83

Feed support blockage in symmetric paraboloid reflectors

Blocage de support d'alimentation dans les réflecteurs paraboloïdes symétriques

By M.S. A. Sanad andL. Shafaï, Department of Electrical Engineering, University of Manitoba, Winnipeg, Manitoba.

The effects of the primary feed supporting struts on the radiation patterns of a symmetric paraboloid reflector are investigated. Both linear and cir­cular polarization of the feed are considered, and the reflector secondary fields are generated using the physical optics approximation for the surface current on the reflector. The strut fields, on the other hand, are computed by assuming the strut currents as those generated on an infinite cylinder il­luminated by a plane incident wave. For struts of circular cros-section, the over-all radiation patterns of the reflector are computed and compared with those of an unblocked reflector. Based on this comparison, the effects of the strut dimensional parameters on the reflector gain, sidelobe levels and the cross-polarization are determined and presented graphically.

Une étude est effectuée sur les effets des traverses d'alimentation primaire sur les diagrammes de rayonnement d'un réflecteur paraboloïde symétri­que. La polarisation aussi bien linéaire que circulaire de l'alimentation est prise en considération et les champs secondaires du réflecteur sont générés en utilisant l'approximation optique physique pour le courant de surface sur le réflecteur. D'un autre côté, les champs des traverses sont calculés en supposant que les courants des traverses sont ceux générés sur un cylindre infini éclairé par une onde incidente plane. Pour les traverses de coupe transversale circulaire, les diagrammes de rayonnement équivalents du réflecteur sont calculés et comparés à ceux d'un réflecteur non bloqué. En se basant sur cette comparaison, les effets des paramètres dimensionnels des traverses sur le gain du réflecteur, les niveaux des lobes latéraux et la polarisation symétrique sont déterminés et accompagnés d'une présentation graphique.

Introduction

In symmetric paraboloid reflectors, the feed is located at the focal point and is normally supported by struts of varying con­figurations. The aperture of the reflector is therefore blocked by the feed itself and the supporting struts, causing scattering, which results in the reduction of the reflector gain and the rise of the sidelobe and cross-polarization levels. To determine the perfor­mance of the reflector, it is desirable to evaluate these blockage fields. However, the overall scattering geometry of the blocking members is too complex and its field cannot, in general, be solved exactly. An approximate approach which simplifies the problem considerably is based on the null field hypothesis.1 In this method, it is assumed that the currents on the shadowed portions of the reflector are non-radiative. Thus, the field of the blocked reflector can be determined from its surface currents by neglecting the regions under the feed and the supporting struts.

Although this method is simple to apply, it fails to take into ac­count the scattering properties of the struts, which are naturally frequency and polarization dependent. Nevertheless, it has been used by early investigators.2*3 to determine the reflector fields ap­proximately and many useful results for estimating the blockage ef­fects are obtained. In recent studies, the problem has been solved with a considerable improvement to the approximation of the strut scattering.4 5 In this method, the effect of the strut blockage is determined by computing their scattered field using the surface currents on the struts. It is, however, approximate since the strut currents are assumed to be those of an infinite cylinder generated by a plane incident wave. The approximation improves as the strut length increases. This is particularly true for struts supported at the reflector rim, where the strut ends are beyond the reflector aperture and the strut scattered field is primarily due to the illuminated por­tion of the struts. The representation of strut currents by those of an infinite cylinder becomes therefore a reasonable one, and neglects only the currents on the top and the bottom surfaces of the finite strut.

Because the above method computes the scattered field from the surface current data, it provides information on the effects of the strut dimensional parameters. In particular, the results indicate the dependence of the scattered field on the strut cross-sectional dimensions, its tilt angle as well as the polarization and the frequen­cy of the illuminating field. Using this method, Rusch et.al. 5 have studied the forward scattering by finite cylinders of various cross-sectional shapes and defined an Induced Field Ratio (IFR) to in­dicate the scattering efficiencies. Their studies indicated that a cir­cular cylinder generally gives lower scattered fields and generates much smaller cross-polar components. Similar results were also ob­tained experimentally by measuring the scattered field of a finite cylinderical rod illuminated by an offset reflector.6

I j X

•Z

Figure 1: Reflector geometry.

Can. Elec. Eng. J. Vol 9 No 3, 1984

84 CAN. ELECT. ENG. J. VOL 9 NO 3, 1984

Aside from the scattered field of the struts, the feed also causes the scattering of the reflector field. However, practical feeds have diameters in order of few wavelengths and their scattered field can normally be computed accurately by the null field approach. Thus, in evaluating the total blockage effect, one can handle the feed blockage using the shadowing principle and that of the struts by the above scattering technique. Except in large reflectors, where the struts are supported in the interior part of the reflector, which cause blockage of the feed primary radiation and result in the spherical shadowing. To date, no satisfactory solution for the spherical shadowing problem has been found and its effect is usual­ly determined approximately using the null field approach. For small earth stations, this problem seldom arises and the struts are normally supported at the reflector edge.

In this work, we consider small reflector antennas of a gain about 40 dB. The reflector diameters are therefore in the order of 48λ, where λ is the wavelength of the operating frequency. Because the existing literature lacks a comprehensive data on the blockage ef­fect of these reflectors, this paper is prepared so that the most significant design data can be made available. The scattering ap­proach is used to determine the strut fields and various reflector performance data as a function of strut parameters are generated. To indicate the strut effects clearly, a single strut case is considered throughout, but representative data for multiple strut cases are also included. The computed data are presented for both linear and cir­cular polarization of the field and their results are compared.

Analysis

Linear polarization Figure 1 shows the geometry of a paraboloid reflector with a

single blocking strut. At the reflector plane, the secondary field of the reflector can be assumed as a non-uniform plane wave, having a uniform phase and tapered amplitude distributions. Due to this aperture field, the currents induced on the struts generate the strut scattered field which at far zone region can be computed from1

EST = 4wR ( \[J>- (JS*R)R] ejk'rRds (1)

where, r is the distance from the focal point to the integration point on the strut surface, Js is the strut current, 5 is the strut surface and the other geometrical parameters ARE as defined in Figure 1.

For an arbitrary orientation of the strut, with respect to the aper­ture field, the induced currents on the struts are in both axial and circumferential directions about the strut axis. Since for small reflectors the strut diameter is normally less than a wavelength, these induced currents can be determined from the electric and the magnetic fields along the strut. When the electric field is along the strut, the induced current is also in the strut axial direction. However, for the magnetic field along the strut, the oblique nature of the strut induces both axial and circumferential currents. From the analysis of the plane wave scattering by an infinite circular cylinder, these currents can be shown7 to be for the strut along the ^-vector

j f = 4 , Γ — ^ — V j-> L2TÂ:acosaJ

and for the strut along the //-vector

ρΐηφ

//£2>(kacosa) (2)

nka w V A:acos2a

//J2)(A:acosa) (3)

3 6 . 0 0

F I - M F L X

Figure 2: Local maxima of the strut scattered field.

Ι Ϊ ΰ Τ Ο Ο

D E G R E E S

1 8 0 . 0 0

where EA and HA are the aperture fields, a is the strut radius, α is the strut angle with the aperture plane and z' and φ' are the axial and azimuthal coordinates with respect to the strut, and Hn

2 is the Hankel function of nth order and second kind. Using Eqs. (2) and (3) in (1), the strut scattered field can be determined in terms of the reflector aperture field. The final results can be shown to be for the strut along the afield 8- 9

frs t _ jka *[ë0IFRE(D,ô,a)] j EA(r')eJkr'Aodr' (4)

and for the strut along the //-field

jkav EE-POI —

TTR {êcIFRH(D,à,A)+ - (άα+άφβφ)

sina kacos2

-] JFRH(D,ô9a)} ^ HA(r,)eikrAo dr' (5)

where the integrations are along the projection of the strut on the aperture plane and η is the characteristic impedance of free space (η = 120 χ). The expressions for various vectors and functions, in the above two equations, are provided in the Appendix. Now, an addi­tion of the strut fields to that of the reflector itself provides the total field. The expressions for the reflector field can also be obtained from Eq. (1), using the feed radiation pattern, which for a linearly polarized field can be assumed as

SANAD/SHAFAI: FEED SUPPORT BLOCKAGE

CCo

χ: ι

ο

Ο REFLECTOR WITH CENTRAL RND STRUT BLOCKING

<•> REFLECTOR HITH CENTRRL BLOCKING

^ UNBLOCKED REFLECTOR

2 . 0 0 4 . 0 0 THETR IN

6 . 0 0 8 . 0 0 DEGREES

Figure 3(a): Reflector co-polar patterns with cosd illumination, single strut at φ0 = 0ό, and a = .25λ, φ = 0, D = 48k, d = 2.5 \, y-polarization.

. 0 0 4 . 0 0 THETR IN

6 . 0 0 8 . 0 0 DEGREES

1 0 . 0 0

Figure 3(b): Reflector co-polar and cross-polar patterns with cosd il­lumination, single strut at φ0 = 0°, and a = 0.25\, φ = 45°,D- 48k, d -2.5k, y-polarization.

2 . 0 0 4 . 0 0 THETR IN

ID.oo 0 . 0 0 2 . 0 0 4 . 0 0 THETR IN

6 . 0 0 8 . 0 0 DEGREES

1 0 . 0 0

Figure 3(c): Reflector co-polar patterns with cosB illumination, single strut at φ0 = 0° and a = 0.25k, φ = 90°, D = 48k, d = 2.5k, y-polarization.

Figure 3(d): Reflector co-polar patterns with cosd illumination, single strut at φ0 = 90°, and a = 0.25k, φ = 0 ° , D = 48k, d = 2.5k, y-polarization.

85

CAN. ELECT. ENG. J. VOL 9 NO 3, 1984

Θ REFLECTOR WITH CENTRAL AND STRUT BLOCKING

J Φ REFLECTOR WITH CENTRAL BLOCKING

i ^ UNBLOCKED REFLECTOR

I + CROSS POLARIZATION

2.00 4.00

THETR IN 6.00 8.00

DEGREES 2.00 4.00 6.00 8.00

THETR IN DEGREES

10.00

Figure 3(e): Reflector co-polar and cross-polar patterns with cos€ il­lumination, single strut at φ0 = 90°anda - 0.25k, φ-45°,Ό- 48k, d = 2.5k, y-polarization.

Figure 3(f): Reflector co-polar patterns with cosd illumination, single strut at φ0 = 90° and a = 0.25k, φ = 90°, D = 48k, d = 2.5k, y-polarization.

0 . 0 0

Θ REFLECTOR MITH CENTRAL AND STRUT BLOCKING

Φ REFLECTOR WITH CENTRAL BLOCKING

^ UNBLOCKED REFLECTOR

2.00 4.00

THETR IN

6.00 DEGREES

8.00 10.00

Figure 4(a): Reflector co-polar patterns with cosB illumination, quad struts, a = 0.25k, φ = 0, D = 48k, d = 2.5k, y-polarization.

2.00 4.00

THETR IN

10.00

Figure 4(b): Reflector co-polar and cross-polar patterns with cos θ il­lumination, quad struts, a = 0.25k, φ = 45°, D = 48k, d = 2.5k, y-polarization.

86

SANAD/SHAFAI: FEED SUPPORT BLOCKAGE 87

Ό.00 1 . 0 0 2 . 0 0 STRUT DIAMETER 3 . 0 0 4 . 0 0

IN WAVELENGTHS

^ GAIN REDUCTION DUE Τβ ONE STRUT

Ο INCREASE IN THE FIRST SIDELOBE LEVEL

"T~ INCREASE IN THE PEAK CROSS-POL. LEVEL

0 . 0 0 1 8 . 0 0

STRUT 3 6 . 0 0

PLANE 5 4 . 0 0 7 2 . 0 0

IN DEGREES 9 0 . 0 0

Figure 5: Effect of strut diameter on the reflector gain, the first sidelobe level and the peak cross-polarization level, cosd illumination, single strut at φ0 — 90°, d = 2.5k, y-polarization.

Figure 6: Effect of strut plane on the reflector gain, the first sidelobe level and the peak cross-polarization level, cosQ illumination, single strut, a = 0.25k, d — 2.5k, D = 48k, y-polarization.

£inc _ (β')$[ηφ'fa, + (Ιχ (0')COS0' άφ9] Ρ

(6)

where the subscript L refers to the linear polarization and ax and dx

are arbitrary amplitude constants. With this form of the feed inci­dent field, the reflector secondary fields are of the form (for a ^-polarized feed)

eJ'kr f Εθ = jkFûn<l> —— 1 exp[ - jkp(\ — cos0cos0' )] 1 - cos0'

0 ' 2jaxurS cot — .AO?)jsin0'd0'

Εφ = jkFcos<t> ~-~ J _ ^ P [ - ^ P ( l - c o s 0 c o s 0 ' ) ]

(7)

1 - cos0 r

ΊΒ Ι [Λ<0) + Λ ( Ρ ) ] - A [ / O W - Λ 0 3 ) Η woB'dO' ( 8 ) where β = kç sin0 ' , Fis the reflector focal length and J0, Λ, and J2

are Bessel functions. In these equations, 00 is the shadowing angle of the feed and the aperture integrations are from the reflector edge angle 0O to π - δθ, to include the effect of the central blockage. The total reflector field can therefore be obtained by an addition of the strut scattered fields to those given in Eqs. (7) and (8).

Circular polarization For a circularly polarized feed, the strut scattered fields must be

determined for two orthogonal field vectors. A convenient method is to utilize Eqs. (2) and (3) and combine the results of two polariza­tions at a phase quadrature. Specifically, the incident circularly polarized field may be represented by

(9)

Each component of this incident field generates its respective 0 and φ components of the radiated field, and the total field can again be represented by

Er = E% + jEi = \Eceir\ εχρΟ'Φι)

Et = Εφ + jE\ = I Ef I exp (/Φ2)

(10)

(11)

Since, in general, the magnitude and the phase of the 0and φ components of the field will have different values, the total radiated field will be elliptically polarized. Such a field can be represented as a sum of two circularly polarized fields of opposite

CAN. ELECT. ENG. J. VOL 9 NO 3, 1984

ο ο

S ^ GAIN REDUCTION DUE TO ONE STRUT

Θ INCREASE IN THE FIRST SIDELOBE LEVEL

§ j ~"T~ INCREASE IN THE PEAK CROSS-POL. LEVEL

oo_j

ο 1

ο I . 1

7-1 . τ - r - τ -

0.00 -5.00 -10.00 -15.00 -20.00 -25.00

EDGE TAPER IN DBS Figure 7: Effect of the aperture illumination on the reflector gain, the first sidelobe level and the peak cross-polarization level, cosd illumination, single strut at φ0 = 90°, a - 0.25k, D - 48k, d = 2.5k, y-polarization.

ο ο

ο ο ο 7ϊ 1 1 : 1 1 1

0.00 2.00 4.00 6.00 8.00 10.00

THETfl IN DEGREES Figure 8(b): Reflector co-polar and cross-polar patterns with cos θ il­lumination, single strut at φ0 -0°,a- 0.25k, D = 48k, d = 2.5k, circular polarization, φ = 45°.

ο ο

THETA IN DEGREES

Figure 8(a): Reflector co-polar and cross-polar patterns with cos θ il­lumination, single strut at φ0 = 0°,a = 0.25k, D = 48k, d = 2.5k, circular polarization, φ — 0°.

ο ο

ο ο

ο

ο ο

ο

Ό.00 2.00 14.00 6.00 8.00 10.00

THETA IN DEGREES Figure 8(c): Reflector co-polar and cross-polar patterns with cos θ il­lumination, single strut at φ0 = 0°,a= 0.25k, D = 48k, d = 2.5k, circular polarization, φ = 90°.

88

SANAD/SHAFAI: FEED SUPPORT BLOCKAGE 89

ο ο

S T R U T D I A M E T E R I N W A V E L E N G T H S E D G E T A P E R I N D B S Figure 9: Effect of strut diameter on the reflector performance, cos θ illumination, Figure 10: Effect of aperture illumination on the reflector performance, single strut at single strut αίφ0 = 0°,a = 0.25k, φ = 90°, D = 48k, d = 2.5k, circular polarization. φ0 = 0°, a = 0.25k, φ = 90°, D — 48k, d = 2.5k, circular polarization.

senses, one being the co-polar component and the other the cross-polar field. To determine these components, Eqs. (10) and (11) can be used in a combined vectorial form as

Ëcir = \E%tr\ εχρΟ'ΦιΗ + \E$r\ exp(/<2>2)a*

= I Et I exp (j Φ0 [a, + m exp (/Φ ' )άφ) (12)

where m = \Ect\ / \Et\ and Φ' = Φ2 - Φι. Eq. (12) can be modified to a combination of the left and the right handed circular­ly polarized components to give

Results

In small reflector antennas, three different strut configurations are commonly used; a single strut in the form of a 7-hook, a tripod configuration, and a quad strut geometry. An evaluation of the reflector performance with any of these strut configurations is desirable and has been carried out in the course of this investiga­tion. However, for brevity, mostly the results for the single strut case are presented and for multiple struts only few representative data are included. In all cases, struts of circular cross-sections are assumed, which are supported at the reflector edge. The geometrical parameters are:

Ecir = c[âe + ]άφ] + d[âe - j άφ] (13)

where c and d denote the co-polar and the cross-polar components of the field respectively, and their magnitudes are given by

|c | = î \Et\ [1 + m2 + 2 m s h ^ , ] 1 / 2

\d\ = -\Et\ [1 + m2 - 2mûn$']xn

(14)

(15)

With these definitions and the expressions of the previous sec­tion for the linearly polarized case, the required results for the cir­cular polarization can be obtained from those of the linearly polarized ones.

D = 48λ F/D = 0.375 W=2a = 0.5X a = 45° d = 2.5\

reflector diameter focal length to diameter ratio strut diameter strut angle with the aperture plane feed diameter

The computed data are generated using a feed pattern represented by | at \ = 1̂1 = cosm0, where AW is a real number. Such a feed pattern closely approximates the radiation patterns of practical feeds and is selected to generalize the results. Since the strut scattered field is a function of the observation point, it is desirable to evaluate its maximum effect on the reflector field. From Eqs. (4) and (5) the maxima of the strut scattered fields occur along the contour5

cos(0m e x - φο) = tan(0 m e x /2)tana (16)

90 CAN. ELECT. ENG. J. VOL 9 NO 3, 1984

ο ο

ο ο ο

-ρ ο 0Ο_| ! ! ! !

Ό . 0 0 2 . 0 0 4 . 0 0 6 . 0 0 8 . 0 0 1 0 . 0 0

THETfl IN DEGREES Figure 11 : Reflector co-polar and cross-polar patterns for a quad strut configuration, φ0 = 0°, 90°, 180°, 270°, φ = 90°, a = 0.25k, D = 48k, d = 2.5k, circular polariza­tion.

where φ0 is the plane of the strut, φηαχ is the plane of the observation point and the boresight direction, and a is the strut angle with the aperture plane. For a selected value of a = 45°, the required angle emax is given by

dmax = 2tan-'tcos (</>mex - φ0)] (17)

Figure 2 shows the dependence of dmax on (</>mex - φ 0), which can be used to identify the regions of maximum strut scattered field. In particular, it indicates that near the boresight directions, Bmax — 0 corresponds to (φηαχ - φ0) = 90°. This means that the strut effects on the near-in sidelobes occur at, or near, the plane perpendicular to the strut.

Linear polarization For a single strut, the computed patterns are shown in Figures 3a

to 3f for a linearly polarized feed and a cos0 illumination. In Figures 3a to 3c, the strut is perpendicular to the aperture electric field, while in Figures 3d to 3f it is parallel to the field. Comparing these results, it is evident that the effect of the strut on the sidelobes is more significant in the plane perpendicular to the strut, as in­dicated in Figure 2. Also, when the strut is along the aperture field polarization, it deteriorates the reflector pattern by a larger degree. This result is, of course, expected since the induced currents are along the strut and the strut is a stronger scatterer. The cross-polarization patterns are shown in Figures 3b and 3c, which again show higher levels for the strut along the field polarization, but otherwise are small in both cases.

The corresponding results for a quad configuration are shown in Figures 4a and 4b. Again, in the φ0 = 0° plane, which is perpen­dicular to two struts, the deterioration of the reflector pattern due to the strut is more significant than that of the φ = 45° plane case. For a tripod configuration, the results were found to be similar and are not included. Instead, Table I is included which shows the ef­fect of various strut configurations on the reflector gain. Upon generation of the overall reflector patterns for various strut parameters and the feed illumination, the effect of each parameter is identified and is shown in graphical forms. The results are discussed in the following sections.

Effect of strut diameter For a linearly polarized feed, ^-polarization in this case, the strut

effect is large in the plane perpendicular to the strut. Increasing, the strut diameter increases the sidelobe and decreases the reflector gain. Figure 5 shows the results for the strut diameter up to 5λ and for two different reflector diameters. Since the percentage aperture blockage increases with a reduction of the reflector diameter, its ef­fect on the sidelobe and the gain is larger for a smaller reflector. The effect of the strut diameter on the cross-polarization is, however, more complex and reduces initially the peak cross-polar losses.

Effect of the strut plane Practically, the polarization of the field is difficult to align with

respect to the strut. It is therefore desirable to understand the effect of their angle on the reflector performance. Figure 6 shows the computed results, where the co-polarized data are obtained in the plane normal to the strut, φ0 + 90°, and the cross-polarization is given in the plane φ = φα + 45°. The aperture field is polarized along the ^-direction and the reflector and the strut diameters are 48λ and 0.5X, respectively. Note that, for this assumed aperture field polarization, the strut is perpendicular to the electric field when φ0 = 0 and becomes parallel for φ0 = 90°. An examination of the results reveals that the amount of reflector gain reduction and the first sidelobe level rise increase as φ0 increases. That is, as the strut tends to become parallel to the aperture field, its effect on the gain and the sidelobe level increases. The peak cross-polarization, however, has again a more complex dependence on the strut align­ment. Its contribution to the cross-polarization rise is negligible when the strut is perpendicular to the field polarization. In addi­tion, the maximum rise in the peak cross-polarization does not oc­cur when the strut is along the field polarization, but when it is located at a 45° angle with respect to the field polarization. In this latter case, it increases the cross-polarization by about 9.5 dB.

Effect of the aperture illumination The effect of the strut on the reflector performace also depends

on the aperture illumination. Although the results of this work are generated by computing the actual scattered field by the strut, the effect of the aperture illumination can most conveniently be ex­plained by the null field approach. By increasing the edge taper, the effective aperture size of the reflector decreases, resulting in both gain and sidelobe reductions. However, since the reflector shadow­ing area remains constant, both strut and feed blockage areas in­creases relative to the reflector effective aperture.

Thus, their effect on the reflector gain reduction and the rise of the sidelobe and the cross-polarization levels increases. Figure 7 shows the computed results for a 48λ reflector with a 0.5X strut diameter. Since, again, a ^-polarized field is assumed, the strut is aligned along the j>-axis and the computed co-polar data are at the x-z plane, which is normal to the strut. The results indicate that the edge illumination has the strongest effect on the sidelobe level and both gain reduction and the cross-polarization, while increasing, are rising slowly.

Circular polarization The performance of a 48λ reflector with the circularly polarized

feed was also studied. For a single strut, the radiation patterns are

SANAD/SHAFAI: FEED SUPPORT BLOCKAGE 91

T A B L E I

Efficiencies of single strut, tripod and quad strut configurations. Feed diameter = 2.5λ, strut diameter = 0.5X, reflector diameter = 48λ, cos 0 illumination ^-polarization.

Unblocked reflector

Single strut Single strut perpendicular to along the

the ΖΓ-plane £-plane

Tripod with strut planes: 0,120°, 240°

Quad with strut planes: 0, 90°, 180°, 270°

Spillover 5.69% 81.342% 80.196% 78.33% 77.12% power

Efficiency V

82.803% 42.67dB 42.61dB 42.51dB 42.44dB

Gain G

42.75dB

shown in Figures 8a to 8c and the effect of the strut parameters are presented in Figures 9 and 10. In this case, the gain reduction and the sidelobe level increase fall between the results of two linearly polarized cases, one along and the other transverse to the strut direction.

The significant difference between the results of the circularly polarized and the linearly polarized cases is in the cross-polarization. In the linearly polarized case, the axial cross-polarization is negligible and its peak cross-polarization occurs at an angle near the 10 dB co-polar pattern. On the other hand, for a single strut, the axial cross-polarization of the circularly polarized feed is nearly maximum, and the rise in the cross-polarization level is significantly larger. This large axial cross-polarization can be eliminated by symmetric strut configurations, such as the quad geometry. Figure 11 shows the co-polar and cross-polar patterns of this geometry, which indicates the elimination of the axial cross-polarization.

Conclusion

The effect of strut blockage on the radiation characteristics of small reflector antennas was investigated, the computed results, in­cluding the effect of feed blockage, were presented for different strut configurations. Both linear and circular polarizations were considered and it was shown that, aside from the cross-polarization, both polarizations were affected to a similar degree by the blockage.

The main conclusions to be made are: 1) for the circular polariza­tion, the increase in the cross-polarization level due to the strut blockage is higher, which also causes an axial cross-polarization; 2) the reduction of the sidelobe levels using higher edge tapers is not an effective method. Both strut and feed scattered fields raise the sidelobe levels at an increasing amount with a higher edge taper. In other words, a reflector with a feed or strut blockage has an in­herent limitation in the sidelobe performance.

Appendix

In the Eqs. (4) and (5), the underlined vectors and functions are given by the following expressions.

eQ = [cos0cos(</> - φο) — tan α sin 0] aQ - sin(</> - φ0)άφ d )

P0 = (kz' ι - Α:/·/tan a) (cos 0 - 1) (2)

A0 = : sin 0 cos (φ - φ0) + tan a (cos 0 - 1) (3)

B = sin a sin 0 cos (φ - φ0) - cos a cos 0 (4)

C = sin 0 sin (φ — φα) (5)

δ — tan

IFRE(D, δ, a) = - 1 ka cos a Σ *"fji

Jn (kaD) 2\ka cos a)

(6)

(7)

(8)

ëc = ά θ [sin δ cos α sin 0 + sin δ sin a cos 0 cos(<£ - φ 0 ) — cos δ cos 0 sin (φ — φ0)] + άφ [ — sin δ sin a sin(</> — φ 0 )

- cos δ cos (φ - φο)] (9)

ês = άθ [cos δ cos α sin 0 4- cos δ sin a cos θ (φ — φσ) + sin δ cos 0 sin (φ — φ0)] + ά φ [ — cos δ sin α sin(0 - φ 0 )

+ sin δ cos (φ - φα)] (10)

êa = cos oi cos 0 cos {φ — φο) — sin α sin 0 (11)

βφ = - cos a sin (φ - φ0) (12)

IFRHiD, «.«>-- ^ f . * ° > Η β Ζ Ζ α ) ( 1 3 )

JFRHiD, «.«)=- ^ ^ H ^ k a L a ) ( 1 4 )

EA{r' ) is the focal-plane E-field in the r' -direction and HA(r' ) is the focal-plane //-field in the r' -direction.

References

1. Silver, S., Microwave Antenna Theory and Design, McGraw-Hill Book Com­pany, New York, 1949, pp. 87-89.

2. Gray, C.L. , "Estimating the Effect of Feed Support Member Blocking on Anten­na Gain and Sidelobe Level ," Microwave Journal, March 1964, pp. 88 -91 .

3. Ruze, J., "Feed Support Blockage Loss In Parabolic Antennas ," Microwave Journal, Vol. 11, N o . 12, 1968, pp. 76-80 .

4. Rusch, W . V . T . and Potter, P . D . , "Analysis of Reflector Antennas ," Academic Press, New York, 1970.

5. Rusch, W . V . T . , Hansen, J .A. , Klein C.A. , and Mittra, R., "Forward Scattering from Square Cylinders in the Resonance Region with Application to Aperture Blockage," IEEE Trans, on Antennas and Propagation, A P - 2 4 , N o . 2, pp. 182-189, March 1976.

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