NATIONAL RADIO ASTRONOMY OBSERVATORY

GREEN BANK, WEST VIRGINIA

ELECTRONICS DIVISION INTERNAL REPORT No. 277

APERTURE EFFICIENCY FOR PRIME FOCUS

PARABOLOIDAL REFLECTORS AND

CASSEGRAIN ANTENNAS

SIVASANKARAN SR1KANTH

FEBRUARY 1988

NUMBER OF COPIES: 150

APERTURE EFFICIENCY FOR PRIME FOCUSPARABOLOIDAL REFLECTORS AND

CASSEGRAIN ANTENNAS

Sivasankaran Sri kanth

A program in basic by R. Fisher [1] on the HP9825Acalculator has been in use for the calculation of prime focusefficiency, blockage, spillover and scattering on the 140-footand 300-foot telescopes. In the antenna test range at GreenBank, radiation patterns of feeds were recorded on an X-Yplotter, which was the only form of output available. Values hadto be read off these plots and input into the HP9825A calculatorfor the computation of aperture efficiency. This did not givethe best accuracy, in addition to the time and effort involved.

Since then, a personal computer has been interfaced to therange for data acquisition [2]. The PC stores the amplitude andphase vs azimuth information of the test feed on the hard disk.This report describes a Turbo Pascal efficiency program nowrunning on the PC, which can read the values off the hard diskand compute the aperture efficiency readily.

Features of the Program

A list of features of the Turbo Pascal program are includedhereunder.

1. Both the principal plane pattern values are used incombination as opposed to using them separately as in[1].

2. Crosspolarization efficiency is included.

3. Equations for taper, phase and crosspolarizationefficiencies are taken from a paper by R. E. Collin[3].

4. The effect of non-coincident phase centers in theprincipal planes is accounted for.

5. Efficiency calculation for a Cassegrain antenna isincluded.

6. Blockage and scattering computations for a prime focusantenna is done using the same approach as in El].

7. For a Cassegrain antenna, center blockage andsubreflector edge diffraction effects as analyzed by P.S. Kildal [4] have been included. Also, subreflectorstruts blockage effect is accounted for.

COS — X2

0 [" fea q)2

-2jkf

0) sin (1) cos (I)

2

8. Efficiencies on the 140-foot, 300-foot as well as theVLBA antennas can be computed. Since the taperefficiency is computed for a Cassegrain system, a wordof caution, this efficiency for the VLBA antenna wouldbe lower than the actual value, the reason being theVLBA antenna is a dual shaped reflector.

Prime Focus Reflector

The radiation pattern of a corrugated type of feed is givenby

—

Ef 0 e (0) sin (i)

-jkr [6 e(1)(0) cos (f) (1)

where 0 and q) are the polar angles in spherical coordinates asshown in Figure 1, e 0 and e ; are the far-zone field patterns inthe principal planes and k 13 the free space wave number.

The aperture field of a parabolic reflector illuminated bythe above feed, computed by ray optics is of the form

+ y (e cos2

(I) + e0 sin2 (2)

where f is the focal length of the reflector.

Fourier transform of the aperture field in (2), gives the far-zone radiated field of the reflector. The co- and crosspolarizedfields of the feed are proportional to ee sin 2 + ecp cos 2 4) and(e

0 - e ) sin 4) cos 4), respectively, and these are translated

into E and Ex on the aperture plane of the reflector as seen in

(2).

The aperture efficiency of the reflector can be factored as

n a

n nt sp x ph11 • • • (3)where

nt ' Ti sp, n x and n

ph are the taper, spillover, cross-polarization and phase efficiencies. The other factorscontributing to losses like blockage, random surface error,defocus, squint, etc., have not been shown.

Thomas in [5] defines the efficiencies in the followingform:

Lo

f ®0 (lee,

l

ed)tan de

nph

2

of (e,

(6)

3

tan de

sin 0 dOle0

(5)00

2 f [le I sin 0 dO

sin 0 dO

(4)

20

0132 (f/D)2

4) 1) tandeol

0

(le

0

16 f (7)sin 0 dO

where f and D are the focal length and diameter of the reflectorand 0 0 is the half angle subtended by the paraboloid at the focus( Figure 2).

The expressions in (4) and (6) have been used in [1] exceptthat the field in only one plane, has been used at a time. It isnoticed from (5) that when leo! = leqd, the crosspolarizationefficiency is unity, which is not always correct. Collin in [3]gives the radiated copolarized power intercepted by the reflectoras proportional to

o

It1 0 I2 + I e(t,

0

sin 0 dO (8)

2

tan 1

dO2

e (pl tan 2. dO2 )2

n ph

(

(12)

nt

64(ol®°

o

2

ee

+ e —

o do2

2e

0e)2

(

(9)

sin 0 dO

f°

e61)1 isin 0 de

e0

- e 41, 2 sin 0 dO

4 sin 0 de

11

+ e 2 +

2 +

sp(10)

0e -

r°0( )

2 in 0 de

and total radiated power as proportional to

Using (7) and (8) , the equations for taper, spillover, crosspolarization and phase efficiencies are given as:

The effect of feed house blockage and scattered and spill-over radiation from the ground have been computed using the samemethodology in [1]. Measured E and H plane field patterns of aprime focus feed are shown in Figure 3 and the computed effi-ciency in Figure 4. The scattered temperature P(J) in Figure 4has three components, namely:

(1) Fraction of energy scattered to ground by thefeed house assembly.

(2) • Fraction scattered off the feed supports bythe outgoing plane wave.

(3) Fraction scattered by the feed supports bythe spherical wave from the feed.

The aperture efficiency with and without blockage are computed.

Cassegrain Antenna

For the Cassegrain system also, equations (9) through (12)have been used for the efficiency conputations with the followingexceptions. The factor 64 (f/D) 2 in (9) is replaced with 64(fM/D) 2 , where M is the magnification of the Cassegrain system.Also, 0 0 in the limits of integration is replaced by ipo, which isthe half angle of an equivalent paraboloid from the secondaryfocus as shown in Figure 5.

Subreflector Diffraction and Blocka g e , and Struts BlockageEffects:

In the prime focus case the effect of blockage by the feedhouse and support struts is accounted for, by introducing acorrection factor in the numerator of the taper efficiencyintegral, resulting in a taper efficiency with blockage [1].Whereas, here, a separate interference efficiency fl int iscomputed and the aperture efficiency is given as

n n • n • n • Ti • nsp x ph ia t nt

The interference efficiency as given in [4] is

(13)

n. = 11int

+ A 4. A + A 12

cb sb d

where Acb, Asband Ad are due to subreflector center blockage,feed support blockage and subreflector edge diffraction,respectively.

The center blockage term is given by

(1Pd.

1V7)

i en(*) + ( d tan 1 dlp0 2(

: 11) 0 ieo

( 1 ) + e (1) ( 0) tan I dip2o

A cb (14)

This includes the effect of optical shadowing by the subre-flector weighted by the feed illumination taper.

Ad

(1 - j) Cd (16)

6

The feed support blockage is given by

ilPst/p) Y(4)) tan dip

A sb(15)

where

0

t

e e + e (E) ) tan chi)

NW'Y( 10 =

4fffM I sin IP

( + cos tp

N is the number of feed supports and W' is the width of eachsupport, projected vertically on the reflector. The angles ipd,ip st and cp o are shown in Figure 5.

Kildal in [4] shows that the effect of diffraction from thesubreflector edge can be included in the aperture efficiency byadding a single line integral to the geometric optics apertureintegral. He expresses the diffraction term by

where

e,0 0 ) + yipo)0

2 E(0)

is the mean amplitude illumination at the edge of the sub-reflector and

sin 4)0

2ff 1[71;

00-

is the diffraction parameter.

2 E(0) tan —2--

e0 + e

(t. tan —2

d 11)

Aisc, is the wavelength of operation, d and D are thesubreflector and main reflector diameters, respectively.Measured principal plane patterns of a Cassegrain feed are givenin Figure 6 and the computed efficiency on the VLBA antenna isshown in Figure 7.

The Turbo Pascal Program

The efficiency program is stored on the hard disk of the IBMPC at the antenna test range. The feed pattern data should besaved in data files in order to compute the efficiency. Afterthe data is taken, the range software [2] returns to the mainmenu and by pressing the F4 function key the data can be saved ina file by giving it a name. When all the data is taken or atleast the E and H plane patterns at a particular frequency havebeen taken and saved, exit the range software program by pressingF10 function key. Control returns to DOS and you are in thec:\patterns directory. Now type the command

scopeff

which executes the efficiency program.

The program lists all the files saved and asks you to select thetwo files, which have the E and H plane patterns, in that order.If you wish to calculate the aperture efficiency based on oneplane only, just type the number of the particular file twice.You will then be asked to input the distance (in inches) betweenthe phase centers in the two planes. Next you will be asked ifyou want to input the pattern level, past the azimuth boundary.If you said yes (y), then you will be asked to enter the level( in dbs). If not, the program takes the level at the azimuthboundary and assumes the same value for the rest of the patterns.

Caution: When the azimuth boundaries are less than 90° and ifthe pattern levels are high at the azimuth boundaries, spilloverefficiency may be lower than actual and so it would be better toinput the level past the boundary.

The phase patterns in the principal planes may be offset from oneanother, due to reasons like drift during the time intervalbetween the measurements, position of the thumbwheel switches onthe receiver, etc. The program takes into account this offsetand corrects for it.

Other parameters like the telescope, frequency, type of focus,etc., which are required in the efficiency computations are readfrom the data file itself. So caution must be exercised inentering the correct parameters in the main menu of the datataking program.

REFERENCES

[1 ] Fisher, R., "Prime Focus Efficiency, Blockage, Spillover andSat t t er i ng Calculations on the HP9 825 A Calculator,"Electronics Division Internal Report No. 174 (November1976).

[2] Will, W. A., Norrod, R. D., Srikanth, S., "Antenna TestRange Automation," Electronics Division Internal Report No.272 (November 1987).

[3] Collin, R. E., "Aperture Efficiency for ParaboloidalReflectors," IEEE Transactions on Antennas and Propagation,Vol. AP-32, No. 9 (September 1984).

Kildal, P. S., "The Effects on Subreflector Diffraction onthe Aperture Efficiency of a Conventional CassegrainAntenna-An Analytical Approach," IEEE Transactions on Antennas and Propagation, Vol. AP-31, No. 6 (November 1983).

[5] Thomas, B. M., "Theoretical Performance of Prime FocusParaboloids using Hybrid-Mode Feeds," Proc. IEE, Vol. 118,pp. 1539-1549 (1971).

FIGURE 1 .

Paraboloidal reflector and the coordinate system.

FIGURE 2. Prime focus geometry.

0

1

-11 MINN _

NEMill II' - ---,. 11,111,ale

IIIIII ., 131 IIIIII; I 1 1

11111111 - 1111UD aa 11111 MENS11 1 E

d0/div

1111111111111 ii'' W

mom am MI

:II II 11 I 11 III1 I NM

5e MIN

V

0 170AZIMUTH ( 10/div )

FOCUS = PRIME EDGE ILLUMINATION : RIGHT = -11.28 LEFT = -12.49FEED = INTERFEROMETER/RCA,S/X FREQ = 2.7000 (GHz) PLANE = ECOMMENTSDATE : 01/28/88

-170 0 170AZIMUTH ( 10/div )

FOCUS = PRIME EDGE ILLUMINATION : RIGHT = -11.40 LEFT = -12.71FEED - INTERFEROMETER/RCAsS/X FREQ = 2.7000 (GHz) PLANE = HCOMMENTSDATE : 01/28/88

FIGURE 3. E and H plane patterns of a prime focus feed.

IMM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

M E

FFIC

IEN

CY

& T

EMPE

RA

TUR

ES M

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

M,

ON

TH

E 1

40

FO

OT

PR

IME

FO

CU

S T

EL

ES

CO

PE

FR

EQ

UE

NC

Y =

2.7

00

Gh

zF

EE

D: I

NT

ER

FE

RO

ME

TE

R/R

CA

,S/X

: WIT

HO

UT

BL

OC

KA

GE

:W

ITH

BL

OC

KA

GE

SP

ILL

OV

ER

EF

F.

=0.9

234

TA

PE

R E

FF

.=

0.8

128

TA

PE

R E

FF

.0

.71

42

CR

OS

SP

OL

AR

EF

F.

--0.9

998

PH

AS

E E

FF

.=

SC

AT

. T

EM

PS

. P

(J)

=.

0.8

157

1.1

5.

0.9

513

0.8

51.0

000

0.8

0.

0.9

499

0.8

133

TO

TA

L S

CA

T.

TE

MP

.2

.80

.S

PIL

LO

VE

R T

EM

P.

17

.86

SP

ILL

OV

ER

TE

MP

.-

16

.02

AP

ER

TU

RE

EF

F.

0.7

504

AP

ER

TU

RE

EF

F.

=0

.65

94

HMM

MM

MM

MM

MM

MM

MM

MD

IMM

MM

MIIM

MM

IIMM

EMNI

MM

ITIM

MM

IIMM

MM

MM

MM

MM

MM

IMM

MM

MM

MM

IMM

MM

IIMM

MM

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MM

MIl<

FIG

UR

E 4

. E

ffic

ien

cy o

f a

pri

me

focu

s fe

ed.

FIGURE 5. Cassegrain geometry.

EquivalentParaboloid

I-- -ft--

Hyperboloid

Paraboloid

39 40 59 69 79 89 99-99 -89 -79 -69 -50 -49 -39 -29 -19AZIMUTH

589 19 29( 19/div )

0.1

-99 -89 -70 -60 -50 -40 -38 -20 -19AZIMUTH

FOCUS = CASSEGRAINFEED = 'MBA 2.3 GHZCOMMENTS : COPOLARDATE : 12/30/87

EDGE ILLUMINATION : RIGHT = -11.28 LEFT = -14.23FREQ = 2.1599 (GHz) PLANE = H

59 10 29( 19/div )

9959 69 79 8939 40

AB (3/aiv)

FOCUS = CASSEGRAIN EDGE ILLUMINATION : RIGHT = -11.27 LEFT = -14.19FEED = ULBA 2.3 GHZ FREQ = 2.1509 (GHz) PLANE = ECOMMENTS : COPOLARDATE : 12/38/87

FIGURE 6. E and H plane patterns of a Cassegrain feed.

IMM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

M E

FFIC

IEN

CY

& T

EM

PER

AT

UR

ES

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

;

ON

TH

E 8

2 F

OO

T C

AS

SE

GR

AIN

TE

LE

SC

OP

EF

RE

QU

EN

CY

=2.1

50 G

hz

FE

ED

= V

LB

A 2

.3 G

HZ

SP

ILL

OV

ER

EF

F.

-T

AP

ER

EF

FIC

IEN

CY

CR

OS

SP

OL

AR

EF

F.

PH

AS

E E

FF

ICIE

NC

YA

PE

RT

UR

E E

FF

.(W

/0 B

LO

CK

AG

E)

=C

EN

TE

R B

LO

CK

AG

E T

ER

M--

ST

RU

TS

BL

OC

KA

GE

TE

RM

--D

IFF

RA

CT

ION

TE

RM

- -INTERFER. EFFICIENCY

APERTURE EFF.(WITH BLOCKAGE) =

0.9095

0.84

101.

0000

1.00

000.7649

-2.6423884267E-02 -2.6956767146E-05

-2.1501264165E-02 -2.1212624423E-05

-2.8624935190E-02 2.8787906920E-02

0.8536

0.6529

HM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

EMM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

MM

‹

FIG

UR

E 7

. E

ffic

ien

cy o

f a

Cas

seg

rain

fee

d.