) will be equal to the effective number of cells of the body model if symmetry exists otherwise equal to the total number of cells in the body model. NQD NSYM CRNT Data File No. 2 FIELD ALLOCATED Col. 1 to 10 Col. 11 to 20 Col. 21 to 30 FMEG 112 Specifies the number of identical volumes generated by the symmetry conditions. (NQD)=01 for no symmetry. (NQD)=02 for Z—QUAD VPS or 2-QUAD HPS. (NQD)=04 for A-QUAD SYM. Specifies the type of symmetry. (NSYM)=OO symmetry code for A-QUAD SYM, 2-QUAD HPS or no symmetry. (NSYM)=01 symmetry code for 2-QUAD VPS. signifies the symmetry condition for the current distribution on the antenna. (CRNT)=8 for symmetric current assumption. (CRNT)=9 for non-symmetric current. This file has one card. FORMAT VARIABLE CODE NAME F 10.1 FMEG F 10.1 H F 10.1 ANTRD (FMEG) is equal to the frequency of the system in MEGA HERTZ. (H) is equal to the height "h" of antenna in 113 ANTRD (ANTRD) is equal to the radius of antenna "a" in meters. The h/a value ranges between 40-125 for best results. Data File No. 3 This file has exactly Nb cards. To every cell there must be one card and the cells must be numbered in the same sequence as the cards are arranged in the file. In the following description, details are for the "nth" array element of XB, SIGIA, EPRA and DBXA and will contain the data from the nth card of file No. 3. FIELD ARRAY FORMAT ALLOCATED ELEMENT CODE Col. 1 to 10 XB(n,l) F 10.1 Col. 11 to 20 XB(n,2) F 10.1 Col. 21 to 30 XB(n,3) F 10.1 Col. 31 to 40 DBXA(n) F 10.1 Col. 41 to 50 EPRA(n) F 10.1 Col. 51 to 60 SIGIA(n) F 10.1 . th XB(n,l) Its contents are the x- coordinate of n cell in meters. . th XB(n,2) Its contents are the y— coordinate of n cell in meters. . th XB(n,3) Its contents are the z- coordinate of n cell in meters. DBXA(,n) Edge size of nth (cubic) cell in meters. 114 I 0.10 m 1r-' _— $.02}. _ _ m 2 4 1 3 5 6 h d—Ib - l—" homogeneous __" biological body ' Y h = 0.15 m a = 0.0015 m f = 600 MHz 2a __I E Cré 5.00 S/m E = 80.00 I‘ N = 11 a Nb= 6 Fig. 7.4. Theoretical model of the system given in the example of section 7.4. 115 EPRA(n) Relative permittivity (real constant) at the th . n cell 13 stored here. SIGIA(n) Effective conductivity (S/m) at the-nth cell is stored here. 7.4 Example. Let us assume that a theoretical model of a physical problem has been obtained as discussed in section 7.1, where symmetric current distribtuion and a 2-QUAD HPS is anticipated. This situation is shown in the Fig. 7.4. The body is homogeneous and all cells are of the same size and reasonably small. All input information is listed in Fig. 7.4. Preparation of Data Deck: Data File No. l Following is the list of numbers and the corresponding variable names that the user should provide in File No. l. VARIABLE NUMBERS NAME FIELD REMARKS 02 NDIV Col. 1 & 2 Economical choice 10 NA Col. 3 & 4 Since Na=ll 06 NB Col. 5 & 6 Since N =6 02 NQD Col. 7 & 8 Two identical parts 00 (blank) NSYM Col. 9 & 10 Symmetry code for 2-QUAD HPS. 8 CRNT Col. 11 Code for symmetric current distribution. 116 Data File No. 2 Following is the list of numbers and corresponding variable names that the user must provide in File No. 2. VARIABLE NUMBERS NAME FIELD REMARKS 600.00 FMEG Col. 1 to 10 Frequency in MHz. 0.1500 H Col. 11 to 20 Height "h" in meters 0.0015 ANTRD Col. 21 to 30 Radius of antenna in meters. File No. 3 This file will contain exactly 6 data cards, with information entered as follows. Card numbers in Table 7.1 correspond to the cell numbers in Fig. 7.4. 7.5 Free—Space Program "ZFREE". This program is used in cases where free—space input impedance of the antenna under consideration is needed. It also gives the current distribution on the antenna at an excitation voltage of 1 volt peak value. In this program an additional feature is incorporated by the use of subroutine "EIMP" and it is an optional. By virtue of this subroutine, electric fields at any location or various locations in space, can be computed. Even though this is an independent program, it is suggested that the same effective number of segments Na be used in this program as were used in FIELDS. The following data file is prepared to determine the free-space current distribution and input impedance of the antenna. A listing of this program appears after the 117 mnmapmzz>m cane m N u>aomaw to 2:2 aaum»w oz» to mezaemzouu---uua--- CtfifiCCfifiiti¢'fifififiicCflitc‘flc“#¢¢¢tflii*i‘fifi‘fi H .02 mo.~m .z\>.>m .z\>.xm w 3 u Na-mm¢m¢m.- noumomn-.- ~a-mmo-«. aa-mHm~ma.- “a-u~mm-. aoumm¢e¢¢.- H ~a-msmamw.- ea-mmmqam.- mauunmmam. a=-mnmem_.- ae-uceae_. aa-oeemmn.- M ma-mae¢¢m.: no-mmmnwn.- ma-mmnaem. mo-umamcn.- do-meeaec. eo+eq~_=~.- me-mamen..- caammwaan. NarmaSamm. neumewann.u “asmmnnae. ea.mmm¢n~.« . Neumaowee.- nonmeaaem.s wa-menem¢.u _anmmmfimu. «a-meeq¢m. "aumseoao.- , maumesema.- ca-esmawm.a N=-ucmeca. ma-mm¢mmn. ~o-umneee. eo.m~e~ma.s .2\>.Nw a£\>.>m azx>uxu . a pzaeoasa 2H manual oaeeouam QUQDQZH m.OZ momz.aoz.>~oz.mz.ooz.mz.moz.« o¢mm ofio . >mmZ.DOZ.Jom >m .>Qom MI» mommzm QJNHL Qwosazu o ‘00 oz< czzwhz< zo zonhbmumhmua hzwmmao MI» mwzmzmmhmo ZQDm Zn mddwo no zmmZDZ "m2 . (ZZwa( ZU mZDHPHFmm (Z meF¢ZmDm .I .m mull: NIP mmZHmePmQ mm (Z XHZPe mzenhm th mm>40m mhnezemmheem 2H mJJme ue zmmzezumz o eoe mzm >9 mzm xamhtzmem m.I.m mmzeJ th mmz~2mwhme mehdz wzuheemmem e **#*##*****#*******#*****#*************#sa*s#*#¢#**##*#***¢*#****###***s****s**o ewe . mzsamleze+z+eem Zn mqqme ue mwmzez umz <22mez¢ ze mzerHhmcm me mmmzezn¢z . o ¢he (z >m mzm xnekczmem m.I.J mwzea MIH mwznzmmhwe (mh¢z wzuheemmem e ###*#¢*#*#**#***s*#*******#*¢*##*#*#*#****#*##**#*##***¢**¢##*##***###*#¢##*#*#e who me 0k 00 xxo.ew.hzmov.ez<.A«.em.JeeuH who . mu eh eeaDme o fi+¢mz< no zonmzmzmo ehAmzme zmzemImA.o ehA xmA.A:\>VNMIh.xAA.AZ\>v>th xAA.A:\>exMIh.xm.ZIA.on.\\.eIAeh¢:zeu 00A meA A. A hzmhmzz>m ecee ION mA xAN hoA .\\.NA.I >Aemem ue ZDZIvA.xm.mA.I.m>m mIb ue mhz Nm MIh.xmm.Az\>e>MIn.xmm.Az\>vmeh xmA.ZIA.xN.eIAVk¢szu meA hnA A¢ .¢Awm.mu.eIAeh¢zmeu meA omA .A. <22wez< MIh ze zeAthAmkmAe hzmmmeeInm xem AIAeh+o :*2w>w>+m>A>.+Jnaoo> on (moA . m 0h 00 moA mx5<+zw>w>nzm>w> om . 0h 00 m\§<+m>A>flm>A> 0A ZAOA.Om.om.ow.om.om.om.om.om.om.OAv OF 00 AAm#DmI.O.ovxqmzovmxwofl54 A0.m**am#2<+m**A< Ao.o.o.ova&Zoflzm>m> A.O .o.o .ovamZoflm>A> ¢ OF 00 AAA .Gw .xv .QZ<. AJ .ow. AvvuA N\x¢QI JxI ( A A0 .0.0 .va4m20u4(%0% m DH 00 AA&.Gm.thov.QZ<.AA.0m.JVAuA m Oh Do A.Zm>m>.m>A>.JAU xNJmZDo A #220 mmomeA AJAO~J.A.Jx.Ax.Om. , Ao 0.0.va4mzouzm>m> Ao.o.o.ovamZUflo>A> xvuox AN UP 00 vac: mm OF 00 A0.0m.z>mzvun mm OF 00 AA.6m.xfiva A.QOZ.AHI5 0 DD A.m.AIGZ 0 Do Am.vaxI fix 0 .m**xmo#AAO. AI Immmv*mmm*om20#3< + AOAmA*A0m\Dm#DZ*0mZDVIhmZDO xxxAAv¢xn xh_ma Am*omAqu Ao.A.o.ovam:ouU< A+xxnxz mmuxx szAhzoo Ao.o.o.ovx4mZUquvo A.¢ u: ooA on F4 5 OF 00 A0 .0 .0w. AAVmZ.DGZ.¢AOAm.(mmm mmw\¢NP¢Z\ZO£ZDo {xmo mz..Zm>w>.&>A>.*o.m+zm>m>*o.e+o>A>vnonva mozAhzoo bmzoo¢¢u4A>um>A> , n o» co hmzoo*m>uzm>m> m a» no meDo#¢uJ(m+QQD>flQDD> 0m.om.omAZIxMWbuw oA 0h 00 Asz.om.zv.zo.AA.om.zvvuA m**m\Am> fl Zm>w> ON n Oh no szootuoao> on OM.ON.ONAZI&x#mvuA N\2Imx DA DE DOAAXZ .om .ZV .mO. AA .Gw .ZAAuA G N**z\Ao <1m4<85<*o.m+mt* Ao.o‘o.ovx4mzonzm>m> Ao.o.o.ovx4m20nm>A> o.m\x.zw>m>.m>A>.mZAuA mm Oh DG AA .om .xfiALA . A.QGZ.AHX3 m 00 O W\Amz.GOZ.#o .N+Zm>m>*o .¢+m>A>A+A&ZA42uIAmZAJZL mDZAPZDo szootA>fl m>A> E1 OF) A 136 oo~mm¢m~m~mo~o Os-Iv-u-u-u-oq-Iv-oo-IHHN ¢¢¢¢¢¢¢¢¢¢¢¢ mmwmehhm oooooooo ¢¢¢¢¢¢¢¢ sz Zmbhmm ANAmcmOIAnAz¢m0IA¢Am¢mo+AAAzm NIH LO P o Z¢mo Z< ZAZszmD thI Ax xA%\ can wIkIQ Am I A4 1 J.§A< # A 0A.DA.NA ZO l-VWG UZ\5XZO $.5uézo sac-1. QDHV(HDLO Qm< UUHQ . A+ZHAmZ A0.0.0.AAmeZUnwa AON.DNA( ZDAmZmZAG m.hm200.hwa.m.< xMJiZDQ Anm.hma.z.z.mZ.QGZ..£ FZAmm D>\0.AHDN .AA&¢Z.SAO%DQ Am.mfiwm~x¢.mH.xm.\\.ozfivp.Aon‘mer.4Hu.7< xmgmzoo aJmHum mmomkzu Amma¢h.Ammck.haahso.»:azfi.mmmu~ zcmoomm \ P7 141 JxIIJx A+zu x .h.&AmI IxAmA . 0AA .ow .AAuA Ao. x4mzon 4¢h0r AAAr.z*2cmbz<+m.z2 Ah \AAmk x:czr+zA>A>*¢. >A>A+4HQQD> 0 OF 00 m\7<+Zw>m>Izm>m> m OF 00 1\7<+m>A>Im>A> ZAOA.ON.Om.ON.CN.ON.ON.ON.ON.ON.OAA OF 00 AAm*.GmI.O .OAleZoAmmev U4 AN*#Q¢ZPZ(+N##A< AC.O~O.CAXJ&EUfizm>m> AC.0.0.oAleEUfln>A> 5% Do AAA.Om.xA.QZ<.AJ.Ow.AAALA N\X¢QIJWEM AO.O.O.OAXJQZUH4.ZU>m>.n>A>.JAU XMJLEDU AJAU.J AA<m mIb LO PZ{ZAZKMPUQ NI.—.Im¢.x \ A: KA<\Am I A4.xA¢A AA.7A¢ # A DA.0A.WA iAfi AZZ. AI? c 0m .0 . < 20A m.hmZDU A.mo. Aim rwo.z.z.wAmmunA>m V hmzootAanAxm . szAwmoon ** omxAAom*OXI.o.oAmeEoAuxmo*Aem#ox.o.AAxJazoIm##m:\AAmmgoxl.o.oAmem ZoAmxmotAmm#ox.o AAx4m20+m##¢m\AAvm#osI.o.oAmeEuAmxmo#A¢m*ox.o.AAA mezoIn**nm\AAmm#oxI.o.oAxJazoAmxmo#Amz#ox.o.AAxu_mzoA¢N*zA+ANwmemm #* em\AAom*OXI.o.oAx4mzoAmxmu*Aéz#ox.o.AAxgmzoImgtmc\AAnm*OXI.o.chJmm ZoAmxmozAmmtox.o. AAx4mzo+0*#¢z\AA¢m*oxI.o.oAxALEUAmxmo*A¢m#ox.o.AAA mezoI nttmm\AAmm:OXI.o .oAmezoAmxwo¢Amm#ox.o.AAxJanA#>#ZA+A>qu>w . . Am#*ez\AAcm*oxIm .o oAmezoAmxwotAem*ox.o AAXAazotAAo .m\xQIAzA&xIAIXNIm#¢mm\AAmm*oxw I.o oAxAmZoAmxwo*Amm#ox.o. AAmeZU#AAo .m\xAA+AzAmxIAIxA+m**¢m\AA¢m30m xI.o.oAmezoAmxwo#Avmxox.O AAx4m£o:AA o.m\xQIAzAmxAIxAIm**mm\AAmmtom XI.o oAx4mzoAmxmo*Amm#ox.o. AAx4mzo#AAo .mxxD+AzA1xAIxA+xo#Amz\Asz*A oxI.o.oAmezoAmxmo+Am\AAAm*OXI.0 .oAxAmEoAuxwoA*Am##oxAA#ZA+AanAxw Am#*N+u *#>+m*gAAo .m\xaIAzAmx!AIxAAhzomu£m Am*#N+W**>+m2*AAO .mxxo+AzAmx1AIxAAhzomumm Amg#N+.m##>+m#*AAo .mxeIAZAmxAIxAAhmomuvm AmggN+mgt>+m**AAo .m\xo+AzAmxAIxAAhmomumm Am*2N+m$*>+m**AAzAmx+xAAhmomumm Am.##N+m#a>+mx*AAzAmxIxAAhmomuAm o.m\AzAkzcuzA AA Oh so a AzAhzcnzA om.oA.oAAAIzAuA 5 A.Azz.Auz m an m A A0 0 o oAxwmuwuwflw . .o.oAme£ouANw a Ao.o.o.oAx4&20uA> _. . ... H A0 0 Am.mZAmxuN Am.mzAmxu> AA.mzAmxnx A.mz Anmz a Do 56 AAOX#A&*O .¢A\ONI.O A.quAAAaAfiAAIAHA thOo. OJanao .mio: 5 omzm\m+wo .MHOJ e+mo. Atowquowmu A1*o.omAuoN a onmcmomA¢A muAm mz.omzu.Am.ocAmx 202200 Achmx zoAmzsza 05.04 Acuz wm>h zA.A&€Ahz<.bmzoo ANw A>w Ax.m qumzoo wm>h A A.z¢ mx xo.zzAmzAw szhDDmmDm CHAPTER VIII SUMMARY The objective of this thesis was to solve the problem of Electro- magnetic coupling between an antenna and a biological body. This thesis has verified experimentally the theoretical results that were obtained by computer aided numerical analysis. The study was necessary to under- stand the nature of the coupling problem and to make an assessment of the potential radiation hazard to Operators exposed to high power radiation from thin-wire antennas. As an introduction a rigorous mathematical analysis was carried out for linear dipole antenna having a biological body in its vicinity. Integral equations which have been named as coupled-integral-equations were obtained and later transformed by the method of moments into a system of consistent equations for the unknown electric fields in the body and the currents on the antenna. These were solved by standard numerical techniques on a computer. Experiments were conducted to verify the theoretical results obtained for an antenna-body coupled system. These results were verified for (a) the input impedance of the antenna; (b) the induced electric field distribution inside the body; (c) the current distribution on the antenna. The experimental verification of the theory developed earlier gave us enough confidence to get additional information about various 144 145 practical situations. This information was gathered by the computer program "FIELDS". The prominent features resulting from this were the effect on the radiation pattern due to coupling, the effect on the current distribution on antenna, and the effect on induced fields in the body due to direct contact with ground and isolation from the ground. Ratios of the power dissipated to the power radiated and power input to antennas,were also determined. It was concluded that quarter wave monopole antennas with input powers of about 140 Watts at 27 MHz or 30 watts at 90 MHz would dissipate the same amount of power in the body of an operator in the near-zone of antenna. as would a plane electro— magnetic wave of intensity 10 mW/cmz. In addition the computer program FIELDS which furnishes all the required quantitative information regarding a coupling problem has been explained by working out an example. This program is compatible for all FORTRAN IV systems. The problem of a linear dipole antenna or a monopole antenna over infinite ground plane has been dealt with success in this thesis. As a next step it would be interesting to attempt solving a problem involving thin-wire antenna of arbitrary shape. BIBLIOGRAPHY 10. 11. 12. BIBLIOGRAPHY H.P. Schwan, "Radiation biology, medical applications and radiation hazards", Microwave Power Engineering, Vol.-2, E.C. Okress, Ed., New York: Academic Press, 1968, pp. 215-232. C.C. Johnson and A.W. Guy, "Nonionizing electromagnetic wave effects in biological materials and systems", Proceedings of the IEEE, Vol. 60, No. 6, pp. 692-719, June 1972. K.M. Chen and B.S. Guru, "Induced electromagnetic field and absorbed power density inside human torso", Engineering Research Report, Michigan State University, East Lansing, Michigan, 1976. K.M. Chen, D.E. Livsay and B.S. Guru, "Induced field in and scattered field from a finite cylinder with arbitrary conductivity and per- mittivity", IEEE Transactions on Antennas and Propagation, Vol. AP-24, No. 3, pp. 330-336, May 1976. D.P. Nyquist, K.M. Chen and B.S. Guru, "Coupling between small thin-wire antennas and a biological body", IEEE Transactions on Antennas and Propagation, Vol. AP-25, No. 6, pp. 863-866, Nov. 1977. CheneTo Tai, "Dyadic Green's function in electromagnetic theory", Intext Educational Publishers, Ed., Pennsylvania: Haddon Craftsmen Inc., Scranton, pp. 46-65, 1971. K.M. Chen, "A simple physical picture of Tensor Green's function in source region? Proceedings of the IEEE, Vol. 65, No. 8, pp. 1202-1204, Aug. 1977. D.E. Livesay and K.M. Chen, "Electromagnetic fields induced inside arbitrarily shaped biological bodies", IEEE Transactions on Microwave Theory and Techniques, Vol. MT-22, No. 12, pp. 1173-1280, Dec. 1974. B.S. Guru, "An experimental study on the interaction of electro- magnetic fields with arbitrarily shaped biological bodies", Ph.D. dissertation, Michigan State University, East Lansing, Michigan, 1976. R. Cooper, "The electrical properties of salt water solutions over the frequency range 1-4000 MHz", The Journal of the Institute of Electrical Engineers, Radio and Communication Engineering, Vol. 93, part III, No. 22, pp. 69-75, March 1946. L.K. Lepley and W}M. Adams, "Electromagnetic dispersion curves for natural waters", Water Resources Research, Vol. 7, No. 6, pp. 1538—1547, Dec. 1971. J.A. Saxton and J.A.-Lane, "Electrical properties of sea water", Wireless Engineering, pp. 269-275, Oct. 1952. 146 13. 14. 15. 147 S.H. Mousavinezhad, "Implantable electromagnetic field probes in finite biological bodies", Ph.D. dissertation, Michigan State University, East Lansing, Michigan, 1977. R.W.P. King, "Theory of Linear Antennas", Harvard University Press, Cambridge, Massachusetts, pp. 251-252, 1956. G.S. Smith, "The electric-field probe near a material interface with applications to the probing of fields in biological bodies", IEEE Transactions on Microwave Theory and Techniques, Vol. MIT-27, No. 3, pp. 270—278, March 1979. 16. J. Van Bladel, "Some remarks on Green's dyadic for infinite space", 17‘ 18. IRE Transaction Antennas Propg., Vol. AP-9, pp. 563-566, Nov. 1961. K;M.Chen, S. Rukspollmuang and D.P. Nyquist, ”Measurement of induced electric fields in a phantom model of man”, presented at International Symposium on Biological Effects of Electromagnetic Waves held on July 31 to Aug. 8, 1978, in Helsinki, Finland. H. Massoudi, C.H. Durney and C.C. Johnson, "Long-wavelength EM power absorption in ellipsoidal model of man and animals?. IEEE Transactions on Microwave Theory and Techniques, MTT—ZS, No. 1, pp. 47-52, Jan. 1977. HICHIGQN STRTE UNIV. LIBRQRIES WWIWIN"“WIWIIHIIWIIWIHWWW" 31293100635212