3051-2-T = RL-2093 3051-2-T THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINEERING Radiation Laboratory VOR PARASITIC LOOP COUNTERPOISE SYSTEMS- II Interim Report No. 2 (1 November 1969 - 31 January 1970) By Dipak L. Sengupta and Joseph E. Ferris 15 February 1970 Contract FA 69-WA-2085, Project 330-001-03N Contract Monitor: Mr. Sterling Anderson CONTRACT WITH Federal Aviation Administration Radar and Navaids Section 800 Independence, SW Washington, DC 20590 Ann Arbor, Michigan

3051-2-T 1. Introduction This is the Second Interim Report on Contract FA 69-WA-2085, Project 330-001-03N "VOR Parasitic Loop Counterpoise Systems-II" and covers the period 1 November 1969 to 31 January 1970. During this period we have carried out some basic theoretical and experimental investigations of the radiation characteristics of parasitic loop counterpoise antennas having a figure-of-eight type of excitation in the azimuthal plane. As a result of this kind of excitation, the induced currents in the parasitic loops become non-uniform. The non-uniformity of the parasitic currents causes the optimum parameters (if any) and the performance of the antenna to be different than those obtained in the omnidirectionally excited antennas. The major effect of the non-uniform excitation has been found to give rise to a strong lobe in the axial direction of the far field pattern. The investigation reported herein has been undertaken in order to optimize the performance of the antenna under such situations. The theoretical problems discussed in this report have the ultimate objective of developing complete theoretical expressions for the radiation field produced by non-uniformly excited parasitic loop counterpoise antennas. Experimental investigation has been confined to the case of non-uniformly excited double parasitic loop counterpoise antennas. Special emphasis has been given to obtain an optimum configuration for the 5. 2' diameter counterpoise case. 2. Mutual Coupling Effects in Parasitic Loop Counterpoise Antennas This section deals with the theoretical investigation of mutual coupling effects in a double parasitic loop counterpoise antenna. The theory of a single parasitic loop counterpoise antenna has been discussed elsewhere (Sengupta and Weston, 1969). In a previous report (Sengupta et al, 1968), an approximate theory was developed for the double parasitic loop counterpoise antenna by neglecting the effects of mutual coupling. There, the far field radiation pattern produced by the antenna was obtained by simply superposing individual free space fields. This theory explains with a fair amount of accuracy the far field for the cases when the spacing between the parasitic elements is large compared too widely spaced, the interaction betical situation where the loops are not to widely spaced, the interaction between the parasitic currents may become quite important. It is the purpose of ths sectionto develop theoretical expressions for the parasitic currents and also for the far field produced by a double parasitic loop counterpoise antenna by taking into account the effects of mutual coupling. 1

3051-2-T 2. 1 Parasitic Currents Consider a double parasitic loop counterpoise antenna as shown in Fig. 1. i Parasitic Loops * -B2^ y, / -f 0 ---; —( 1K- B. A, / H2 - - 1- - '0 2b H 1 Ih -- Alford Loop K- A - b FIG. 1: Double Parasitic Loop Counterpoise Antenna. The Alford loop situated at a height h above the counterpoise is the only excited element. Let T and T be the total currents in the two parasitic loops maintained by the excited element. Symmetry of the system and the nature of the excitation dictate that the distribution of the current along each parasitic element will be constant. Let us assume that in the absence of mutual coupling between the parasitic loops, the induced parasitic currents will be represented by If and IO respectively. The method of determining I1 and 1O for the above configuration has been discussed elsewhere (Sengupta et al, 1968). By taking the mlutual interaction into account we can writeT 0 T 1 12+K 21I2 T O T I2 I2 +K12 l, (2) where K12 and K21 may be defined as the coefficients of coupling for the mutually induced currents. 2

3051-2-T Notice that these are not the conventional coefficients of mutual coupling and hence K12 t K21. From (1) and (2) the following are obtained for the parasitic currents: 0 0 T1 +K2112 T~I +K I T 2 ( 2= 1-K. (4) _l121 2 In general K12, K21 are complex constants for a particular configuration.of the antenna and |K121, IK2 11 < 1. Thus the problem reduces to the determination of these two coefficients. We discuss this in the next section. 2.2 Determination of the Coupling Coefficients K12, K21 We outline here the basic mathematical setps involved in obtaining K12. For this purpose we represent the antenna configuration as shown in Fig. 2. W, a B2 9 P / 2/ ( / / i t / r" FIG. 2: Rays Contrbutng to 12 FIG. 2- Rays Contributing to K12 3

3051-2-T In this representation the first parasitic loop is replaced by a point source of suitable strength placed at a height H1 above the counterpoise. The current T in the first parasitic loop being I, the field produced by this current at the point P located on the second parasitic loop is given by: kB ikr12 ine 12 Ein(P) ^ (- ) JkBl B 1 ine '-11 2 li12 r12 ikr' r12 -JkB sin' )e r' ] (5) 12 10C 1 2 a (5) where no is the intrinsic impedance of free space, k = 2r/X is the propagation constant in free space, 22 2 2 (22 2 (6) r12B2+H2-H1); 2=B2+ (H2+H1 (6) B2 B2 2 2 sinG gin)' I (7) si12 r; sin 2 r12(7) '12 12 J1 is the Bessel function of the first kind and first order. In Eq. (5) only the direct and the reflected fields due to the parasitic current IT are used to obtain the incident field at P produced by this current; the contribution to the field at P due to diffraction effects at the edges of the counterpoise are neglected for the present. If necessary, they will be taken into account later. The current induced on the second parasitic loop due to the field inc (P) is obtained by using the following relation. IT' ^ 27r nc ) (8) 2 ilklM where kb77 +. (9 M 0.577 +in() in2 4

3051-2-T After introducing Eq. (5) into (8) we obtain the following expression for K12. ikr12 12 i M 12 12 ikr' 12 -Jl(kB line'2 ) (10) Following a similar procedure it can be shown that the other coupling ooefficient K21 is given by: kB ikr21 21 -Jl(kB2sine2l) er~ 2 21 kr' 21 where 2 2 2 2 2 2 r21 B +(H2-H1); (r) = B +(H2+H1) (12) B1 B1 sin - sine' = (13) 21 in21 r * ( This completes the derivation of expressions for the coupling coefficients. Do the next section we derive the explicit expressions for the parasitic currents due to the fields produced by the Alford loop carrying a current of magnitude I. 2,3 Expressions for the Parasitic Currents It can be shown (Sengupta, et al 1968) that in the absence of mutual coupling the current induced in the first parasitic loop is given by I = I ok2 +) +Q (14) 1 O2 5

3051-2-T where a is the radius of the excited loop and, 27r(kB ) Eikr 1 ikr2 e 1 i M (krl)2 (kr2; ] (15) (kB1) ekr [ 1 Y2 i(2kB1+ /4) M2 (kr)2 rkB1 ( 1 2 i(2kH-7/4)-,H e (16) 2 2 2l2 2 2 r B1 +H-h); r2 B+ (Hl+h) (17) r B 1 H1h); r2 1 1 (1 Similarly, the current induced in the second parasitic loop due to the field produced by the Alford loop only is given by the following: O2 k 2EP 22 -I2= +o (,' (18) where 2wh (kB) ikrl ikr 2 '(krB) e (kr) (kB_ e 1 _ 1/2 i(2kB2+7/4) P2 = 1 1M2 2 M (kr') B2 1/2 i(2kH2-/4) (20) -(-H) e,rkH2 222 22~ 2 e(20) (r) = B2 +(H2-h); (r2 = B2 + (H2+h)2 (21) = B2 2 T T After using (3), (4), (10), (11) and (14) and (18), the parasitic currents I1 and I2 are obtained as follows are obtained as follows: 6

3051-2-T I1 o(2 ) 12K21 [ 1+Q 1)21(2Q2) (22) kT= 2 )2 1 P+ +K (Pi+Q 1)] (23) Equations (22) and (23) are expressed so that they may be computed numerically. This would be done in the future. It should be noted that in the absence of mutual coupling, (22) and (23) reduce to (14) and (18) respectively. 2A Far Field Expressions In this section the far field produced by the double parasitic loop counterpoise antenna will be given. The method of obtaining the expressions is similar to that discussed in the case of single parasitic loop counterpoise antennas (Sengupta and Weston, 1969) and hence will not be repeated here. All the expressions are arranged such that they may be programmed for numerical computation. The far field is expressed formally as: EkS a I ( e - S(e), (24) where S(e) = SA(O) + S (e) + 8(0). (25) In the above equations S(e) is identified with the complex far field pattern of the antenna; the three terms on the right hand side of (25) are the complex far field patterns produced by the Alford loop, the first and the second parasitic loops above the counterpoise. Explicit expressions for the three terms in (25) are given below for future reference. SA( F ()sinO -ikAsine cosesin( ) ikro LO e) + krosn e () (26) T2-1 47kr0in 7

305 1- 1-T '2 L (6)= 3/ [Cos 0sin e ikAsin8 Cos83/2 0 0 (27) -.00 (28) ikr sin(e-00 F0(6)=e 0) f iirt2/2 ikr s inW+400) e dt -e kro1/2 0.07r2 (29) kr 1/ R = 2 (0 ) 0co 0 -e-7/2 ) 2 2 2 h r = A+h; ton 0= I o o A sA) kB1 I 2(111K2= [3P14Q1) +K21(P2+Q2) F1(6) where P1. Q1 are as given by Eqs. (15) and (16), an (30) (31) (32) J1(kB1sin6) p -ikAsin8 F (0)- 4 - M~ F (9)e i 1 Op1 Icosel sin f +2 s~in 0 ikrp e L 0 (33) i(- -kAsin6) P e L 1(9)= 1 -,n [ 081/2 (0 )J1(kB cos0p),in/6i~k ie 1 1 sl G ] 1 sie i J(kB lOOSOP Os Y2( 1 MA sine K 1 pwIC eO (34) 8

3051-2-T ikrp sin(e-pl) 5 ir t2/2 F1 ()=e e dt -wa ikrplS in(pl) P6 it2/2 -e 1 1 e dt, (35) P= 2 (- cos (- (36) krP 1/2 'r 2 2 2 2 r2 = A2+ H (38) 1 tan p 1/A (39) 2(e)= 2(1-K1 K 2+Q2+K 12(P 1+Q F2() (40 where P2o Q2are given by Eqs. (19) and (20), F2(O) is given by Eqs. (33) - (39) with the parameters H1, B1 replaced by H2 and B2, K12, K21 are as given by Eqs. (10) and (11). 2.5 Discussion Expressions for the parasitic currents and the far field produced by a double parasitic loop counterpoise antenna have been derived above by taking into account the dominent effects of mutual interaction between the parasitic elements. The relevant expressions for the induced currents and the far field are being computed at the present time. The results will be discumed in a future report. 9

3051-2-T 3. The Radiation Field of a Circular Loop Carrying a Non-Uniform Current 3. 1 Introduction The radiation field produced by a circular loop carrying a non-uniform current is discussed theoretically in this section. The problem under investigation has direct bearing on the determination of the radiation field of a parasitic loop counterpoise antenna with a figure-of-eight type of excitation in the azimuthal plane. The non-uniform excitation causes the induced currents in the parasitic loops to be non-uniform. The performance of parasitic loop counterpoise antennas with non-zniform excitation cannot be explained by the theory developed for similar antennas with omnidirectional excitation. The present investigation is the first step toward the development of a theory for the non-uniformly excited parasitic loop counterpoise antenna. 3.2 Nature of Excitation In a practical VOR antenna system, the figure-of-eight pattern in azimuth is obtained by placing two Alford loops side by side and exciting them with equal but out of phase signals. Let us consider two small circular loops (i.e. radius of the loop < < X ) carrying the currents of the form _ -itt, I -i(at+ ~) I e1 and Iei( t+ ) o o be oriented along the x-axis as shown in Fig. 3. 10

3051-2-T z P (Ro0 e,) eI Alford Loop Alford Loop i d x FIG. 3: Coordinate System Used. The two loops lie in the xy plane. The two loops are separated by a distance 2d and the phase difference 0 between their currents is kept arbitrary for the present. It can be shown that the far field produced by the system at the point P(Ro, e, 0) is polarized in the p-direction and is given by: i(kRo- u/2) E ka2e ( E0=t^oio( 2 ^) R~ - 2sin~cos[kdsinecos0+ ] (41) where r~ is the intrinsic impedance of free space, k = 27r/X is the propagation constant in free space. If b = ir, then Eq. (41) reduces to the following 11

3051-2-T ikR E i2r Ik 2 R sine sinkd sin0 cos. (42) Eq. (42) indicates that in the azimuthal plane (6 = constant) the far field pattern is a figure-of-eight having maxima along: = 0 and r. Usually kd < 1 and under this assumption we can simplify (42) as follows: ikRo E= i 2r (!)2 e (d) sin2 0 cos. (43) Any parasitic loop, placed with its axis along the z-axis will carry an induced current proportional to the field given by (43) 'or (42) as the case may be. To simplify our analysis we assume that the parasitic current in the present case is of the following form: I =1 oos, (44) 0 where I, is a constant and p is measured around the loop, the origin being at the x-axis. Equation (4) physically means that I(0) vanishes at 0 = 7/2 where it reverses direction, so that the currents in the range 2-v-2 are always counterclockwise when the currents in the range I c < 37r are clockwise. This may be looked upon as a dipole mode such that the charge density on the loop is q (a) a sin p. This means that the loop is oppositely charged at 0 = -r/2 and 0 = - 7r/2 and the current oscillates in synchronism on the two halves much as in two parallel dipoles that are driven in phase. Notice that this is true regardless of the fact whether the parasitic loop is large or small. 12

3051-2-T 3.3 Far Field Expressions In this section we obtain the far field produced by a circular loop carrying a current of the form given by Eq. (44). The loop is oriented in the x-y plane as shown in Fig. 4. z P (Re, 0) / ) = Io coos 0 B x FIG. 4: Orientation of the Circular Loop. To obtain the far field it is convenient to determine the vector potential A produced by the current at the far field point P(Ro, 8, 0) and then obtain the field from the potential. With time dependence e and using standard notation the following expressions define the relationships between the fields and the vector potential: A A - E -iwr x (r xA) iw= Ae+ A, o - 0 ' B (45) B = ik (r x A) = ik[ A- ^, (46) A A A where ro, a, 0 are the unit vectors in R, O and 0 directions respectively. The components Ae, Ap of the vector potential in terms of the rectangular components are: 13

3051-2-T Ae =Axcos +Ay sin] cos,. (47) A0= -Ax sino+Aycos *. (48) In the present configuration, as shown in Fig. 4, Ax and Ay are given by the following: A B ikR4 2 fd A = e 1 I( ' ) e-ikBsin9cos(-) s d' (49 0 B ikRo 2r BA = kQ R e2 R r e-ikBsincos(0-') Co)(50) y) e os )' djb (50) where o is the permeability of free space. After introducing (44)into (49)and (50) the following two equations are obtained: BI ikRo 2v To evaluate the integrals in (51) and (52) we make use of the following result: A B: o inl e-ikB sin0cos(.',) sin, d' y = oI~e eoikBsineoos(o_0,) (1+cos2~')d'. (52) 87r Ro 27 ei(n 1)' eikBsincos(-') do =2rin+ i (ne 1) j (kBsine) (53) where J +1 is the standard notation for the Bessel function of the first kind. n.l 14

3051-2-T Using (53), we obtain the following from (51) and (52): p BI ikRo A = R J2(kBsin0)sin 2, x 4 Ro p BI ikRo A = -~ R [J (kBsin0)-J (kBsin9)cos 2 0]. o (54) (55) After introducing (54) and (55) into (47) and (48) and with some algebraic manipulation, we obtain p, BI O O A = 19 2 p BI O o A = - 0 2 eikRo J (KBsin0) R (kBsine) cos sin 0 ikRo eR J (kBsin8) cos, 1 0 (56) (57) where the prime in Eq. (57) indicates differentiation with respect to the argument. Using Eq.(45) along with Eqs. (56) and (57), we obtain the two components of the electric field in the far zone as given by the following: 9 'o o0( 2 R 0 J (kBsin8) (kB sin@) cossin0 (58) (59) B kRo 00 2 R 1 With uniform current, a circular loop does not produce any 0-component of the electric field. Thus, the existence of Es in the present case is attributed to the non-uniform current carried by the loop. 15

3051-2-T 3.4 Discussion On the basis of Eqs. (58) and (59), we make the following comments with regard to the radiation field produced by a circular loop carrying a non-uniform current I = I cos 0: (i) Near 6,0~ the Bessel functions in (58) and (59) may be replaced by their small argument values i.e. J'(x) -- 1/2 and J1(x) /x A 1/2. Thus the total far field may be written as -* A A E = Eo +0 E0 kB eWRO 1 oAs 0 =kB eik 0 1 A 0 Eq. (60) means that hear the axial region of space (6^0~) the far electric field is not equal to zero and it is polarized along the y-direction. (ii) In the 0=0~ plane, i.e. in the vertical plane containing the directions of maxima of the figure-of-eight excitation, the field is polarized in the 0-direction and is given by: EO= 0 kB e (61) E i770 Io (-R) Jt (kB sin (61) 0 16

(iii) In the 0 = - plane i. e. in the vertical plane containing the directions of minima of the figure-of-eight excitation, the horizontal (i. e. 0-component) component of the electric field is identically equal to zero and the electric field is given by: kB eikRo J (kBsinO) E= i n o I o (-) R0 (62) 0 o 2 R (kBsin) cos e, (62) 0 E 0 87r (iv) Inthe = - plane ikR J (kBsine) kB e o cos 6 Ee Io ( ) R (kBsinR) (6) 0 ikB kR J (kBsine) E 7i'( ) 0 e (64) 0 2 Ro (v) In the horizontal plane (0 = ) 2 E =0 Ee-0 kB eikRo E in k(B ) R J (kB) cos (65) 2 R o The implications of the above comments will be investigated in the future in connection with the radiation field produced by a non-uniformly excited parasitic loop counterpoise antenna. The results obtained can be used in the future to develop a theory for the radiation field produced by a non-uniformly excited parasitic loop counterpoise antenna. The important findings of the present investigation are that the non-uniformity of the current produces the following two effects: (i) the field is non-zero in the axial direction, and (ii) there -exists a crosspolarized component of the field. 17

3051-2-T By assuming an excitation of the form given by Eq. (42) (which is the case with the standard VOR antenna) we have obtained theoretical expressions for the far field produced by a loop counterpoise antenna (no parasitic loops). Currently this expression is being programmed and the results will be reported later. 4. Experimental Investigation of Non-Uniformly Excited Double Parasitic Loop Counterpoise Antenna Non-uniform excitation of the parasitic loop counterpoise antenna gives rise to some new phenomena not encountered in the uniformly excited cases. In general for the non-uniform case, the fields incident at the parasitic loops are different than in the uniform case. As a result of this the performance of the antenna is expected to be different than the latter. The non-uniform currents in the parasitic loops produce strong lobes in the axial directions. If they are found objectionable, their amplitudes can be considerably reduced by properly choosing the heights of the parasitic loops above the counterpoise. For example the axial lobe amplitude would be minimum if the height H of the parasitic loop satisfies the relation H = n /2 where n is an integer and X is the wavelength. Since the nature of the excitation is different, it is also anticipated that the optimum parameters necessary for obtaining the best field gradient from the antenna would be different than those for the uniform case. In view of the above, we have undertaken a systematic experimental investigation of the non-uniformly excited parasitic loop counterpoise antenna. The results reported below have been obtained from a 5. 2' diameter counterpoise case and the measurements have been carried out in our indoor antenna pattern range. This was done because of bad weather conditions outside. The pattern characteristics have been measured at the frequency 1080 MHz (X = 10. 93" ). The excitation used has been a pair of Alford loops spaced 3.2" apart and located at a height 4'8" above the counterpoise. The two loops are excited out of phase so that the combined field produced by them has a figure-of-eight variation in the azimuthal plane. All the parasitic loops 18

3051+2-T used have been fabricated from 1" wide conducting strips. 4.1 Preliminary Experiment An initial radiation pattern investigation has been carried out for a double parasitic loop system with H = 22 " 2B2= 36 " 2 8' 2 and H B1 variable, (see Fig. 1 for the notations). The purpose of this experiment has beento determine the effects of the parameters H1, B1 on the pattern and in particular to search for those values of H1 andB1 which may produce large field gradients at the horizon. The parameters H2, B2 were chosen on the basis of our previous investigation of single parasitic loop counterpoise antennas (Sengupta and Ferris, 1969). The far field elevation patterns of the antenna have been measured at 1080 MHz with 2B1 varying in steps of 4" from 36" to 60" for each value of H1. H1 was varied from 4" to 7" in convenient steps. The main conclusion from this set of pattern results is that for low axial lobe and reasonably large field gradient Hi~ 6" and 2B1 should lie between 48" - 60". The important pattern characteristics obtained from this experiment are shown in Table 1. The different nOations used in Table 1 are given below. E max E(T/2) E(960) ES g E (00) Ea=E(r/2) The amplitude of the far field in the direction of the principal maximum. Amplitude of the far field in the direction of the horizon i.e. 0 = r/2. Amplitude of the far field in the direction e = 96~. Amplitude of the first secondary lobe maximum below the horizon. The field gradient/6~ at the horizon. Amplitude of the far field in the direction 0=00. Level of the secondary lobe maximum field relative to the field at the horizon. All the above results are expressed in dB. 19

3051-2-T Table 1: Pattern Characteristics of a Non-Uniformly Excited Double Parasitic Loop Counterpoise Antenna. H2= 22 3/8", 2B2=36', H1=6", 2B1 variable. 2B1 36" 40" 44" 48" 52" 56" 60" E -3.0 -5.5 -3.0 -3.0 -5.0 -5.0 -6.0 max E(7r/2) -28.5 -22.0 -19.0 -25.0 -22.0 -22.0 -32.0 E(96~) -35.0 -25.5 -28.0 -35.0 -29.0 -33.0 <-40.0 E -27.0 -- -32.0 -28.0 -- -35.0 -33.0 E(00) -22.0 -17.0 -16.0 -19.0 -19.0 -25.0 -23.0 ag 6.5 3.5 9.0 10.0 7.0 11.0 > 8.0 Es-E(7r/2) 1.5 --- -13.0 -3.0 -- -13.0 -1.0 The values that are left out in the above table were found to be not applicable to the measured patterns. Three complete patterns are shown in Figs. 5a - 5c for three selected cases. 4.2 Optimization of the Lower Parasitic Loop Parameters The next set of data have been taken for the purpose of obtaining the best values of the lower parasitic loop parameters H1, B1 for some fixed values H2, B2 of the upper parasitic loop parameters. During this experiment the upper loop parameters were fixed at H2= 22 3/&", 2B2= 36". The diameter of the lower parasitic loops were varied from 54" - 60" in steps of 2". For each value of 2B1, H1 was varied from 5" - 7" in some convenient steps. The various pattern characteristics as obtained from the measured elevation patterns are shown in Tables 2, 3, and 4. 20

FIG. 5a: Measured Elevation Patterns of a Double Parasitic Loop Counterpoise Antenna. 2A=5.2', h=4.8", f=1080 MHz, 2B2=36", H2= 22 3/8", H1=6" and 2B1=36". 21

FIG. 5b: Measured Elevation Patterns of a Double Parasitic Loop Counterpoise Antenna. 2A=5.2', h=4.8", f=1080 MHz, 2B =36", H2 22 3/8", H1 6" and 2B = 44 22 22

FIG. 5c: Measured Elevation Patterns of a Double Parasitic Loop Counterpoise Antenna. 2A=5.2', h=4.8", f=1080 MHz, 2B2=36", H2 22 3/8; H1=6" and 2B= 60". 23

3051-2-T Table 2: Pattern Characteristics of a Non-Uniformly Excited Double Parasitic Loop Counterpoise Antenna. 2B2=36", H2= 22 3/8", 2B1=54", H1 variable. H1 E max E(ir/2) 5 1/2" -7.0 -22.0 5 3/4" -7.0 -23.0 6" E(960) -28.0 E8 E(0o) Cg -30.0 -28.0 -23.0 -32.0 -22.0 9.0 -27.0 6.0 7.0 Table 3: Pattern Characteristics of a Non-Unlformly Excited Double Parasitic Loop Counterpoise Antenna. 2B2=36", H2=22 3/8", 2B1=56", H1 variable. H1 5" 5 1/2" 5 3/4" 6" 6 1/4" 7" Eax -5.0 -5.0 -5.0 -5.0 -5.0 -5.0 E(r/2) -20.0 -21.0 -22.5 -23.0 -24.0 -26.0 E(960) -26.5 -30.0 -32.0 -32.0 -33.0 -35.0 Es -37.0 -- -- -36.0 -33.5 -31.0 E(0) -22.0 -30.0 -30.0 -24.0 -20.0 -15.0 ag 6.5 E -E (r/2) -17.0 5 9.0 9.5 9.0 -13.0 9.0 -9.5 10.0 -5.0' Table 4: Pattern Characteristics of a Non-Uniformly Excited Double Parasitic Loop Counterpoise Antenna. 2B2=36", H2= 22 3/8", 2B1=58", H1 variable. H1 5 1/2" 5 3/4" 6" Emax E(7r/2) E(96~) ES E(Oo) -6.0 -24.0 -35.0 -36.0 -28.5 -6.0 -25.0 -35.0 -36.0 -29.0 10.0 -11.0 -6.0 -26.0 -35.0 -35.0 -26.5 9.0 -9.0 cg 11.0 Es-E(7r/2) -12.0 24

3051-2-T From the previous tables it is found that for values of the parameter H1 between 5 1/2"? and 5 3/4?? the lobe maximum in the direction 0=0~ is minimum. Notice that theoretically, for minimum axial lobe H1= X/2 = 5.465" at f=1080 MHz. From the results given in this section, it appears that the best pattern for possible VOR application is obtained when 2B2= 36", H2= 22 3/8?", 2B1= 56? and Hi= 5 3/4". The measured elevation pattern for this case is shown in Fig. 6. 4.3 Optimization of the Upper Parasitic Loop Parameters In this set of experiments the lower parasitic loop parameters were fixed at 2B1=56" and H1=5 3/4". The height of the upper loop was fixed at the value H2= 22 3/8" while the diameter 2B2 was varied from 34" -- 40". The results are shown in Table 5. Note that the field gradient values shown in Table 5 have been obtained from the measured polar plots and hence are approximate. More accurate values for ag in some specific oases will be discussed in the next paragraph. Table 5: Pattern Characteristics of a Non-Uniformly Excited Double Parasitic Loop Counterpoise Antenna. 2B1=56?", H1=5 3/4", H2= 22 3/8", 2B2 variable. 2B2 34" 35" 36" 37" 38?" 3 9" 40" Emax -5.0 -5.0 -6.0 -6.0 -6.0 -5.0 -5.0 E(r/2) -19.5 -20.5 -21.0 -22.5 -24.0 -25.5 -24.5 E(96~) -26.5 -28.0 -29.5 -32.0 -35.5 -36.0 -34.0 E.. --- -- -36.0 -34.0 -32.0 -31.0 E (0O) -27.0 -28.0 -28.0 -29.0 -35.0 -35.0 -35.0 g 7.0 7.5 8.5 9.5 11.5 11.5 9.5 E -E(7r/2) --- --- -13.5 -10.0 -10.0 46.5 A typical measured pattern having desirable characteristics is shown in Fig. 7. To obtain more accurate estimates for the field gradients, rectangular plots for the patterns have been obtained in ordinary and expanded scales for some selected cases. The patterns obtained in a few interesting cases are shown in Figues 8, 9a - 9b, and 10a - 10b. As can be seen from these figures a field gradient value better than 12 dB can be obtained without appreciably increasing the field in the axial direction. 25

FIG. 6: Measured Elevation Pattern of a Double Parasitic Loop Counterpoise Antenna. 2A=5.21, h=4.8", 2B1=56", H1= 5 3/4", 2B2=36", H2= 22 3/8", f - 1080 MHz. 26

FIG. 7: Measured Elevation Pattern of a Double Parasitic Loop Counterpoise Antenna. 2A=5.2', h=4. 8", 2B1=56", HI= 5 3/4", 2B2= 40", H2= 22 3/8", f = 1080 MHz. 27

-44 i J - i - ~ 62 50 ' 90 0 320 00205 FIG. 8: Measured Elevation Pattern of a Double Parasitic Loop Counterpoise Antenna. A5.2,h48,2B=56", 111= 5 3/" B= 40"1, H= 22 3/8"1, f = 1080 MHz.

I. . I I i, i - . + -- I i.. I I t 'IQ CV cq4 0 29

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Xio ~d!: ' 6 - FIG. 10a: Measured Elevation Patterni of a Double Parasitic Loop Counterpoise 25' i -i2'0 - - I \ 2I J L4:..: ' -: ---r..?,,o, o- 1- 0,, 6,0 3, 'o0 6,0- 10 0 150 1 FIG. 10a: Measured Elevation Pattern of a Double Parasitic Loop Counterpoise Antenna - Complete Pattern. 2A=5.2',h=4.8", 2B1=56", H1=5 3/4", 2B2= 38", H2== 22 3/8, f=1080 MHz.

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3051-2-T 4.4 Maximum Obtainable Field Gradient Two main criteria governed the basis of the investigations discussed in the preceding sections. These are (1) the field gradient at the horizon be high, and (ii) the axial lobe amplitude be as small as possible. In this section we give the results obtained from an experiment where the second restriction on the pattern has been removed. The aim of this part of the investigation has been to determine the largest value of the field gradient that can be obtained from a double parasitic loop counterpoise antenna. The results are shown in Figs. lla and lib. In this particular case the field gradient at the horizon is found to be better than 22 dB/6~ which may be considered to be a dramatic improvement. 5. Discussion The above results represent the present status of the theoretical and experimental investigation of the radiation characteristics of non-uniformly excited parasitic loop counterpoise antennas. The experiments results for the 5.2' diameter counterpoise case are almost complete. Development of the theortical expressions for the radiation field and their numerical evaluation will be done during the coming period. 6. Conclusion On the basis of the results given above it can be concluded that the parasitic loop concept has been found to be highly effective in improving the field gradient characteristics of a non-uniformly excited parasitic loop counterpoise antenna. From our investigation of the -radiation characteristics of a double parasitic loop counterpoise antenna having figure-of-eight type of excitation we make the following two important observations. (i) It is possible to obtain a field gradiant at the horizon better than 12 dB/6~ while maintaining the field in the axial direction to be less than 25 dB down from the field in the principal maximum direction. (ii) It is possible to obtain a field gradient at the horizon better than 22 dB/6~ while maintaining the axial field to be less than 16 dB down from the field in the 33

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O )1.9 C o4: '-4 I 35

3051-2-T principal maximum direction. In all the above cases the secondary lobe maximum below the horizon has been found to be about 9 - 12 dB down from the field at the horizon. 7. References Sengupta, D. L., J. E. Ferris and V.H.Weston (1968), "Theoretical and Experimental Investigation of Parasitic Loop Counterpoise Antennas - Final Report, t The University of Michigan Radiation Laboratory Report 8905-1-5, FAA Report No. SRDS, RD-68-50. Sengupta, D. L., and J. E. Ferris (1969), "VOR Parasitic Loop Counterpoise System-Ht," Interim Report No. 1, The University of Michigan Radiation Laboratory Report 3051-1-T. Sengupta, D. L. and V. H. Weston (1969), "Investigation of the Parasitic Loop Counterpoise Antenna,?t IEEE Trans., AP-17, No. 2, pp. 180-191. 36