3051-3-T = RL-2094 30513T THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL ENGINIERING Radiation Laboratory VOR PARASITIC LOOP COUNTERPOISE SYSTEMS - H Interim Report No. 3 (1 February - 30 April 1970) By Dipak L. Sengupta and Joseph E. Ferris 15 May 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 Administered through: OFFICE OF RESEARCH AD-MINISTRATION * ANN ARBOR

3051-3-T 1. Introduction This Is the Third Interim Report on Contract FA 69-WA-2085, Project 330-001-03N "VOR Parasitic Loop Counterpoise Systems-1I," and covers the period 1 February to 30 April 1970. During this period we have developed theoretical expressions for the radiation field produced by a loop counterpoise antenn having a figure-ofeight type of radiation pattern in the azimuthal plane. This is the type of antenna which is n actual use n an existlng VOR system. The theoretical patterns have been compared with measured results at the frequency 1080 MHz. Excellent agreement has been obtained between the two. As far as we are aware, this Is the first time that an accurate theory has been given for the existing VOR antenna radiation patterns. This theory has been modified and generalized to the oase of the parasitic loop counterpoise antenna with a figure-of-eight type of excitation. Theoretical patterns obtained from numerical computation of these expressions are given for some typical cases. The experimental investigation during this period has been directed towards the 151 diameter counterpoise case. This has been done to develop the appropriate parameters for the full scale parasitic loop counterpoise antenna. 2. VOR Antenna Radiation Patters In this section we develop and discuss the theoretical expressions for the radiation field produced by existing VOR antennas. Such an antenna consists of a pair of Alford loops sdiably excited and placed at a convenient height above a circular ground plane or counterpoise. We refer to this antenna as the loop counterpoise antenna. The two Alford loops lie in the same plane which is parallel to the plane of the counterpoise. The Alford 1

3051-3-T loops are separated by a distance, 2d, small oompared to a wavelength and are exoited with signals having equal amplitude but opposite phase. Thus the free space azimuthal pattern of the antenna would be a figureof-eight. 2.1 Theory For the purpose of theoretical analysis the VOR loop counterpoise antenna is replaced by a point source with appropriate far field variation placed above the counterpoise as shown in Fig. 1. z ~ f 'P(R,Q,p) point source. o /o I ro // / / I. // A 7 7 7 - 2A - z -x FIgure 1 2

3051-3-T The free space radiation field of the point source (in the absence of the counterpoise) can be repreented by: i 2 ikR E,=0I0(fo, (2.1) where, R, 0, 0 are the usual spherioal coordinates of the far field point with origin at the point souroe, 7O Is the intrinsic mpedance of free space, k = 2/X is the free space propagation constant, I is the amplitude of the current in the Alford loops, a is the equivalent radius of the Alford loop, f(0, 0) is the pattern function which is determined by the method of excitation and orientation of the two loops. Note that the field in (2.1) is polarized in the 0-direction. The symmetry of the system dictates that the far field produced by the antenna shown in Fig. 1 will also be polarized in the p-direction. In the present case, the two Alford loops are excited with equal amplitudes but opposite phase so that f(,, 0) can be written explicitly as follows: f(, =2 sin (kdin d cos ). (2.2) Equation (2.2) means that in the azimuthal plane 0 = 1/2, the pattern is a figure-of-eight having a maximum along the x-axis. With the incident field given by (2. 1), the far field produced by the loop counterpoise antenna shown in Fig. 1 can be obtained by applying the concepts of geometrical theory of diffraction and the 3

3051-3-T results of Sommerfeld's theory for half-plane diffraction. We do not give the details of the method here since it has been discussed in a previous report (Sengupta et al, 1968) where it was assumed that f(e,0) i. It can be shown that the far field expression valid in the transition region and defined by < < + 0 is givenby ik(R-A sin ) Er~n ~R (,.0) I[u(r.,.)-v(ToU, ~'). (2.3) ~ o o I ~ R - — )1 o 1 o 2.. where o~ikr (0 t lfplr U(r e-)=ikr (ci) e 2 dt (2.4) -o) ~1 o Po 2 9 (22 - - - +j+e (2.5) k2 co % o+ p = 2 ( o8 (2.6) 2f 2 The near edge diffracted field valid in the region 0 <_6< - is given by: 0 co e sin( ) Eo - %I o() f(o't). i.. 3 12 I lk(R-A sO +r ) coo (2.7) Xrkr in0 81-inG e e (27) The far edge diffracted field valid in the region 0 < < - < is given by: 4

3051-3-T -i (-kAsine) ikr ka2. e 4 e 0ik 0E- - 2 0i _ _ 0_ R cos3/2 cos Osin (2.8) co0+ 4i1 _i__'_ With the above field expressions it ti now poMsible to develop a single expression for the far field which is valid in the region 0 < <. This can be done by starting from the transition region field given by (2.3) and modifying it to account for the different contributions in the various regions of space. The complete far field expression, thus obtained, can be expressed as: i(kR-/4 ) E 0070 (' R S (), (2.9) where, A = F~() sine f(e, 9)-ikA sin +....... e L(.() (2.10) k osin Pi S2 F~(8)= e o) i 7 dt -Mo ikr sin(9+0 fP 1t e e 2 dt (2.11) -00 5

3051-3-T i( -kA sin, /2 ) h-si n' P - 81sn 312 eikA dsin fO.. (2. 1) /1 +' oo..+si.'. f(e, I = 21 in (kd sine co ). (2.13) Equations (2.9) through (2.13) have been used to oompute the far field field pattern produced by loop counterpoise antennas that are used In existing VOR antennas. To the best of our knowledge the expressions given above are new and appear here for the first time. 2.2 Comparison Between Theory and Experiment The measured free space far field elevation patterns of loop counterpoise antennas are shown in Figs. 2, 3 and 4 for three selected values of the counterpoise diameter. All the patterns have been measured in the x-z plane of Fig. 1 and at the frequency of 1080 MHz. The corresponding theoretical patterns as obtained by numerical computation of Eqs. (2.9) through (2. 13) are also shown in Figures 2 through 4 for comparison. The agreement between theory and experiment for the cases with kA = 17.92 (2A = 5.2') and kA = 51.69 (2A = 15') may be considered to be very good. The minor lobes in the pattern in directions e > r// 2, as well as the kink in the pattern near 9 6 ir/2 for the case kA = 51.69 are attributed to the outside pattern range and the feed system. The agreement between theory and experiment for the case kA = 6.32 (2A = 22" ) is not as good although it may be considered to be fair over 6

FIG. 2: Far-Field Elevation Pattern of a Non-uniformly Excited Loop Counterpoise Antenna. kh = 2.75, kd = 0.92, f = 1080 MHz, ka = 17.92 Experimental, ~ * ~ ~ Theoretical. 7

FIG. 3: Far-Field Elevation Pattern of a Non-uniformly Excited Loop Counterpoise Antenna. kh = 2.75, kd = 0.92, f = 1080 MHz kA = 51.69 - Experimental *~ * * Theoretical. 8

FIG. 4: Far-Field Elevation Pattern of a Non-uniformly Excited Loop Counterpoise Antenna. kh = 2.75, kd = 0.92, f = 1080 MHz, ka = 6.32, Experimental * * * * Theoretical. 9

3051-3-T most of the region. The reason for this is due to the small size of the counterpoise for which the theory becomes poor. It may be concluded from the results given in this section that the present theory can be used with sufficient accuracy to compute existing VOR antenna patterns having counterpoise 2A > 22"; the theory becomes more accurate for largeroourpoises. 3. Non-Uniformly Excited Parasitic Loop Counterpoise Atena Patterns In this section we give the theoretical expressions for the radiation field produced by non-uniformly excited parasitic loop counterpoise antennas. The theoretical model of a single parasitic loop counterpoise antenna is shown in Fig. 5. A double parasitic loop counterpoise antenna may be obtained from Fig. 5 by inserting another parasitic loop at the appropriate place. z z parasitic loop 2B- - _ p point source e F2AWe Figure 5 10

3051-3-T 3.1 S 1.gle Parasitic Loop Counterpoise Antenna Pattern As before, the free space far field produced by the excited elements only (represented by the point source in Fig. 5) is: ikR E = 0l (T M, ) sinO-I R (3.1) where f(6, 0) = 21 sin(kd sinO cos 0 ). (3.2) The first step in the analysis involves the determination of the current induced in the parasitic element. Parasitic Current. Let the total field incident at the point P on the parasitic loop be denoted by E (P). Then the parasitic current Ip is given by 0O 2w n (3.3) where kb r M = 0. 577 + In ( ) - i(3.4) The basis and nature of approximations involved in (3.3) has been discussed elsewhere (Sengupta and Weston, 1969) and will not be reported here. The incident field inc (P) consists of direct, reflected and diffracted fields. The derivation of the different field components that would be used inc in obtaining the parasitic current are shown in Fig. 6. Thus E (P) can be written formally as follows: E (P)E 2(P)+E56 (P). (3.5) P6 F E 11

3051-3-T Typical point on parasitic loop 6 A Figure 6 Explicit expressions for the oomponent fields E2 (P) and E (P) oan be obtained by following the method discussed by Sagupta et al (1968) and by Sngpts and Weston (1969). These expressions are; kr2 aIkr2 where r2 * B2 + (-)2, = B2 + (H+), (3.7) r ' (A 12

305 l3-T E 56(P)= ' 7 Ika2 2 81,0 0 o2 1 r 1 r, x ( 1)1/2i(2kIB+1) ir /2 1 -( 1jj)2 7T i (2k.H.j — e j (3. 8) Usin (3.3) ad(3. 6) through (3. 8) it can be shown that = 12 Ipop1 +I56 0 (3. 9) whore 12,ka 2 'p = I (-Mm-.~ 0 56 ka 2 0 2BF ir1 2 )2] Volbs 0) - 0 1kM L 1 2 r2 (3.10) 2 N 2 M ikr 1 - f2 [1/ i(2kB+ j ) 1 i(2kH-!!) e -M;( ) /20 4] (3. 11) We now make the following approximation valid for kId ~ 1,I f (GI$ ) =21 sin (kd sinG1o' 008 0'.. f (01) Cos f0o2* 0) = f(92 ) Cos where f (01) = 2i kd sin601 = 21 (kd) B fW )=2ikdsInO = 2i (kd)-B 2 2 r (3. 12) (3. 13)i (3.14) (3. 15) 13

3051-3-T After introducing (3. 12) through (3. 15) into (3. 10 and (3. 11) we obtain ikrl ikr 12 ka 2 2rB ( e 1P =Io( 2 ).B.1) 2 ( 2) ]<36) =o eo ( ) ( 02 (3.16) o r1 2 2 ikr 56 ka 2 r(kB)e 1 "^ ' T)....V o 2 M2 (kr )2 1/2 i(2kB+) I/ (2kHxe e coso (3. 17) Thus we can write the parasitic current expression Ip in the following form. I = 112 +56 co (3.18) o +o os, where explicit expression for Ip may be obtained after introducing Eqs. (3.16) and (3. 17) into (3. 18). I is important to note me'tthat due to the nature of excitation, the parasitic current is not independent of 0. This completes the derivation of the theoretical expressions for the current induced in the parasitic loop in a single parasitic loop counterpoise antenna with figure-of-eight type excitation. The Radiation Field. The complete radiation field produced by a non-uniformly excited single parasitic loop counterpoise antenna is obtained by vectorially adding the individual fields produced by the pair of Alford loops above the counterpoise and the parasitic loop above the counterpoise. The Aford loop counterpoise field is as given in the previous section. The parasitic field expression is derived below. 14

3051-3-T The free space radiation field produced by a circular loop carrying a current of the form given by Eq. (3.18) has been discussed earlier (Sengupta, 1969). In general the far 6lectric fields are: ikR E iIp (i 2) J' (kB sinG)coa - (3.19 k (kBuin) A.ikR E Ov 1II 0k 8$1n(3.20) where R, 0, 0 are the usual spherical coordinates of the far field point with origin in the center of the parasitic loop which lines intthe x-y plane, and J is the first order Bessel function of the first kind. For obtaining the principal plane field we are interested in the J = 0~ plane and thus we have: IkR E -I (kB siRn ) (3.21) E - 0. Let us obtain the p-component of the field. With the incident field given by (3.19) it can be shown that the far field produced by the parasitic loop above the counterpoise is given by the following expression valid in the region 0 < 0 <, iREP Ip ( i) F(-) cosj, (3.22) o P0 o -) R 15

3051-3-T where J' (kB sinG) -kAin F~o) =? F (O)e kAsn ikr~ p (3.23) l (j -kA sinG) [, Y2 )i'/2 L2G Coll__ OPJ'1(kB co6 -i J l(kB iO ~J1-siconL005 -sinG j -ikA sin 0 0 #1+mB (3.24) F~ p(6) =ekps-p) r5 Ur2 ikrs pi(96 2~ f edt.-e p n(+9 edct -00 (3.25) I v kr 1, Ma-6- krp 1/ 0 ++ p 9p,2 p 2 =2( ) coos( I 1 62 -- cos ( 2 0 (3.26) 2 2 2 rp A+H tan 0H (3. 27) The complete far field ts now obtained by combinin Eqs. (2. 9) ad(3. 22). It can be written formally as: I10kR-! EO^I (ka)o 2 e R S(G), (3.28) where SOe = StA(e) + SP'(e) + SP' (e) (3.29) 16

3051-3-T Explicit expressions for S (8) are given by Eqs. (2. 10) through (2. 13). The last two terms on the right-hand side of (3.29) are given by: P10( B) f8 _0-f62 F(6)o 00 (3. 30) 12 M(kr 2) (kr 2 - 2 2 ikr1 P iw(kB) e S (0= 56 2M2 (kr 2 1 1 i(2kB 1 1/2 i(kHW j)] X rkB eckH 3 For the purpose of numefical computation, the principal plane pattern (0-00 plane) is written in the following final form. A ( d 2 A sine Icosl sin( 02 ) ikr S (6)_ e + 2 e L to 4Irkr 0ine (3.32) i (! kA sinG) iOkd)co -1s'2 kd s 4wkr sine' coos0 - sin G 0 5/ ikA sin 6 -2kd)cos /2 41+ine' I os0+sin, (3.33) P r(kB)2 k e BMr, B e ilr2 = ()ikd - k 2ikd - F(G), (3.34) 12 M L_ r (r)2 r2 (kr )Y rl (k2 17

3051-3-T 2 2 ikr P (o) =i (kB)2 e 1 (kSB) ~k ) e ) e (), (3. 35) and the other parameters are as defined before. 3.2 Double Parasitic Loop Counterpoie Antenna Patterns In the absence of mutual coupling between the parasitic loops, the theoretical expressions for the radiation field produced by a double-parasitic loop system can be obtained by a simple modification of the theory given in Section 3. 1. The far field produced by an antenna consisting of the excited Alford loops, parasitic loop No. 1 and the counterpoise can be written as iO(R-j ) Eka = o 2 e (.36). 1 2 R 1 where Sl(O) = sA() + S 2 (6) + S 6 () (3.37) and all th6 other notations are as explained in Sect. 3. 1. All the parameters involved in the detailed expressions of Eq. (3. 31) (see 3.32 through 3.35) should pertain to the parasitic loop No. 1. Similarly, the far field produced by the parasitic loop No. 2 above the counterpoise can be written as i(kR- ) = ( R (3.38) 00 R 8 18

3051-3-T where 2 (e) = S 12(e) + ( (3.39) In Eq. (3.39) the terms on the right hand side are given by (3.34) and (3.35) with the understanding that the different parameters involved pertain to the parasitic loop No. 2. Thus the complete far field produoed by the non-uniformly excited double parasitic loop counterpoise antenna in the range 0 < 0 < r is given by i(kR-4) Ik)2 [S1(8)+ S () (3.40) 3.3 Numerical Results The theoretical expressions given above have been computed numerically to obtain the far field patterns produoed by non-uniformly excited inqle and double parasitic loop counterpoise antennas. One of the typical patterns is shown in Fig. 7. Observe that in Fig. 7 the theoretical field gradient is about 20 dB/6~. Detailed discussions of the numerical and experimental results will be given tn'a later report. 4. Exprimental Investigation The experimental investigation of the patterns produced by the nonuniformly excited double parasitic loop antenna with 151 diameter counterpoise is in progress. The optimum performance obtained theoretically are being tested experimentally. All these results will be reported later. 19

0 r -10 I-20 I9 a% wz flG. 7: Theoretical Far-Field Elevatiorn Pattern of a Non-uniformly Excited Double PakWi Loop Counterpoise Antenna. kh = 2. 75,0 kd = 0. 92, kBI =16.02, kH = 3. 45, kB2 = 11., kH2 =12. 65.,kA =51. 69, f =1080 M 31 [Hz. -.40 I -50 -60 I 0 10 2- 30 40 50 60 70 80 90 100 110 120 130 140 150 0 in degreeis 160 170 180

3051-3-T 5. Conclusions The above results represent the current status of the theoretical and experimental investigation of the radiation characteristics of nonuniformly excited parasitic Idop counterpoise antennas. The significant contribution during this period has been the development of a satisfactory theory for the existng VOR antennas consisting of Alford loops above a counterpoise. We have also developed a theory for the patterns produced by a non-uniformly excited parasitic loop counterpoise antennas. The theory would be compared with measured results during the coming period. On the basis of the theoretical results given above and the experimental investigation currently in progress, the design parameters for the full scale double parasitic loop counterpoise antenna will be developed. 6. References Sengupta, D. L., J.E. Ferris and V. H. Weston (1968), "heoretical and Experimental Investigation of Parasitic Loop Counterpoise Antennas Final Report," FAA Report SRDS RD-68-50, University of Michigan Radiation Laboratory Report 8905-1-F. Sengupta, D. L. (1969), "The Radiation Field of a Circular Loop C&rrying a Non-Uniform Current," Radiation Laboratory Internal Memorandum 3051-504-M. Sengupta, D.L., and V. H. Weston (1969), "Investigation of the Parasitic Loop Counterpoise Antenna," IEEE Trans., AP-17, No. 2, pp. 180-191. 21