or antenna by feed ocusing

A.D. Olver J.U.I. Syed

Indexing terms: Defocusing, Antennas

Abstract: The beamwidth of a reflector antenna may be varied by defocusing the feed. The radi- ation characteristics are studied for both axi- symmetric and offset single reflector antennas using both geometric optics for understanding the operation and physical optics for a parametric study. The beamwidth may be increased by over 200% compared to the focused reflector before the main beam bifurcates, but the on-axis gain is reduced. Better performance is obtained with an offset reflector antenna. The study quantifies the limits of beam broadening which can be achieved. Measurements on a 30 CHz experimental antenna show good agreement with theory.

1 introduction

The growth of remote sensing by satellites and aircraft has demonstrated the potential advantages of using an antenna where the beamwidth of the main radiation pattern can be varied dynamically. Other applications such as secure communications and radar could also benefit from the ability to control the beamwidth. This paper studies the radiation characteristics of reflector antennas where variable beamwidth is obtained by defo- cusing the feed of the reflector. Both axi-symmetric and offset configurations are investigated. An experimental antenna has been used to demonstrate the variable beam- width and verify the theoretical predictions.

The minimum beamwidth is obtained when the feed is at the focus of the reflector antenna. As the feed is moved along the axis of the symmetric reflector, the beam is broadened. Using geometric optics and physical optics, it is shown that beamwidths which are over 200% greater than the focused antenna can be achieved, although there is a loss of gain in the process. The relationship between the beam broadening and the gain loss is investigated. The results show that a viable and useful variable beam- width antenna is achievable by feed defocusing.

There does not seem to have been any recent papers which study the effects of feed defocusing. The degrada- tion of the radiation pattern by defocused apertures was studied by a number of authors [l-61 in the early days of the development of reflector antenna theory. Ingerson and Rusch [3] showed how the main beam bifurcates

0 IEE, 1995 Paper 2082H (Ell), first received 23rd December 1994 and in revised form 10th May 1995 The authors are with Queen Mary and Westfield College, University of London, Mile End Road, London E l 4NS, United Kingdom

394

and indicated the gain loss due to axial defo their results are only valid for small d the diameter of the reflector antenna. Rusch, and Kaufman and Crosswell capability for broadening the beam the consequences. Johnson et al. [ defocusing can be used to focus the main beam at a distance so that the far field radiation patterns can measured in the near field.

2 5efocusing using geometric optics

The geometric optics ray picture of focused and de cused paraboloids are illustrated in Figs. 1-3. When

Fig. 1 at focus of reJector

Ray diagram of front-jed parabolic re$ector antenna, with fee8

Fig. 2 cused feed (towards reflector)

Ray diagram ojfront-fed parabolic reflector antenna, with defo-

real focus

Fig. 3 cused feed (away from reflector)

feed is at the focus, the reflected rays are parallel to the axis, Fig, 1. Moving the feed along the axis and away from the focus causes the rays to fan out into space. By moving towards the paraboloid, Fig. 2, a virtual focus forms behind the real focus and the rays continuously diverge. When the feed is moved away from the parabol-

IEE Proc.-Microw. Antennas Propag., Vol. 142, No. 5, October 1995

Ray diagram offront-jed parabolic reflector antenna, with defo-

oid, Fig. 3, the rays converge to a real focus in front of the actual focus of the paraboloid and then diverge. This simple ray picture shows the beam broadening which occurs, but it also shows how the energy is spread out to a larger solid angular region of space. This must be mani- fest as on-axis gain loss by the reflector antenna.

The simple ray picture does not indicate how the transverse field distribution varies. This will be deter- mined by the interaction of all the rays emanating from the feed and can be assessed by studying the phase dis- tribution across the aperture of the reflector antenna. A focused feed produces a uniform phase across the aper- ture. A defocused feed produces a nonuniform phase dis- tribution and an ideal radiation pattern, the extent of which leads to beam degradation and eventually a useless radiation pattern.

With the geometry of Fig. 4, the radiated far-field of an axi-symmetric paraboloid is given by the Fourier

/ 1 Y f

projected aperture

Fig. 4 Geometry of symmetric parabolic rejector antenna

transform integral,

E(0, 4) = [“ r F ( r , &) exp [jk(l p’ I - P’R)]r dr d4‘

(1) where F(r, 4’) represents the aperture field distribution. The phase term, representing the path length, can be expanded as

- b’fi = 2F - z cos 8’ - p sin 0 sin 8’ cos (4 - 4’) + p cos el(l - cos 0) + z cos I3 (2)

or in terms of the radial distance r and the focal length of the paraboloid F,

- r sin 0 cos (4 - 4’) - F(l - cos 0)

x [ 1 - (31 + z cos 0 (3)

where only the lowest order terms have been retained. This may be done within the restriction of the defocused distance z < D/10. The first term in eqn. 3 is constant and the third term shows a linear variation of phase with

IEE Proc.-Microw. Antennas Propag., Vol. 142, N o . 5, October 1995

defocused distance, z. The second and fourth terms show a quadratic phase variation, proportional to z. It is these terms which lead to spherical aberration. This causes both the wanted effect of broadening the main beam and the unwanted effect of filling in the nulls in the radiation pattern and raising the average sidelobe level relative to the peak gain. These consequences are seen in Figs. 5-7

-10 T3

0 0.5 1.0 1 5 2.0 2.5 3.0 3.5 angle 8 , deg.

Fig. 5

__ physical optics z = 01

Focused and defocused radiation patterns ....... geometric optics D = 1201

FID = 0.4

O r

il -50t -601 I I 1 I I I I

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 angle 8 , deg

Fig. 6 Focused and defocused radiation patterns ....... geometric optics D = 1201

~ physical optics z = 1.41 FID = 0.4

O r

I 1 I 0 0 5 1 0 1 5 2 0 2 5 3 0 3 5

angle 8 , deg

Fig. 7

~ physical optics z = 1.81 FID = 0.4

Focused and defocused radiation patterns . . . . . . geometric optics D = 1201

395

which plot the radiation pattern using eqns. 1 and 3 for a focused and two defocused cases. The patterns are for a linear polarised feed with a quadratic feed distribution in a reflector of diameter 1201 and FID = 0.4. The focused case is in Fig. 5. At z = 1.41, Fig. 6, the main beam has broadened, the sidelobe nulls have been filled in and the on-axis gain has dropped in compensation. For larger defocusing, Fig. 7, a null appears on boresight and bifur- cation of the radiation pattern in one plane occurs. The theoretical limit to which the beamwidth can be increased is just before the beam bifurcates. The practical limit may be less than this partly due to the assumptions inherent in eqn. 3 and partly due to the limitations of the geometric optics model. These may be determined using physical optics which also enables a parametric study of the beamwidth broadening and gain loss to be per- formed. The feed in the PO analysis is a cos4(8”) function which is centred on the (r, 6”, 4”) coordinate system, Fig. 4. The radiation characteristics are computed with both an in-house PO program and the commercial program GRASP7 [7] for various combinations of F/D, edge taper and defocused distance.

*- - 5 - m - - 1 0 - .- U E -15 .- 0“ c - 2 0 - 0

-25

3

The geometry of the axi-symmetric reflector antenna is shown in Fig. 4, where the amount of axial defocusing of the feed is specified by z. The radiation patterns, com- puted using physical optics, are shown in Figs. 5-7 to allow comparison with the geometric optics results. The small differences in the focused case are due to differences in the amplitude of feed model between GO and PO. For the defocused cases, the PO results differ from the GO patterns because the phase distribution across the aper- ture becomes important. The lower on-axis gain shown in Fig. 7 is due to PO taking account of the phase cancel- lation from the edges of the reflector. The PO results confirm that the limit of beamwidth broadening which is possible occurs when the feed is moved 1.41 towards the reflector. The PO computed pattern for z = 1.81 agrees with the general pattern published by Ingerson and Rusch [3].

Two factors influence the rate at which the beam broadens and the point at which beam bifurcation occurs. These are the amount of power illuminating the edge of the reflector and the ratio of the focal length to diameter of the reflector. The percentage change in beam- width ABW, defined as ABW = 100 x [(BW,,,,,,, - BW,,,,,)/BW,,,,,], is shown in Fig. 8, against the amount of feed shift for a number of edge tapers. A 100% increase in beamwidth is equal to a doubling of the beamwidth. As the feed is moved away from the focus, Fig. 8 shows that the beamwidth increases slowly until about z = 0.81. After this value, the beamwidth increases rapidly with increasing defocusing. The curves in Fig. 8 stop at the point where a null appears on the axis, which is around z = 1.41 for this size of reflector. This is the useful range for an application requiring dynamic beam- width broadening.

The loss in gain as the feed is defocused changes monotonically with feed position, as shown in Fig. 9. The maximum amount of beam broadening which is possible depends on the edge illumination. A lower edge illumi- nation leads to the ability to achieve a wider beam, up to 225% for an edge taper of -20 dB. The limit on a well formed main beam is determined by the diffraction which takes place at the edge of the reflector, a lower edge taper

Prime focus axi-symmetric reflector antenna

396

-

-

gives less diffracted power and hence more scope for beam broadening. However, a lower edge taper also reduces the efficiency of the reflector antenna and gives lower gain.

250 1

L o Q

0

- 50 0 0 4 0 8 1 2 1 6 2 0

Change in 3 dB beamwidth against defocusing for different edge

feed shift,h

Fig. 8 taper

F / D = 0.4 D = 120L

...O... ET = -8 dB -0- ET = -10dB --+-- E T = -20dB

5r o t

- 0 5 0 0 5 1 0 1 5 2 0 25 30 3 5 feed shift h

On-axis loss due to feed defocusing for different edge taper Fig. 9 ET = - 8 dB FJD = 0 4

-0- ET = -1OdB D = 1201 - -+-- E T = -20dB

.... .

The influence of the focal length on the gain loss is shown in Fig. 10 for four values of the F / D ratio. These are computed for an edge taper of - 10 dB which gives optimum efficiency. For a small focal length reflector the gain falls very rapidly as the feed is moved away from the focus position, but falls much more slowly for a reflector with F / D = 0.6. Thus a longer focal length reflector is to be preferred. The gain loss is less sensitive to a higher F/D because the phase error across the aperture decreases as the FID increases, as can be seen by examin- ing eqn. 3.

A computational study in which all the available parameters were varied shows that the maximum increase in beamwidth which can be obtained is about 230%, although at this amount of beam broadening the main beam radiation pattern shows a certain amount of ripple on the top of the pattern.

4 Experimental measurements

The theoretical predictions have been verified by mea- surements on a 1.22 m diameter, FID = 0.375, axi- symmetric reflector antenna operating at 30 GHz, so that

I E E Proc.-Microw. Antennas Propag., Vol. 142, No. 5, October 1995

the normalised diameter was 1221. The feed was an open- ended rectangular waveguide which had a measured E- plane edge taper on the reflector edge of -7.7 dB and an H-plane edge taper of -14.4dB. It was mounted on a movable carriage which enabled the feed to be axially defocused by k3.21. The antenna was measured at 30 GHz in a Compact Antenna Test Range [8]. A pho- tograph of the antenna is shown in Fig. 11.

-25

U - 5 m

-

E -5 0

c - .- c& -10 - m .-

- 1 5 - C 0

-20

Fig. 11 reflector antenna

Photograph of experimental model of variable beamwidth

The radiation patterns showed the expected behav- iour. Fig. 12 shows a comparison between the measured E-plane -3 dB beamwidth and the computed results as the feed is defocused from the focus position. Agreement is observed over the complete range of feed shift. This is particularly functional because the predicted results did not include the influence of feed blockage and scattering of the feed support. The results in the H-plane were similar. The plot confirms the behaviour discussed above with only a small increase in beamwidth until the feed is moved about 11 followed by a rapid increase in beam- width from 0.6" to 1.6" for the next 0.41 movement. The

I E E Proc.-Microw. Antennas Propag., Vol. 142, No. 5 , October 1995

-

-

plot is approximately symmetric about the focus position showing that the beam broadening is achieved for the feed movement towards or away from the reflector. The corresponding on-axis gain is compared in Fig. 13 and

1 . 6 1

0 4 1.4

I I I I - 2 0 -15 -10 - 0 5 0 0 5 1 0 1 5 2 0

feed shift A Fig. 12 Change in 3 dB beamwidth with feed defocusing -0- measured D = 1222 . . . . . . computed F / D = 0.375

5~

V O t

I I I

-3 -2 -1 0 1 2 3 feed shift A

On-axis gain loss with feed defocusing

-25,

Fig. 13 -0- measured D = 1.221 . . . . . . . computed FID = 0.375

again shows an agreement between theory and measure- ment. The beam broadening is not achieved without a loss in gain. The aperture efficiency is lower due to the distorted phase and amplitude distribution. At z = 11 the gain loss is about -5 dB and at z = 1.41 it has decreased to - 10 dB.

5 Offset reflector antenna

For some applications the feed blockage inherent in the axi-symmetric reflector antennaL would be unacceptable so it is worth studying an offset reflector to see if the limits of defocusing are the same. The geometry is sketched in Fig. 14, which shows that the feed should be moved along the offset focal axis to keep the amplitude and phase distribution across the reflector aperture to be symmetrical. For a feed defocusing of i' = zL2 + z:?, eqn. 2 becomes

16'1 - 6'ff = 2F - Z: COS 8' - p sin 6' sin 8' cos (4 - 4')

+ z; cos 4 sin 8 - z: cos 4' sin 8' + cos el(i - cos e) + z: COS e

(4)

391

In this equation the first five terms are the same as in eqn. 2 and their effect on the far field radiation pattern

40

3 0

20 U

- 1 0 - U m

0 -

-10

- 2 0

x 4 parabolic

-

-

-

-

-

z J.'

Fig. 14 4 = 0" plane

Geometry for ofset reflector antenna

will be the same. The remaining terms in eqn. 4 will produce some additional phase aberrations in the offset plane. The terms give rise to linear, comma and astig- matic phase errors across the aperture and produce addi- tional constraints on the radiation characteristics.

A selection of computed, physical optics, radiation patterns are shown in Fig. 15. These are for an offset

50 r

I I

- 3 0 I I I I I I I -6 -4 -2 0 2 4 6

angle 8 , deg

Fig. 15 rejector antenna ___ z' = 01 (4 = 90" plane) -0- z' = 4.62 (6 = 90" plane)

Beamwidth broadening by defocusing the feed in an offset

~ - 0 - ~ z' = 01 (4 = 90" plane) ... x ... I' = 4.61 (4 = 90" plane)

reflector antenna with D' = 69.511 and the focal length of the parent paraboloid is 4811. The offset angle 8, is No, where 8, = (Om,, + OmLn)/2. The feed is defocused along this axis. The radiation patterns in Fig. 15 show the same behaviour as an axi-symmetric reflector in the yz plane but in the xz plane the defocused patterns are asym- metric. This is due to the appearance of a comma lobe and is caused by the asymmetrical illumination of the main reflector as the feed is defocused along the 8, axis. The percentage change in beamwidth and the corre- sponding gain loss are shown in Fig. 16. The beamwidth can be increased by 100% for a gain loss of 6 dB, which is better than achieved with the axi-symmetric reflector

antenna of Figs. 12 and 13. The comma phase error at the edge of the reflector caused by feed defocusing along the offset axis can be determined from eqn. 4 as

where D is the diameter of the parent paraboloid. It is evident from eqn. 5 that the comma phase error may be reduced by using either a reflector with a high FID ratio or a small offset angle 8,.

L ;; 200 r 1 2

m m 100 U

C .-

$ 50

a 0

U

5 L 3 C !? -50 I I I I I I.

j -14 -I2 - b o 1 2 3 4 5 6 7

feed shift (2'1, A a

Fig. 16 -e-

Zoom performance of an offset rejector antenna percentage change in - 3 dB BW on-Bx1s loss . ...

6 Conclusions

The paper has shown that a variable beamwidth antenna can be achieved by defocusing the feed. It is pos- sible to achieve an increase of over 200% in width, but the peak gain decreases as th broadened. The theoretical results have been v 30 GHz experimental reflector antenna. It is shown that an offset reflector antenna can give an improved per- formance.

7 References

1 CHENG, D.K., and MOSELEY, S.T.: 'On axis defocus char istics of the paraboloidal reflector', I R E Trans, 1955, AP-3, pp. 214- 216

2 RUSCH, W.V.T., and POTTER, P.D.: 'Analysis of reflector antennas' (Academic Press, 1971), Chaps. 3 and 4

3 INGERSON, P.G., and RUSCH, W.V.T. : 'Radiation from a parabol- oid with an axially defocused feed', IEEE Trans., 1973, AP-21, pp. 104-105

4 KAUFMAN, J.F., and CROSSWELL, W.F.: 'Off-focus character- istics of the offset parabola'. IEEE Int Digest for Ant. and Propagat. Symp., 1975, Urbana, Illinois, pp. 358-361

5 RUSCH, W.V.T., et aZ.: Chaps. 2 and 3 in 'The Handbook of antenna design', RUDGE A.W., et al.

6 JOHNSON, R.C., ECKER, of far-field antenna patterns from near-field measurements', Proc. IEEE. 1973,61, p. 1668

7 SORENSON, S.T., and NIELSEN, P.H.: 'Manual for Grasp7 package'. TICRA, November 1988

8 PARINI, C.G., OLVER, A.D., McNAIR, P., and PRIOR, C.J.. 'The design, construction and use of a millimetrewave compact antenna test range'. 6th IEE Int. Conf. on Antennas & Propagation, Warwick, UK, April 1989, pp. 345-350

398 IEE hoc.-Microw. Antennas Propag., Vol. 142, No. 5, October 1995