IHIHMIIII \ I 145 780 .THS. SCATTERENG FROM A SLOTTEC! CYLINDER Thesis for the Degree of N18. MlCi-éiGAN STA‘I‘E WIVERSETY JOHN R. SHORT 1988 THES|S ‘ ~. LIBRAK'I' 3 Michiga! 312$: ’Univc .slt'y _q . H a. ABSTRACT SCATTERING FROM A SLOTTED CYLINDER by John R. Short It is well known that illuminating a metallic object by an electromagnetic wave induces currents on the object which, in turn, radiate to produce a scattered electromagnetic wave. This scattered field can be controlled by loading the surface of the ob- ject with lumped impedances. This thesis presents a theoretical and experimental study on the control of backscattering from a thick cylinder illuminated by a normally incident plane electro- magnetic wave which has its electric field vector polorized perpen- dicular to the axis of the cylinder. The control is achieved by loading the surface of the cylinder by a narrow, impedance backed longitudinal slot. An exact theory is developed for the fields scattered by an infinitely long slotted cylinder illuminated by a plane wave as in— dicated above. A theoretical analysis is carried out to determine: (1) the optimum slot loading impedance required to force the backscattered electromagnetic field of the slotted cylinder to JOHN R. SHORT vanish, and (Z) the extent of the control over the backscattered field which can be obtained with a purely reactive loading. It is verified experimentally that significant minimization of the backscattered field of a slotted cylinder may indeed be ob- tained through the use of a purely reactive loading. The experi- mental results agree excellently with the correSponding theoretical values. This study should prove significant in the understanding of the modification of scattering from thick cylinders, which has practical application in the area of radar camouflage. SCATTERING FROM A SLOTTED CYLINDER BY A5!" John R." Short A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Electrical Engineering 1968 ACKNOWLEDGEMENTS The author wishes to eXpress his indebtedness to his major professor, Dr. K. M. Chen, for his guidance and encourage- ment in the course of this research. He also wishes to thank the members of his committee, Dr. B. Ho for reading the thesis and Dr. D. P. Nyquist for correcting the manuscript and valuable suggestions. Appreciation is also expressed for the help extended by Mr. J. W. Hoffman of the Division of Engineering Research. The research reported in this thesis was supported by the Air Force Cambridge Research Laboratories under contract AF 19(628)—5732, ii SECTION I. II. III . IV. TABLE OF CONTENTS INTRODUCTION. 0 I C 0 O O O O I C O O O THEORETICAL FORMULATION FOR SCATTERING FROM A SLOTTED CYLINDER. C O O O O O O C O O O O O O O O 2.1 Formulation of the Problem. . . . . 2,2 Boundary Conditions. . . . . . . . . 2.. 3 Scattering from a Solid Cylinder . . Z, 4 Radiation from a Driven Slotted Cylinder............... 2.. 5 Scattering from a Slotted Cylinder . 2.6 The Backscattering Cross Section . Z. 7 Optimum Impedance for Zero Backscattering. . . . . . . . . . . . Z. 8 Optimum Reactance for Maximum or Minimum Backscattering. . . . . 2.9 Numerical Results . . . . . . . . . EXPERIMENTAL STUDY OF BACK- SCATTERING BY A SLOTTED CYLINDER 3. 1 Experimental Arrangement and Measurement Technique. . . . . . . 3. 2 Experimental Results and Comparison to Theory. . . . . . . . CONCLUSION . . . . . . . ........ REFERENCES. . . . . . . . . ...... iii Page 10 13 15 18 19 20 36 36 41 47 49 Figure 2.9 LIST OF FIGURES An Infinite Cylinder with a Longitudinal Slot Illuminated by a Plane EM Wave with its E Field Vector Perpendicular to the CylinderAxis................... Superposition for an Illuminated Slotted CYIinder. O O O O O O O O O O O O O O O O O I O O 0 Optimum Slot Impedance for Zero Back- scattering as a Function of Slot Position with ka : l. O O O O O O O O O O O O O O O O O O O 0 Optimum Slot Impedance for Zero Back- scattering as a Function of Slot Position With ka : Z. Z O O 0 O O O O O O O O O O O O O O O 0 Optimum Slot Impedance for Zero Back- scattering as a Function of Slot Position Withka:5.oooooooooooooooooooo Optimum Impedance for Zero Backscattering as a Function of Slot Position with ka = 10. O . . Optimum Minimum and Maximum Backscatte ring Cross Section as a Function of Slot Position for ka : 1 O 0 O - O O O O O O O C O O ..... O O O O O 0 Optimum Minimum and Maximum Backscattering Cross Section as a Function of Slot Position for ka : 2. 2 O O O O O O 0' O O O O O O O O O O O O O O 0 Optimum Minimum and Maximum Backscattering Cross Section as a Function of Slot Position for ka’ = 3. 0 O O ........ O 0 O O O O O ..... iv Page 2.3 24 25 2.6 Z7 Z8 29 Figure LIST OF FIGUR ES (continued) Page Optimum Minimum and Maximum Back- scattering Cross Section as a Function of Slot Position for ka = 5. 0 ............ 3O Optimum Minimum and Maximum Back- scattering Cross Section as a Function of Slot Position for ka : 7. 0 ........... . 31 Optimum Minimum and Maximum Back- scattering Cross Section as a Function ofSlotPositionforka:10.0...... .. . .. 32 Relative Backscattering Cross Section as a Function of Slot Position for Various Values of ka with Fixed Purely Reactive Loading . . . . 35 Experimental Model of Slotted Cylinder . . . . . 38 Experimental Arrangement . . . . . . . . . . . . 39 Optimum Minimum and Maximum Back- scattering Cross Section as a Function of Slot Position . . . . . . ..... . . ...... 43 Relative Backscattering Cross Section as a Function of Slot Position, with Constant Impedance (Z = j 7. 9 ohm-meters) ........ 44 Relative Backscattering Cross Section as a Function of Slot Position, with Constant Impedance (Z = j 7. 0 ohm-meters) ........ 45 Relative Backscattering Cross Section as a Function of Slot Position, with Constant Impedance (Z = j 3. 7 ohm-meters) ........ 46 Table LIST OF TABLES Page Optimum Reactance for Minimum Back- scattering Cross Section in Terms of Slot Position 9 and Electrical Cylinder Radiika....°................. 33 Optimum Reactance for Maximum Back- scattering Cross Section in Terms of Slot Position 6 and Electrical Cylinder Radiika....°................. 34 vi I INTRODUCTION In recent years, the modification of the backscattering cross section of metallic objects has received considerable atten- tion. Modification of the scattering from metallic Spheres, plates, (1-6) (7-9) and loops has been studied by several authors Chen (10, 11) have investigated the method for modifying the and others backscattering from a cylinder by impedance loading. These studies were concerned with thin cylinders where it was assumed that only an axial current was induced. When a cylinder is thick electrically in diameter and is illuminated by an E-M wave with its E field vector perpendicular to the cylinder's axis, a circum— ferential current is induced on the cylinder’s surface and it, in turn, maintains a large scattered fielduz), The object of this research is to realize a method for controlling this circumferential induced current, thus controlling the scattering from the thick cylinder. This is accomplished by implementing an impedance backed longitudinal slot on the sur- face of the cylinder. A theoretical expression is derived for the fields scattered from such a slotted cylinder illuminated by a normally incident plane E-M wave whose E-field vector is per- pendicular to the cylinder's axis. The backscattering cross section is then formulated'in terms of the loading impedance, slot position, and other parameters. Optimum loading for minimum and maximum backscattering are obtained. The theory has been verified by an experimental investigation. It has been proved both theoretically and experimentally that the backscattering of a thick cylinder illuminated by an E-M wave with a perpendicular E field vector can be minimized drastically by a properly designed impedance backed slot. II THEORETICAL FORMULATION FOR SCATTERING FROM A SLOTTED CYLINDER 2. l Formulation of the Problem The geometry of the problem is as indicated in Figure l. A perfectly conducting cylinder of infinite length and radius a has an impedance backed longitudinal slot cut on its surface. The slot is located at 9 = 90 and has an angular width 6. The impedance Z backing the slot is lumped into the slot region on the cylinder's surface. A plane electromagnetic wave is incident normally upon the cylinder from the direction 9 = 1r with its E field vector per- pendicular to the cylinder axis. This incident wave induces a circumferential current which in turn reradiates a scattered electromagnetic field. The scattered field from the slotted cylinder can be ob- tained by the superposition of the field scattered by an unloaded solid cylinder illuminated by a plane wave and the field radiated by a slotted cylinder excited by a potential difference impressed Front View Y slot E9 8 5 + ’1“ A V0 . 7? P1 0 E 9 _ .. \p 9:0 »i -> x H k Cross Section View Figure 2. 1: An Infinite Cylinder with a Longitudinal Slot Illuminated by a Plane EM Wave with its E Field Vector Perpendicular to the Cylinder Axis. across the slot. A mathematical statement of this superposition is E3 2 EC + Er (2.1) 9S —> —> H = HC + Hr (2.2) where ES and HS represent the fields scattered from a slotted cylinder illuminated by a normally incident plane wave, EC and He represent the fields scattered by a solid cylinder illuminated by the same incident plane wave and Er and Hr represent the fields radiated by a slotted cylinder with excitation applied across the slot. The excitation of the slot must be chosen in accordance with the total surface current on the illuminated slotted cylinder and the impedance backing the slot. This situation is indicated schematically in Figure 2. l. 2. 2 Boundary Conditions Since the slotted cylinder is assumed to be perfectly con- ducting, the tangential electric field must vanish at its surface except in the slot. If the slot is assumed to be very narrow (i. e. , kaé << 1, where k is the free-space wave number) its electric field may be modeled as 6 = 9 slot - ZK9( ) _ _ 0 §_ E9 (r— a )_ a5 for l9-90|< 2 (2.3) where the surface current K9 is related to the total longitudinal .novcflrwu @03on woumnwgad Gm 90w nounfimomuomsm nopnflcwo ©03on Sufism Au Sean? e28 emuefiga 3 J "N .N 93th .363wa @930: con—MESHHH Am magnetic field at the surface of the cylinder as K6: -H . The impedance Z of the longitudinal slot is defined as V0 E9(6:60)a6 Z = W)- = -H (9:9 ) (ohm meter) (2.4) 9 o z o where V0 is the potential difference across the gap. The boundary condition at the surface of the illuminated slotted cylinder is , Ee(r = a+) = Ee(r = a') which may be expressed as 0 a5 for I 0' < E;(r=a+) +E§(r=a+)= (2.5) Nlo: Nlo- o for le-e | > 0 where E [S the 9 component of the inCident electric field. 6 The superposition technique discussed in the previous section allows the boundary conditions at the surface of the illuminated slotted cylinder to be separated into the boundary condition for the illuminated solid cylinder, ’ + E;(r=a )+E;(r=a+) = o (2.6) and the boundary condition for the driven slotted cylinder as V0 6 r + :5 for l9-90| < E Ee(r=a ) = 5 (2-7) 0 for (9-9 | > — o 2 Boundary conditions (2. 6) and (2. 7) define the scattering and radiating modes to be discussed in the following two sections. 2. 3 Scattering from a Solid Cylinder Consider a perfectly conducting cylinder of radius a which is illuminated by a normally incident plane electromagnetic wave with an E field vector perpendicular to the cylinder axis. The geometry of the problem is defined in Figure 2. 2. b. The incident plane wave can be represented by the follow- . . . (13) mg field expansrons: HI. : e-ka: (3-3er059 2 00 n = E E (-j) cos(n9)J (kr) (2.8) on n n=0 i 1 H9 — Hr — 0 (2.9) i ' a i 00 n E6 = +36 5? Hz = JCO 23 Eon(-J) cos(n9)JI'1(kr) (2.10) 0 n=0 1 j 1 B i j 1 00 n Er = -;é— '; ‘a—e Hz = we ? E Eon(-J)n31n(n9)Jn(kr) o 0 n=0 (2.11) E1 = 0 (2.12) z The Neumann factor Eon is defined as and Jn(kr) is the nth order Bessel function of the first kind. The impedance of free-space 130 is 120 17 ohms, and k is the free-space wave number. The ert time dependence factor is implied. The solution for the fields scattered by a perfectly con- ducting infinite cylinder illuminated by a plane wave are well 4 known,(1 )and are given by: H° = HC = o (2.13) r 6 2 ° 0° ( )n e (k ) H"( mm ( 1 > H = - E E -j cos(n )J' a 2. 4 2 n=0 on n H (z)'(ka) n (2) 00 H (kr) l l n+1 n EC = —-- - Z) 6 (-j) nsin(n9)J'(ka)——-;—— (2.15) r (1160 r n=0 on n Hn(2)(ka) 00 H (2)'(kr) E; = z; E E (-j)n+1cos(n9)J'(ka)—-n-—Z-)-;—- (2.16) 0 n=0 on n H( (ka) n EC = o (2.17) z (2) where Hn (kr) is the nth order Hankel function of the second kind. In the radiation zone (i. e. , kr >> 1), the scattered field behaves as an outward traveling cylindrical wave, which can be observed by replacing Hn(2)(kr) and its derivative by the leading terms of their asymptotic expansions for large kr. This procedure gives: 10 11' -j(kr -—) 00 J' (ka) H” = -.’——2— e 4 z eoncos(ne)—9——— (2.18) z Trkr n20 H (Z)'(ka) n er 2 -j o Nlo» NIO: The magnetic field has only a z-component, and this field must satisfy the wave equation, (V2+kz)H: = 0. (2.21) Since the cylinder and slot are infinitely long, the radiated fields have no z-dependence, that is, 9; E O. The wave equation for r Hz thus becomes: 2 2 [_§_2+%.§_r+_1§_3.._z+kz]Hr=o (2.22) 5r r 59 z An appropriate solution for H; is r °° (2) = ’ 6 9 . Hz 2 [ansm(n ) + bncos(n )] Hn (kr) (2 23) n20 where an and bn are unknown coefficients which are to be evaluated by application of boundary condition (2. 7). The field H: is symmetric with respect to the slot located at 9 : 90. Let 9 in equation (2. 23) be replaced by 6', where e! = 9-9 (2.24) 0 such that H;(-9') = H:(9'). With this change of variable, equation (2. 23)can be written in the following form 0° 2 Hr = E A cos(ne') H ( )(kr) (2. 25) z n20 n n where An is a new coefficient. Other components of the radiated field can be obtained from equation (2. 25) and Maxwell's equations as 12 r r He — Hr = o . (2.26) r _L_ a r 00 (21' E6 = 006 3—1' Hz = JLO Z) An Hn (kr)cos(n9'.) (2.27) 0 n=0 1- ' 1 a r ' 1 (I) (21 E = -—‘1— - — H =-L - Z A H (kr)nsin(n6') r 0-160 r 30 .z 02% r n-O n n — (2.28) Er = o , (2.29) z The arbitrary coefficient An can be determined from equation (2.27) and boundary condition (2. 7) to be . 6 . E V sin(-n—) A = ,_1_ (2X3) ___2_ ____1___ (2,30) n J Q0 1r a6 n H (2)'(ka) n ' The fields radiated from the driven slotted cylinder are now completely determined and are given by: 1 V 00 sin(n76) H (2)(kr) Hr = . (i) E 6 cos(ne') ' (2.31) 2 3111.0 a6 n=0 on n H (2) (ka) n V 00 H (2)(kr) Er: —i—(—%) z e sin(-‘-‘29-)sin(ne') (2)1 (2.32) r 11 r a n=0 on Hn (kr) r 1 V0 00 sin(%6- Hn(zy(kr) E9 = :(E) Z Eon —;—— cos(nG') (2). (2.33) n=0 Hn (ka) In the radiation zone of the slotted cylinder the radiated field behaves as an outward traveling cylindrical wave. Replacing l3 2 Hn( )(kr) and its derivative by the leading terms of the asymptotic expansion for large kr yields: . 1r . no 1(2))? mu: go on 2 a5 11'3kr n=0 n Hn(2)'(k3) (2.34) . 1r , n5 rr V0 (7 'J(kr'Z) 0° .n-l 81m?) cos(ne') E9 = E l 3 e Z Eon“) n (2" 1T kr n20 Hn (ka) (2.35) rr Er : O (2.36) 2. 5 Scattering from a Slotted Cylinder The final problem to be considered is the superposition of the two preceding results in accordance with equations (2. l) and (2. 2) to obtain the total fields scattered by an infinite, per- fectly conducting, slotted cylinder illuminated by a normally incident plane wave. The total scattered fields are H (2)'(kr) oo 13:26 . n+1 nzo 0“ H(2)'(ka) [id-J) cosmenyka) n V sin(£1—6- (—-—) _n cos(n9')] (2- 37) 14 s 00 Eon Hnmhk ) [ {-jlnH E = Z nsin(n9)J'(ka) 1’ n:0 r Hn(2)'(ka) 6o n V +(;%) (Tr-1E) sin(%§-)sin(n9 ')] (2 . 38) s Ez : O (2.39) s 5 H6 = Hz = o (2.40) 00 H(2)(kr) HS: - z e —’-‘E—,— [(-j)ncos(n9)J'(ka) z n=0 0“ Hn( )(ka) n cos(ne')] (2.41) . n6 j V0 Sln( 2 ) + __ —— RC, 3.5 0 while the total scattered fields in the radiation zone of the cylinder are: 1T E“ = .,l e 23 ———-°,n [; cos(n9)J'(ka) 9 1Tk1‘ n20 Hn(2) (ka) 0 n . n6 + (j)n+l (:9) s1n(—) 1T a6 Esr = o (2.43) cos(nG')] (2.42) 15 TT -j(kr-—) oo 6 2 Hsr: -’1rkr e Z Z on [cosnBJI'1(ka) n=0 Z Hmka) (.)n+l V0 sin(2-2§) +-L—§ 11 (:5) cos(nG')] (2-44) 0 It can be observed from the above expressions that the scattered field in the radiation zone is a outward traveling cylin- drical wave, and that by adjusting V0, which is related to the slot impedance Z and 5, the scattered fields may be made to vanish at any point in the radiation zone. 2. 6 The Backscattering Cross Section The backscattering cross section per unit length of the cylinder can be defined as follows with specific reference to an infinite c ylindr ical object: S . ->s 2 e13“): JET—’1‘- : 11m 2m» ET (2.45) S r->oo E 9211' s . . . where Pomni is the total power reradiated per unit length of an . . . . . . . ->s ideal omnidirectional scatterer that maintains the same field E at a radial distance r for all values of 9 as that maintained by the . . . . . (17-) actual scattering cylinder in the direction 6=1r . Equation (42) for the scattered electric field along with the above definition result in an expression for the backscattering 16 (C) cross section (TB of the slotted cylinder as (c) 4 00 6on n a = — >3 ——-— [é(-1)J'(ka) B k n=0 H(2)'(ka) ° “ n 2 (.)n+l Vo sin(%§-) - L— (--) —— cosn('rr-9) (2.46) 1r a6 n 0 V which is a function of ka, —-9- , ands . a6 0 The voltage Vo which excites the slot can now be expressed in terms of the impedance Zcf the slot and the total surface current on the illuminated slotted cylinder. The following result can be obtained from equations (2. 3) and (2. 4): < u z Ke(e = so) -ZH(r=a,6=6) (2.47) Z 0 where Hz is the total longitudinal magnetic field given by H = H1 +H5 2 Z Z = H1 + HC +Hr . (2.48) Z Z Z Note that H; and H: are independent of the driving voltage Vo while H; is a function of V0. With this in mind, the following two quantities may be defined: 17 H 2 [H.1 +HC]r=a z z 926 o 00 n H (2)(ka) : ...' 9 k - 'k . r1230 Eon( J) COS(n O)[Jn( a) Jn( a) H (2)'(ka)] (2 49) n and r Y _ H (r=a,8=80) ‘ V o 1 oo sin(£2§- ) Hn(2)(ka) = . z e —— , (2.50) JTT go 8.5 n20 on n Hn(2) (ka) The voltage VO may now be solved for in terms of com- pletely determined quantities . The above definitions and equation (2.47) give: -——-_ (2.51) o 1+Z Y 00 n Jyka) P = t, 2) E (-1) ————,—— (2.52) 0 n=0 on H (2) (ka) n and _ 1 oo n+1 sin(22§) cosn(1r-60) Q = F3} 2 Eon”) n (2). (2.53) n20 Hn (ka) allows the backscattering cross section to be written in the following concise form. 18 0| r- 2H- 1+ZY .B 4 E (2. 54) If the problem is again considered from the viewpoint of superposition (as discussed previously in this section) P and 2H6 1+zY‘ represent the complex amplitudes of the contribution to the backscattering cross section by the scattering from an illumi- nated solid cylinder and the radiation by a driven slotted cylinder, respectively. 2. 7 Optimum Impedance for Zero Backscattering An Optimum slot impedance that will cause the backscat- tered field to vanish in the radiation zone can be found by equating the backscattering cross section to zero and solving for the opti- mum slot impedance. This impedance is denoted as Zop and is given by "UI : ______ 2.55 Z'op HO-YP ( ) which can easily be derived from equation (2. 54). Generally an active element is required to realize the above impedance function. In some cases it becomes physically impossible to realize this impedance at all. It may thus be more practical to consider the reduction of backscattering by using a purely reactive impedance . 19 2.8 Optimum Reactance for Maximum or Minimum Backscattering In general, the backscattering cross section of a slotted cylinder cannot be reduced to zero with a purely reactive slot impedance. This does not, however, rule out the possibility (C) B of reducing 0' by a suitable choice of the loading reactance. An optimum reactance. Xop’ for maximum or minimum back- (C) with res ect B P scattering can be determined by differentiating 0 to X and setting the derivative equal to zero. The result of this procedure is X = ViJVZ+4W 0P 2 (2.56) where 2. Z 2 2 2 Z V: (E +G)-(C +D)(A +B) (2.57) (c2+ D2)(BE - GA) + D(E2+ oz) D(AZ+ B2) + (BE - GA) W (c2+ DZ)(BE - GA) + D(E2+ o2) (2.58) and the quantities on the right hand side of the above two equa- tions are defined by F = A+jB (2.59) Y = C+jD (2.60) (375—136) = E+jG (2.61) 20 2. 9 Numerical Results The four functions H, T, P, andO involved in the expres- (C) B and slot impedance Z sions for backscattering cross section 0' were numerically evaluated. Except in the case of the imaginary part of 3?, all the series converged very rapidly. The evaluation of the series Y (i. e. . the magnetic field at the center of the slot of the driven slotted cylinder divided by the potential drop across the slot) is complicated by the slow convergence of its imaginary part. It was found that the rate of convergence was directly re- lated to the gap width of the slot in the cylinder and that it was necessary to retain over thirty terms of this series to obtain the desired accuracy even when 6 = 0.1. To investigate the effect of changes in slot width on the ability to control backs cattering from the cylinder, the back- (C) B was calculated as a function of scattering cross section 0' slot position 00 and slot impedance Z for several values of the angular slot width 6 (6 varied from O. 001 radians to 0.2857 radians). The effectiveness in minimizing or maximizing the scattering was found to be not noticeably affected by these variations in the gap width. The Optimum slot reactance to (C) when 80 = 1800 minimize the backscattering cross section 0B and ka : 2. 2.0 was found to range from 3. 508 ohm-meter to 7. 867 ohm-meter when the angular slot width 5 varied from 0. 001 radians to 0. 2857 radians. 21 The effect of the electrical radius ka of the cylinder was next investigated. The angular width 6 of the slot was fixed at 0.10 radians and the backscattering behavior of the slotted cylin- der having radii ranging from ka : 1. 0 to ka = 10. 0 was considered. The optimum impedance for zero backs cattering is indicated as a function of slot position 00 in Figures 2. 3 - 2. 6 for various values of ka. It is observed that for ka : 2. 20 the resistive part of the slot impedance is nearly always negative. The maximum and minimum backscattering cross sections for purely reactive loading are given in Figures 2. 7 - 2.12 as a function of slot position 00, for several values of ka. The correSponding values for Optimum reactance are tabulated in Tables 2.1 and 2. 2. It was found that when ka 5 5 the backscattering cross section could be minimized by at least 10 dB over an excursion in slot position from 00: 1800 of about forty degrees. The enhancement varied from zero to five dB, and depended greatly upon the slotorienta- tion. In general, the control over the scattering was markedly decreased for ka > 5 and also when the slot is oriented in the shadow region. The backscattering cross section as a function of slot orientation for a fixed, purely reactive loading is indi- cated in Figure 2.13. The reactance is chosen to minimize the backscattering at 00: 1800. 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W S S .30 pEOm H (i\ , m4. 0 m D a) D m). m 30 ow .o .m n ox HOM Gonfimom «cam mo cofiocdh a mo con—00m mmouO wcwuoflmOmxomm £55332 pan Edging £32330 $00.“on oo 3on mo GOBMOOA x: .N 2&5 ow~ .76 36... -b du- ‘ .11- 65:62 3 .o .Eo mw-m~.~. o .m -1 (O a) 3 db -1- cc ow on: o- b 5 db Cl)- .1- u- d. .56 0x68 1. 4)- db on: umMu I O M l 'mNI rem- I in H I nioHu 1:- ON 1T MN (qp)(a)qn ‘uopoes ssoxo Supeweosxo'eq 91412193 31 .o .h H ex H8 Gawfimom “—on mo ~830ch a ma nofloom mmouO mfinoflmucmxomm Sewage/H can 85833.4 552330 "3 .N 0.2"th $9.:on om Jo: mo con—mood o 3 3. 3 ow o3 oi oi oi 03 hnurTvuxvuflhvvuthn I'mMI so..- 33.6335 n o . - 3 .80 @338 u a f o4. u 2 .rom- um_- 4o“- rm- M“ o .16 enomn\ r . m Jude Ito.” x m :2 one 1 “1% AION 1 MM - .umm (qp)(o)a .0 ‘uopoes ssoxo Butxan'easnoeq 3111:1219}; 32 .o .3 u ax new sewn—macaw “—on mo sewn—ugh a ma nofluvm amouU wcwnoflmomxomm gang can £3ng ggao .NH .N unamwh q- 4:- db W- -b I. 28:22 3 .o .80 3356 o .3 II ll «30 2 .10 33m Amuvuwmg ow 3on mo :03.»qu 00 cm ooH om“ b L n 1 # ch- 1 d‘ - .GME ounfle L n r on: q. owH (gp)(3§[.o ‘uopoas 9301:) Bugxaneosnaeq 91442193 33 R eactance, in Ohm- meter 8 ka — 00 1.0 2.2 3.0 5.0 7.0 10.0 180° 3.208 3.876 4.023 5.931 7.736 10.663 _170° 3.145 3.655 3.705 4.898 5.512 6.390 160° 2.970 3.125 2.966 3.195 3.148 2.990 150° 2.715 2.475 2.148 2.019 1.860 1.384 140° 2.393 1.837 1.621 1.348 0.832 -1.445 130° 1.965 1.483 1.269 0.527 -2.732 3.978 120° 1.515 1.255 0.830 -2.894 3.608 0.446 110° 1.354 0.982 -0.069 3.874 1.221 5.028 100° 1.276 0.461 -7.303 1.676 -8.243 0.118 90° 1.204 -1.641 3.744 0.362 2.415 3.219 80° 1.109 6.047 2.064 9.364 -0.195 -2.912 70° 0.948 2.690 1.363 2.156 3.750 1.890 60° 0.576 2.015 0.428 0.937 1.115 9.089 50° -l.458 1.674 -4.195 -129.927 6.220 0.459 40° 4.045 1.328 4.729 2.244 2.000 3.101 30° 2.412 -0.112 2.395 1.256 16.819 -2.363 20° 2.078 3.280 1.037 -0.597 2.887 1.247 10° 1.954 2.392 -1.765 1.821 -60.472 -9.235 0° 1.920 2.265 -5.254 1.395 3.404 0.262 Table 2.1 Optimum Reactance for Minimum Backscattering Cross Section in Terms of Slot Position 60 and Electrical Cylinder Radii ka.. 34 Reactance, in Ohm-meter s ka 0 1.0 2.2 3.0 5.0 7.0 10.0 0 ========== 180° 1.308 1.379 1.364 1.487 1.516 1.552 170° 1.304 1.353 1.311 1.363 1.289 1.122 160° 1.289 1.260 1.081 0.745 0.018 -1.859 150° 1.260 0.989 -0.060 -6.989 31.340 8.268 140° 1.202 -0.844 11.292 4.804 4.037 3.109 130° 1.016 5.615 3.514 2.973 2.437 0.062 120° -l.284 3.105 2.603 2.164 0.547 4.471 110° 4.230 2.467 2.146 1.116 5.175 0.731 100° 2.843 2.084 1.790 10.329 2.167 4.038 90° 2.401 1.784 1.318 2.849 -2.936 -1.138 80° 2.118 1.496 -0.473 1.653 3.027 2.776 70° 1.890 1.115 4.014 -3.016 0.656 38.712 60° 1.690 0.258 2.319 3.478 4.757 1.454 50° 1.510 -8.045 1.836 1.862 1.396 4.492 40° 1.348 3.479 1.443 -1.933 -36.079 -1.473 30° 1.207 1.920 0.569 4.349 1.783 2.875 20° 1.089 1.293 2.883 2.471 -0.510 7.121 10° 1.008 0.921 1.929 50.761 1.976 2.336 0° 0.977 0.784 1.815 5.110 0.354 4.208 Table 2. 2 Optimum Reactance for Maximum Backscattering Cross Section in Terms of Slot Position 90 and Electrical Cylinder Radii ka. .wfivdod m>30mom hogan cough gum? ax mo m05~d> mflofiud> new sou—Much “—on mo Goauugh a no :ofloom amouU wnwuufimonxomm o>3d~om “ma .N oufimmh $00.“on ow 3on mo nofidooJ 35 on 34 on ow o2 o: 3; on: as n n .3 .1 .3 4. 4. u 4. n .3 u u h u n u +. u 736 o.m L'mMU ohwfi N.~ lion- mo~.m 04 non—051950 _ r mm: 3 X 8735 u N .13.- S .o u o 2. o.m n 2 \ m 0 1' '0“. o H - 3 I'ml . 1|! . o .rm .10 6:9... o~.~ n 68 :3 11mg m .m IUON M .m‘l llm.N (3p)(3;‘I.0 ‘uogioas ssozo Bugzaneosxo'eq 911119133 III EXPERIMENTAL STUDY OF BACKSCATTERING BY A SLOTTED CYLINDER 3. 1 Experimental Arrangement and Measurement Technique A theoretical expression for the backscattering cross section of an infinitely long cylinder with an impedance backed longitudinal slot was obtained in the previous seCtion. This re- sult expressed the backscattering cross section of the slotted cylinder as a function of its radius, the frequency of the illumi- nating plane wave, and the impedance and position of the slot. The optimum slot impedance for zero backscattering was also found. It was discovered from this expression that the resistive part of the optimum impedance is negative for most slot orienta- tions. An expression for the reactance of an optimum lossless loading to yield maximum and minimum backscattering was also derived. To confirm these theoretical predictions on the back- scattering behavior of the slotted cylinder, a series of experi- mental measurements was performed. Since realizing the necessary slot impedance for zero backscattering (containing a negative resistive part) physically would be extremely difficult, if not impossible, only a purely reactive load backing the slot was examined in this study. 36 37 The experimental model of the metallic scatterer consists of a cylindrical brass tube, 7/8 inch outside diamter and 36 inches long, with a 1/8 inch wide longitudinal slot cut on its sur- face (see Figure 3.1). The slot backing impedance is implemented by installing a parallel plane waveguide structure at the inner wall of the slotted cylinder. One end of the guide opens at the slot on the cylinder while the other end is short-circuited. The short location is adjustable such that the length of the guide can be varied, which in turn varies the slot impedance. The impedance of this structure may be approximated by that of a plane wave- guide. (15) Several methods are available for measuring the back- scattering cross section of a metallic object. In this research, the source separation method is used. The principle of this method is to design the receiving system in such a manner that it does not respond to the incident or source field. A single antenna can then be used to radiate the illuminating E-M wave and sub- sequently receive the scattered wave. (16) The X-band experimental arrangement which was us ed in this research is indicated in Figure 3. 2.a. The experiment was conducted in an anechoic chamber (dimensions of 0. 8m x 1.4m x 0. 7m). A standard gain horn antenna (HP X89OA) is pro- jected into the chamber through one of its ends. The cylinder to be studied is mounted between the sides of the chamber and at 38 $1.5m 0» 55.95 go: 3073 nového @25on mo Hovoz Hounoawnomxm togm mandamsmwm :0m 3 .m 0.5th :wb L._..._.J Ila :N\.n 39 :VVVVVVV AA R.F. absorbe Instru- _ horn cylinder covers 6 walls‘ mentam antenna a) Anechoic Chamber horn antenna load freq. direct. hybrid isolator "—"'" meter "' ‘coupler T ‘ amp. E-H klystron det. tuner power 7 supply 8: matched 1 Khz C°R° 0' term. amp. mod. b) Block diagram of instrumentation Figure 3. 2: Experimental Arrangement. amp. det. SWR ind . 40 a distance of 28 cm from the horn antenna. A block diagram of the instrumentation is shown in Fig. 3.1.b. The reflex klystron generator (FXR type X760A), modulated by a l Khz square wave generator (HP 715A power supply with internal modulation) is us ed as a RF source. The klystron is protected from reflected. energy by the load isolator (Polytechnic Res. and Dev. Co. type 1203). The directional coupler (HP X752C) and associated de- tector (HP X485B) are used in conjection with a CRO to monitor the klystron output. Frequency is measured by the frequency meter (HP X532A). A four port hybrid junction (HP X845A) is us ed to separate the source signal driving the antenna and the scattered field signal received by the antenna. The two remain- ing ports of the junction are coupled to a matched load (HP X910A) through an E-H tuner (HP X880A), and to an amplitude detector (HP X485B). The detector output is then measured by a SWR indicator (HP 415B). An E-M wave with a vertically polarized E field vector normally incident upon the cylinder can be implemented with the arrangement described above. When the scatterer is absent, the receiving system can be nulled by adjusting the E-H tuner. When the scatter is introduced, the reading on the SWR meter will then indicate the relative backscattering cross section. The scattering from a solid cylinder having the same radius as its slotted counterpart is used as reference. 41 It was found that this system was able to detect scattered fields of the order of 25 db. below the backscattering cross sec- tion of the solid cylinder while maintaining its stability for several hours. The horn antenna does not illuminate the cylinder by a plane wave. The amplitude of the incident wave is greatest near the center region of the cylinder, and decreases with displace- ment in either direction parallel to its axis. The phase of the incident wave will also vary along the axial direction of the cylinder. It was found that by placing the cylinder about ten wavelengths in front of the horn antenna the consequences of the non uniform illumination and the end effects (arising from the finite length of the scattering model) were very small, while the detection system provided the desired sensitivity. 3. Z EXperimental Results and Comparison to Theory For comparison with the eXperimental data, the theoretical backscattering cross section for various slot impedances was com- puted from equation (2. 54) with ka : Z. 20 and 6 = O. 2857 radians. The theoretical results discussed above and the corre3pond- ing exPerimental results are indicated in Figures 3. 3 - 3.6, in (C) which the backs cattering cross section GB of the slotted cylin- der is plotted as a function of slot position 90. The backscatter- ing cross section is given in db. and is normalized to that of a 42 solid cylinder of the same radius. Figure 3. 3 represents the maximum arfi minimum backs cattering that can be obtained for a given slot position 90. The agreement between theory and experiment is excellent, and it is found that the backscattering cross section of the cylinder can be reduced by 25 db (1. e. , to the noise level of the detection system) over an excursion in slot positions from 90: 1800 of nearly twenty degrees. Figures 3.4 - (C) B as a function 3.6 represent the backscattering cross section 0 of slot position 90 when the slot impedance Z remains fixed. An appropriate slot impedance is chosen so the backscattering will be minimized for values of 80 equal to 180°, 170°, and 150° in Figures 3.4, 3. 5, and 3.6, respectively. The agreement between theory and experiment is again excellent. It can be concluded that the theory developed in Section II to precict the backscattering behavior of a slotted cylinder gives valid r e sults . 43 .Gofimmom ”~on mo :owuocdh .m mm Gofioow mmoHO mfiuoflmomxomm gawxmz was ggiz SBEMEO o Amounmog 0 Jo? mo dogwood ”m .m 089E 0 ON o¢ oo ow OOH Qua owa ox: ow + x a 4 .. a x u .4 x a i. i. + 356$ 330830me 0 0 0 .3093“. H954 omMoZ Houcofiwuomxm 0° 0 1, l D D O O O I L .10 6:8 o o o o I: ion (gp)(o)g .0 ‘uotioes ssozo Sutzaneosnoeq SA'Q‘BIQH 44 Annouosneao o .N. n n NV menswear»: «Gnu—380 5H3 .soflwmom “—on mo aofiuoash m an nofioom muonU wfiuofimomxoom ozumaom 31m ogmwh $00."on oa do: mo :oflmooq 9 ON Ca. Ob cm 2: CNH 3; on: 0mg - r h F b p 4 q P P h u 1 d . a q I. p F p p p p b u u q q T q - qr- mufionm Hfinoecomxm G 0 0 .CooFH . .r on: 1:54 0302 Hon—Goguodwmlllllll III IIIII .lll'llllilu 0N1 07 v 0 G E G G o .16 381\ g r a 2 LT m .m + 3 Tm. i. (gp)(o)8.o ‘uoypas ssoxo Sutzaneosxaeq OA'Q'BIOH 45 Annouoahugfio o .N. m u NV 005309»: unnumcou an? nofiwmonm “*on mo Gofionfim m m.» nofioom mmOuO mfiuofimomxoom 039.20% um .m onfiwfim $00.“on om 33m mo :ofimooq o ON ow o0 ow on: ONH 0*; on: owH P n h — p p q 4 . 4 . - .P L p b b q q - 1 -. .h D D ‘F' b d F b q d1 350nm Hounognomxm O 0 O anoonh 1. H954 0302 Hounoguomxm GD 0 0 III H om- m. R I. A 9 q - u cm x. S D e n m o7 m. an 3 I o S S o s 3 O 17 m. m D om 8) b N m ow 46 .Amuouoabuggo N. .m_. n NV ooqmvomé «£3380 fig? .coflfimom ”—on mo :ofionfih a no nofloom mmouO wfinotmomxumm o>mum~om S .m mnnwfih $00."qu ca 3on mo non—mood 0 cm 3. oo ow cog om~ 9: ca: owm h P P p b p F b n k b . p p b b - . p q u d J 1‘ u q u u u d u d I d d u q 1. 336m fifiufifluaxm O O O .4. c3023. 1T on. 4' I H254 omwoz Haunoguomxm . 41 ON- J' 0 i1 Cu. O 1 O A. o 1.. A: Ono 6 m rm . o .r 8. oo am. L1 (gp)(3)g.0 ‘uotioas ssoxo Butxan'eosxo'eq 914412193 IV CONCLUSION In the preceding sections, the behavior of a metallic cylinder loaded by an impedance backed longitudinal slot was considered. Theoretically, the scattered field from an infinite cylinder loaded with an impedance-backed slot has been derived exactly. The optimum impedance which leads to zero back- scattering and the optimum reactance which leads to minimum backscattering have been calculated. An experimental investi- gation has been conducted to verify the theory and an excellent agreement between theory and experiment was obtained. The loading impedance required for some particular modification of the scattered fields is in general complex. The impedance required for zero backscattering generally has a negative resistive part, which requires an active loading im- pedance backing the slot. A purely reactive loading can also be very effective in modifying the scattering behavior, but its effectiveness is limited primarily to the case where the slot is located in the illuminated region of the cylinder. The ability 47 48 to modify the scattering using a purely reactive loading also de- creases as the electrical size of the cylinder increases. This suggests that it may be advantageous to implement two or more loaded longitudinal slots on the surface of an electrically thick cylinder to control the backscattering. (1) (Z) (3) (4) (5) (6) (7) (8) REFERENCES Chen, K. M. , and M. Vincent, "A New Method of Mini— mizing the Radar Cross Section of a Sphere," Proceedings of the IEEE, vol. 54, pp. 1929-1630, November 1966. Liepa, V. V., and T. B. A. Senior, "Modification to the Scattering Behavior of a Sphere by Reactive Loading," Proceedings of the IEEE, vol. 53, pp. 1005-1011, August 1965. Green, R. B. , ”The Echo Area of Small Rectangular Plates with Linear Slots, " IEEE Trans. on Antennas and Pr0paga- tion, vol. AP-lZ, pp. 101-104, January 1964. Vincent, M. C. , and K. M. Chen, "A New Method of Mini- mizing the Backscatter of a Conducting Plate," Proceedings of the IEEE, vol. 55, pp. 1109-1111,June 1967. Chen, K. M., J. L. Lin and M. Vincent, "Minimization of Backscattering of a Metallic LOOp by Impedance Loading, “ IEEE Trans. on Antennas and Propagation, vol. AP~15, pp. 492-494, May 1967. Lin, J. L., and K. M. Chen, "Minimization of Back- scattering of a Loop by Impedance Loading--Theory and Experiment, " IEEE Trans. on Antennas and Propagation, vol. AP-16, pp. 299-304, May 1968. Chen, K. M., and V. Liepa, "Minimization of the Back- scattering of a Cylinder by a Central Loading, " IEEE Trans. on Antennas and Propagation, vol. AP-lZ, pp. 576-582, September 1964. Chen, K. M. , ”Minimization of Backscattering of a Cylinder by Double Loading, " IEEE Trans. on Antennas and Propagation, vol. AP-l3, pp. 262-270, March 1965. 49 (9) (10) (11) (13) (13) (14) (15) (16) 50 Chen, K. M. , "Reactive Loading of Arbitrarily Illuminated Cylinders to Minimize Microwave Backscatter, " Radio Science, vol. 690, p. 1481, 1965. Hu, Y. Y., "Backscattering Cross Section of a Center- Loaded Cylinder Antenna, ” IRE Trans. on Antennas and Propagation, vol. AP-6, p. 140, 1958. As, B. 0., and H. J. Schmitt, "Backscattering Cross Section of Reactively Loaded Cylindrical Antennas, " Scientific Report 18, Cruft Lab. , Harvard University, Cambridge, Mass., August 1958. King, R. W. P., and T. T. Wu, The Scatteringnd Diffraction of Waves, Harvard University Press, Cam- bridge, Mass., 1959, Chapter 2, Stratton, J. A., Electromagetic Theor , McGraw-Hill Book Company, Inc., New York, 1941, p. 374. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill Book Company, Inc. , New York, 1961, p. 234. Ramo, S., J. R. Whinnery, and T. VanDuzer, Fields and Waves in Communication Electronics, John Wiley and Sons, Inc., New York, 1965, p. 377. Blacksmith, P., R. E. Hiatt, and R. B. Mack, ”Intro- duction to Radar Cross-Section Measurements, ” Pro- ceedings of the IEEE, vol. 53, p. 901, August 1965. mummumummmmLmuwmzml HHIfllWlH 3129.30 4 47