011218-4-T 11218-4-T = RL-2214 THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINURING DEPARTMENT OF ELECTICAL AND COMPUTER ENGINEERING Rodiation Laboratory COURSE SCALLOPING AMPLITUDES IN STANDARD VOR BEARING INDICATIONS By Dipak L. Sengupta and Philip Chan 15 June 1973 Interim Engineering Report No. 4 Contract No. DOT-FA72WA-2882 Project No. WA5R-1-0526/N1113-739. 0 Contract Monitor: Sterling R. Anderson, RD 331 Prepared for: FEDERAL AVIATION ADMINISTRATION Buzzards Point Building 2100 Second Street, S. W. Washington, D. C. 20591 2216 Space Research Building 2455 Hayward Street Ann Arbor, Michigan 48105 (313) 764-0500

0112 18'4-T I INTRODUCTION This is the fourth Interim Report on Contract No. DOT-FA72WA-2882, "Application of the Large Gradient VOR Antenna, "1 and covers the period 1 March 1973 to 31 May 1973. The theory of course scalloping amplitude in standard VOR bearing indications has been discussed in our third Interim Report [ii. The present report discusses the numerical results for the course scalloping amplitudes in the bearing indications of a standard VOR system under various situations. The scatterer producing the scalloping errors is assumed to be isotropic and located at various heights above a perfectly conducting planar earth. Numerical results for the scalloping amplitudes are obtained when the VOR ground station uses standard and large gradient antennas with variable gradients. The effects of the height of the VOR transmitting antenna above ground on the scalloping amplitudes are investigated in detail. 1

011218-4-T II COURSE SCALLOPING AMPLITUDE EXPRESSION The geometry of the VOR ground station antenna, the isotropic scatterer and the observation point located at a stationary aircraft are shown in Fig. 1. The VOR antenna is located at (Zo, 0, 0), the scatterer at (d1, 0, f ) and the ground plane is at z = 0; the coordinates of the observation point are (r, 0, 0). Sometimes it may be found convenient to represent the location of the scatterer by the parameters H and D as shown in Fig. 1. Note that tan 01= (1) H z P(r, 8, A) OBSERVATION POINT AT THE STATIONARY AIRCRAF VOR ANTENNA ^ (Zo, 0, 0) 1 d (d. 0.) SCATTERER ^ y x ^ GROUND AT z O 0 Fig. 1: Location of the VOR transmitting antenna, the scatterer and the observation point at the stationary aircraft. It is assumed that at the observation point an ideal receiver receives the signal transmitted by the VOR ground station. It can be shown [1i that in the presence of a scatterer the course scalloping amplitudes in the bearing indications of a standard VOR receiver at the observation T 2

011218-4-T point P are given by: T 2A - T sin(kHcos ) sin (0 - 01) s (e) 1~+2A -| sin (kH cos 0) cos (00 1) where, k x 27r/X is the propagation constant in free space, A is the generalized scattering coefficient for the scatterer and is, in general, a function of the coordinates of the scattering object and the observation point, T S (0) is the side-band mode elevation plane complex pattern of the S VOR transmitting antenna located above ground. T S (6) is related to the corresponding free space pattern of the VOR antenna by the s following: -ikZ cos ikZ cos 0 S (0) S (e)e -S (ir- Oe (3) where S s(0) is the side-band mode elevation plane complex pattern of the VOR transmitting antenna in free space. Equation (2) indicates that during an orbital flight around the VOR station, the maximum bearing errors, i. e., the scalloping amplitudes as observed in the aircraft receiver will lie between the limits S1 and S2. We emphasize here the following basic assumptions made in obtaining Eq. (2): (i) the carrier and the side-band mode fields are in RF phase for all 0, (ii) the scatterer is located in the far zone of the VOR antenna. The general effects of the different parameters on the scalloping amplitudes are discussed in [1] and will not be repeated here. 3

011218-4-T For simplicity we shall assume that the scatterer is isotropic, i. e., A is a constant and is independent of the coordinates of the scatterer and the observation point. 4

011218-4-T m FREE SPACE PATTERN CHARACTERISTICS OF THE VARIOUS VOR ANTENNAS In the present section we discuss the pertinent characteristics of the free space patterns of the various VOR antennas used during the investigation of the scalloping amplitudes. The antennas used are the standard four-loop array above a 52' diameter counterpoise (or the standard VOR antenna), the double parasitic loop counterpoise antenna (DPLC antenna) and stacked arrays of VOR four-loop arrays. Detailed discussion of these antennas and the patterns produced by them when located in free space and above ground may be found in [2], [3]. The important free space side-band mode elevation plane pattern characteristics of the above antennas operating at 109 MHz are shown in Table I. Prope: 0 max "f a/6 g ee O 0 I TABLE I FREE SPACE SIDE-BAND MODE ELEVATION PLANE PATTERN CHARACTERISTICS OF VOR ANTENNAS AT 109 MHz rty* Standard DPLC Stacked Arrays VOR 1 2 3 60~ 60~ 74~ 74~ 73~ 9.47dB 16.50dB 8.88dB 7.75dB 6.64dB 0 3.05 dB 21.22dB 16.93dB 10.20dB 6.74dB 4 740 5.72dB 5.22dB miax is the position of the principal maximum field strength at 0 = 0 max zf s field strength at 0 = 7r/2 (horizon) e x field gradient at the horizon per 6. 0 Observe that the antennas listed in Table I have different field gradients. The four stacked arrays are obtained by using four different excitations appro 5

011218-4-T priate for the indicated field gradients [31. Further information about the antennas and their patterns may be found in the references cited. 6

011218-4-T IV VARIATION OF S1 AND S2 For orbital flights Eq. (2) indicates that S1 evaluated at Tr + (0 - 0) S2 evaluated at (0- 01) and vice versa. This implies that in order to study the scalloping amplitude variation during an orbital flight it is sufficient to calculate S1 (or S2) in the range 0 < (0-01) < 2r or calculate S1 and S2 in the range 0 <(l-01) <, s (e It can be seen from Eq. (2) that for A << 1 and 2 --- < 1, the Ss (e) scalloping amplitude is directly proportional to the scattering coefficient A. Figure 2 shows the variation of S2 in the direction (0 - 01) = 60~, 0 X 0in a 78.5~, as a function of A. The results apply to the case of a VOR system using a standard VOR antenna located 151 above ground; an isotropic scatterer is located at a distance D = 1000' and at a height H X 7.21 above ground. The height of the scatterer H is chosen such that for the observation angle 0 =. i 78. 5~, kH cos 0 min 7/2, where 0 min is the direction of the minimum closest to the horizon in the elevation plane pattern of the antenna. This has been done to remove direct dependence of S2 on H (see Eq. (2)). For the range of values of A shown in Fig. 2, the scalloping amplitude is found to increase almost linearly with the increase of the scattering coefficient. The complete variation of the scalloping amplitude during an orbital flight is shown in Fig. 3 (a) for a standard VOR antenna located 50' above ground and for different heights of an isotropic scatterer located at different heights above ground. The scatterer is located 1000' away from the VOR antenna. The scalloping amplitudes shown in Fig. 3 (a) are S1 in the range 0 <(- 0 ) < r and S2 in the range rT < (00-01) < 27r. The orbital flight is assumed to take place at an elevation angle such that it corresponds to the minimum nearest to the horizon (0= 90 ) of the elevation plane of the antenna. Similar results are shown in Fig. 3 (b) when the elevation angle of the flight path corresponds to the first maximum 7

,. STANDARD VOR ANTENNA 28 O 0 A z -( cs I 0 O CV co 0 0.1 0.2 A Fig. 2: Scalloping amplitude S2 in the direction - 01 60~, 6=0 =1 78.5 as a function of A. H=7.2', Z 15' andin oD and D= 1000'. 0.3

STANDARD VOR ANTENNA 40 30 20 10 0 O o w P4 0 o p M w 0 En Co -20 -30 -40 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Fig. 3 (a): Scalloping amplitude in the direction of the first minimum in the pattern as a function of (0 - 01) for the standard VOR antenna. Z = 50', D a 1000', A = 0.1.

STANDARD VOR ANTENNA Uf) 0 CO 0 4 o < C) U) 10 8 6 4 2 0 -2 -.4 -6 — 8 -10 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Fig. 3(b): Scalloping amplitude in the direction of the first maximum in the pattern as a function of (-~01) for the standard VOR antenna. Zo 50', D = 1000' and A = 0. 1.

011218'4-T (nearest to the horizon) in the elevation plane pattern of the antenna. For the range of parameters considered in Figs. 3 (a) and 3 (b) it is found that the maximum scalloping amplitude is about four times larger in the direction of the first min" imum in the pattern. For the case of a large gradient VOR DPLC antenna located 50t above ground, similar scalloping results are shown in Fig. 4 for orbital flight at an elevation angle which corresponds to the first minimum in the elevation plane pattern of the antenna. As compared with Fig. 3 (a) the results in Fig. 4 indicate that the maximum scalloping amplitudes are less for the large gradient antenna. 11

DPLC ANTENNA 1 6 -— _ _- _ _ _ _ _ 14 -H-.- -_ _ - _ _ _ _ _ 12 -_ _ _ __ 30' 50' 8 t2 6 ~~ 60 2 _ _ _ _ _ _ _ _ o o -(-1IN DEGREES <0.4 80' o 0 0.1 20 4 0 8 0 2 4010 1020202026 8 0 2 4 6 Fig.4: calopln amlitde i th diectin o th firt mnimm inthepatern s afuntio of"1)frth PCatna.Z5' =00'ad.1 40'

011218-4-T V SCALLOPING AMPLITUDE VARIATION WITH FIELD GRADIENT In this section we discuss the results obtained for scalloping amplitudes with a VOR antenna having different values of the field gradient. The antenna chosen is the five-bay stacked array [2]. The excitations are chosen such that the field gradients in the free space elevation plane patterns of the antenna are as given in Table 1. The patterns produced by such antennas located above ground are discussed in [2]. In general, for a scattering object located at a height below that of the antenna, the observed scalloping amplitudes decrease with the increase of the field gradient of the antenna. Figures 5 and 6 show the scalloping amplitude vs. (0- 01) for an antenna with variable field gradients and for observation angles (0) corresponding to the first minimum and the first maximum respectively in the elevation plane patterns of the antenna. The variation with the field gradient is found to be more pronounced in Fig. 5. Once again we observe that the maximum scalloping amplitude is larger in the direction of the pattern minimum. In order to present the results in a more meaningful way we define the following parameters characterizing the scalloping amplitudes: average maximum scalloping amplitude S 2 Ss --- —2 — -- scalloping improvement coefficient S for the test antenna P S for the standard VOR antenna The average maximum scalloping amplitude S and the scalloping improvement coefficient p as functions of the field gradient are shown in Fig. 7. For the range of the parameters shown the average maximum scalloping corresponding to the first 13

STACKED ARRAY a - 5.22 -g — a c =6.74 10.20 g a =16.93 g UO 0 I p r~~ -18 - -I - 1__ ____I________1 _ I - I.I 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Fig. 5: Scalloping amplitude in the direction of the first minimum in the pattern as a function of (0- 0 ) for the stacked array antenna. Z = 200'. H = 60'. D = 1000' and A = 0. 02.

STACKED ARRAY cl --- --- —,- --- — I- — - --- —c-, - ---, 1. 0 -.-,I — i i.!!I"I a x1 6. 9 a =10. 20 g I —,a =5.22 g _a = 6. 774 g U) 011 P4 0 0 U) p1 O IL) 0. 8 1 i i i i i:1 4 -- W — 0,6 0.4 0.2 0 -0. 2.10. 4 -0. 6 II I,,- 4- _ __ __ ( )IN DE GRE ES - I_ I_ _,I__ t~~~~__________ _ _ I_ _ _ _ I _ I /II I _ I _ _ _ II -0.8 12 I I ___ II._ _I__ ___ I ___ I _ I ___ I I _I 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Fig, 6: Scalloping amplitude In the direction of the first maximum in the pattern as a function of (O- 1) for the stacked array antenna. Z0 v20010 H = 60', D =1000t and A = 0. 02.

1.4 1.2 1.0 a0.9 0.8,-.I 04 0 0.5 r.0. >0.4 0 0. 3 0.2 0.1 0 STANDARD p IN THE DIRECTIO OF THE FISRST STA KED STACKERRAY.... I I 1 I — — ___- - DPLC I p IN THE DIRECTION t t 1 l l | ---- I \S\ MINIMUM ' " I " I I I ^-'=L ---A-S _ _____ STACKEDARRAY ___ | SCALLOPING IN THE I DIRECTION OF THE 1FIRST MAXIMUM.I. I 1 1 1 I T l *-:~. '~_.. 1 1 1 1 -I.! 24 22 rI 20 9 0 18 C z ~-4 16 M 14 i o 12, I.) 10 8 6 2 4 2 < 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 FIELD GRADIENT a dB/6~ g 19 20 21 22 23 Fig. 7: Improvement coefficient p and average maximum scalloping as functions of the field gradient a Z = 200;, H i60', D = 1000' and A = 0. 02. o

011218-4-T minimum in the pattern is found to decrease continuously with the increase of the field gradient. The dotted extrapolated extensions of this curve at its two ends terminate at the corresponding values for the standard VOR and the DPLC antennas respectively. The average maximum scalloping amplitude corresponding to the first maximum in the pattern is found to be independent of the field gradient for the range of parameters considered in Fig. 7. The improvement coefficient p as a function of the field gradient, shown in Fig. 7, has been obtained for the observation angle corresponding to the first minimum in the pattern, This curve is again extrapolated to the standard VOR and DPLC antenna values. 17

011218-4-T VI VARIATION OF S AND p WITH RELATIVE LOCATION OF THE ANTENNA AND THE SCATTERER The variations of the average maximum scalloping amplitude S and the scalloping improvement coefficient p as functions of the relative location of the antenna and the scatterer above ground are discussed in the present section. Results have been obtained for (see Fig. 1 for notation) D = 500', 1000', 2000' and 3000' and for H x 25', 50', 75' and 100'. The antennas considered are the standard VOR and the DPLC antennas. In all cases the antenna heights have been varied from Z x 15' to Z = 500'. In the following sections we first discuss the o o reulsts obtained when the scatterer is located at a distance D = 1000' from the antenna. Results for D = 1000' Average maximum scalloping amplitude vs. antenna height for two observation angles and for different heights of the scatterer are shown in Figs. 8 (a) and 8 (b) for a standard VOR antenna. In general, for a given scatterer height the average maximum scalloping S is found to be an oscillating function of the height of the antenna above ground. This is indicative of the image effects on the field radiated by the antenna which in turn affects the scalloping. The average value of S tends to increase with the increase of the scatterer height. This may be attributed to the fact that in this particular case with D = 1000' the field incident at the scatterer increases with the height of the scatterer. It should also be observed from Eq. (2) that for a given antenna height the scalloping goes to zero if the height of the scatterer is such that H = 2 where n 1, 2,..., This is due to the image effects on the scattered field at the observation point. The corresponding results for DPLC antenna are shown in Figs. 9 (a) and 9 (b). The ratio of the average maximum scalloping amplitudes observed at the first maximum and the first minimum angles in the pattern of the standard VOR antenna are shown in Fig. 10. The corresponding results for the DPLC antenna 18

36 I. 'L I~N IIfJfI I tIf v %JIA, It -~-I IL IN JL E, IN IN Ari -- 341 — -- I i I At 250 the \ value is 42. 18~ 32 ---- /H = 75' tI....... 301 - -,._..... -~ 28 ---- I fk P~ 1 4 VI z bC4 24 --- 14 ------ <100' 12- 250 O -. -.-..-..._______ 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 8 (a): Average maximum scalloping as a function of standard VOR antenna height with scatterer height as the parameter. Observation angle is in the direction of the first minimum. D = 1000', A = 0. 02.

STANDARD VOR ANTENNA C$) w N P4 0 0 b-f U) 2. 2. 2. 1. 1. 1. 1. 1. 0. 0. 0. 0. 4 2 8 6 2 F \ - t —Is 2 75o =A \ l1 8 6 i i.......50t 25' 2 n I 0 100 200 300 400 500 ANTENNA HEIGHT Z IN FEET o Fig. 8(b): Average maximum scalloping as a function of standard VOR antenna height with scatterer height as the parameter. Observation angle is in the direction of the first maximum. D 1000', A: 0.02.

17 16 15 14 13 12 11 10 9 8 - -- - -- -- I- -— — I 100',.-, - - - -. -.- - - - -. — -!. -- - 4_ w M 0 CD CO3 7 6 5./75 -^^ ---P-,-. ^-. 4 3 2 1 0 0 100 200 300 ANTENNA HEIGHT Z IN FEET o 400 500 Fig. 9 (a): Average maximum scalloping as a function of DPLC antenna height with scatterer height as the parameter. Observation angle is in the direction of the first minimum. D = 1000', A = 0. 02.

2.8i 2.6 2.4 2.2 2.0 1.8 1.6 1.4 CO I \ 1.2 ^~i O12 --- ------ -- ----- -S ----------------- 0.8.- ----- ---- 0 100 200 300 400 500 ANTENNA HEIGHT Z IN FEET 500 o. 4 Fig. 9(b): Average maximum scalloping as a function of DPLC antenna height with scatterer height as the parameter. Observation angle is in the direction of the first maximum. D = 1000', A = 0. 02.

STANDARD VOR ANTENNA 2. 1. 1. 1. -4 E-4 CO Ef 1.2 1.0 0.8 0.6 0. 0.2 0 -0 100 200 300 400 ANTENNA HEIGHT IN FEET 500 Fig. 10: S at the pattern maximum S at the pattern minimum as a function of the standard VOR antenna height with scatterer height as the parameter. D = 1000', A = 0. 02.

01 1218-4-T are shown in Fig. 11. The results shown in Figs. 10 and 11 indicate that except for some isolated points, the average maximum scalloping amplitudes are in general larger at the observation angles corresponding to the first minimum in the pattern of the antenna. However, in some cases, depending on the particular combination of H and Z the scalloping may be larger at the observation angle corresponding to the pattern maximum. The improvements in scalloping obtained by using a DPLC antenna for different heights of the antenna and the scatterer are shown in Figs. 12 and 13. Observe that for the range of parameters used, the DPLC antenna in general reduces the scalloping amplitude except for H = 100', Z a 412' in Fig. 12. Results for D 5 500', 2000t and 3000t Similar results for D x 500', 2000' and 3000' are shown in Figs. 14-16. The elevation of the flight path is assumed to correspond to the first minimum in the elevation plane pattern of the antenna. The general behavior of the results is similar to that of the results for D = 1000'. 24

DPLC ANTENNA 1.5 1.4 1.3 1.2 1.1 1.0 0.9 en X ~-4 H H CO 0.8 g 0.7: 0.6 H c 0.5 uo 0.4 0.3 0.2 0.1 0 100 200 300 400 ANTENNA HEIGHT IN FEET 500 Fig. 11: at thepatternmaimum S at the pattern minimum as a function of the DPLC antenna height with scatterer height as the parameter. D = 10001, A x 0. 02.

S AT TIlE DPLC MINITMUM S AT TIIE VOR MINIMUM 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 cM p 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 12: The DPLC antenna improvement coefficient p as a function of the antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. D 1000', A =0.02.

S AT TIIE DPLC MIAXIMUMl S AT THE VOR MINIIMlUM 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 p 0 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 13: The DPLC antenna improvement coefficient p as a function of the antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern maximum. D 1000', A =0.02.

STANDARD VOR ANTENTNA -- - -r — I - - VI CO ND 07 0 100 200 300 400 ANTENNA HEIGHT IN FEET Fig. 14 (a): Average maximum scalloping as a function of standard VOR antenna height with scatterer height as the parameter. Observation angle is in the direction of the first minimum. D 500', A = 0.02. 500

DPLC ANTENNA 70 60 50 0 CD O 40 30 20 10 0 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 14(b): Average maximum scalloping as a function of the DPLC antenna height with scatterer height as the parameter. Observation angle is in the direction of the first minimum. D, 500', A X 0. 02.

S AT THE DPLC MINIIMUM S AT THE VOR MINIMUM 1.1 1.0 0.9 0.8 0.7 0.6 p CAO 0 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 ANTENNA HEIGHT IN FEET 500 Fig. 14(c): The DPLC antenna improvement coefficient p as a function of the antenna height with scatterer - height as the parameter. Observation angle is in the direction of the first pattern minimum. D 500', A = 0.02.

STANDARD VOR ANTENNA V I 00 O CO 0 100 200 300 400 ANTENNA HEIGHT IN FEET 500 Fig. 15 (a ): Average maximum scalloping as a function of standard VOR antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. D=2000', A = 0.02.

t DPLC ANTENNA 22 CO I ft w 0 a CO 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 15 (b): Average maximum scalloping as a function of the DPLC antenna height with scatterer height at the parameter. Observation angle is in the direction of the first pattern minimum. Dx2000', A =0.02.

S AT TIHE DPLC MINITMIUM P S AT THE VOR MINIMUM 1.0 OW p 0 100 200 300 400 ANTENNA HEIGHT IN FEET 500 Fig. 15(c): The DPLC antenna improve coefficient p as a function of the antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. D 2000', A = 0.02.

STANDARD VOR ANTENNA 12 11 10 I _/! \501 5 o75' 2' ' 0 ^ ----1 --- — ----— _____________________ 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 16(a): Average maximum scalloping as a function of the standard VOR antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. D 3000', A 0. 02,

I DPLC ANTENNA 10 CA O CA 0 wzl 0 100 200 300 400 ANTENNA HEIGHT IN FEET Fig. 16 (b): Average maximum scalloping as a function of the DPLC antenna height with scatterer height as parameter. Observation angle is in the direction of the first pattern minimum. D = 3000', A = 0. 02. 500

S AT THE DPLC M.INIMTUMI p S AT THE VOR MINIMUM 1.1 1.0 0.9 0.8 0.7 0.6 0.5 CO p 0.4 0.3 - 0.2 - 0.1 - 0 - 0 100 200 300 400 500 ANTENNA HEIGHT IN FEET Fig. 16(c): The DPLC antenna improvement coefficient a as a function of the antenna height with scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. D = 3000', A = 0. 02.

011218-4-T VII SCALLOPING AMPLITUDE AS A FUNCTION OF D In this section we discuss the variation of the scalloping amplitude as a function of distance D of the scatterer from the antenna. The scalloping amplitude given by Eq. (2) depends on D through the parameter A and 01. In general, the magnitude of the scattering coefficient varies inversely with the distance D. In order to bring out the dependence of S on D we define a modified scattering coefficient A' such that A x 1000 Al = (4) D where the distance D is expressed in feet. Note that A' is normalized such that at D z 1000t, A' X A. We shall assume that A = 0. 02, as before. With this modified definition of the scattering coefficient we calculate S1 by using Eq. (2). The results obtained for the standard VOR antenna located 15' above ground are shown in Fig. 17. Corresponding results for the DPLC antenna located at Z = 15' and 50' are shown in Figs. 18(a) and 18(b). In all cases, the elevation of the flight path corresponds to the first minimum in the pattern of the antenna. In general the scalloping amplitude decreases with increase of D. The cross-over points in some cases are attributed to the image effects on the scattered field at the observation point, i. e., due to the special combination of the values of H and 0. 37

STANDARD VOR ANTENNA 4 - 2 1 100 I 0 1000' 2000' 3000' 4000t D IN FEET Fig. 17: Average maximum scalloping as a function of D with the scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum. Z a 15', VOR antenna. 0

DPLC ANTENNA co z pq -4 02 co CD 0 1000' 2000' 3000' D IN FEET 4000' Fig. 18 (a): Average maximum scalloping as a function of D with the scatterer height as the parameter. Observation angle is in the direction of the first pattern minimum, Z x 15'. DPLC antenna. 0

DPLC ANTENNA 12 11..., * - I 10 - 9 8 7 --- m I i- F., Cl4 0 I i I I \N I I I - I - -- 3 2 1 0 0 1000 2000 3000 4000 D IN FEET Fig. 18 (b): Average maximum scalloping as a function of D with height as the parameter. Observation angle is in the first pattern minimum. Z = 501, DPLC antenna. O the scatterer direction of the

011218-4-T REFERENCES 1 D. L. Sengupta and P. Chan, Application of the Large Gradient VOR Antenna, Interim Engineering Report No. 3, 011218-3-T, University of Michigan Radiation Laboratory, March 1973. 2 D. L. Sengupta and P. Chan, Application of the Large Gradient VOR Antenna, Interim Engineering Report No. 1, 011218t-1-T, University of Michigan Radiation Laboratory, September 1972. 3 D. L. Sengupta and P. Chan, Application of the Large Gradient VOR Antenna, Interim Engineering Report No. 2, 011218-2-T, University of Michigan Radiation Laboratory, December 1972. 41