IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY RADIATING MECHANISMS IN A REFLECTOR ANTENNA SYSTEM L. PETERS, JR., Senior Member, IEEE, and T. E. KILCOYNE, Student Member, IEEE Abstract-The radiating mechanisms of a re- flector antenna system are discussed. Means of computing the various component fields are given, including aperture radiation, direct feed radia- tion, and diffracted radiation. An offset parabolic reflector antenna system fed with a corrugated horn is treated as an ex- ample. Means of reduction of the undesired components of radiation are suggested. INTRODUCTION The various radiating mechanisms of a re- flector antenna system were described in a previous paper [1] as aperture radiation, direct radiation, and diffracted radiation. The desired main lobe is that which results from aperture radiation. It was shown during World War II that the sidelobes of the reflector antenna system could be reduced to approximately 30 dB below the main beam maximum by control of the aper- ture radiation. These sidelobes, the direct radi- ation, and the diffracted radiation all represent radiation that contributes only to interference. Further reduction of the sidelobes associated with the main beam (i.e., the aperture radiation) can be obtained only by a substantial increase in antenna size to obtain a required gain. However, considerable reduction can be obtained in direct and diffracted radiation by a relatively small in- crease in the reflector size, provided the feed pattern has a large slope in the direction of the edge of the reflector and that it has low back lobes .1 Such a feed pattern has been obtained in the form of the horn with corrugated walls in the E-plane. Manuscript received June 10, 1965. The work re- ported in this paper was supported in part by Contract AF-30(602)-3269 between the Rome Air Development Center, Griffiss AFB, New York, and The Ohio State University Research Foundation, Columbus, Ohio. The authors are with the Antenna Laboratory, De- partment of Electrical Engineering, The Ohio State University, Columbus, Ohio. *This particular boundary determined by the phase cen- ter of the feed and the edges of the reflector is known as the shadow boundary. From optics it is known that the antenna pattern is approximately 6 dB below the feed pattern at this angle. The purpose of this report is, first, to demon- strate the manner in which the entire pattern of a reflector antenna can be obtained from the charac- teristics of the feed and, second, to illustrate the manner in which undesired radiation and conse- quently radio-frequency interference would be reduced. OFFSET PARABOLA In order to simplify the experimental studies, a small reflector surface is treated. Use of conven- tional center-fed reflector systems would, in this case, introduce significant aperture blocking. Con- sequently an offset feed system is used. The antenna and its dimensions are shown in Fig. 1. The feed antenna is the small corrugated horn de- scribed in a previous report [2]. Its pattern at 13.2 Gc/s is shown in Fig. 2. It has nearly identical E- and H-plane patterns. The reflector dimensions are chosen so that the feed pattern is down 18 dB Side View Front View Reflector Reflector 0 p x, eo Feed , i f < Feed 3J-* / ~~~3 Corrugations (Top & Bottom Walls) Feed Horn Detail Fig. 1-Horn reflector assembly, where a= 10.415" f = 14 5/8" Oo = 41.7500 A= 2" 368 December
Transcript
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
RADIATING MECHANISMS IN A REFLECTOR ANTENNA SYSTEM
L. PETERS, JR., Senior Member, IEEE, and T. E. KILCOYNE, Student Member, IEEE
Abstract-The radiating mechanisms of a re-flector antenna system are discussed. Means ofcomputing the various component fields are given,including aperture radiation, direct feed radia-tion, and diffracted radiation.
An offset parabolic reflector antenna systemfed with a corrugated horn is treated as an ex-ample. Means of reduction of the undesiredcomponents of radiation are suggested.
INTRODUCTION
The various radiating mechanisms of a re-flector antenna system were described in aprevious paper [1] as aperture radiation, directradiation, and diffracted radiation. The desiredmain lobe is that which results from apertureradiation. It was shown during World War II thatthe sidelobes of the reflector antenna systemcould be reduced to approximately 30 dB belowthe main beam maximum by control of the aper-ture radiation. These sidelobes, the direct radi-ation, and the diffracted radiation all representradiation that contributes only to interference.Further reduction of the sidelobes associatedwith the main beam (i.e., the aperture radiation)can be obtained only by a substantial increase inantenna size to obtain a required gain. However,considerable reduction can be obtained in directand diffracted radiation by a relatively small in-crease in the reflector size, provided the feedpattern has a large slope in the direction of theedge of the reflector and that it has low backlobes.1 Such a feed pattern has been obtained inthe form of the horn with corrugated walls in theE-plane.
Manuscript received June 10, 1965. The work re-ported in this paper was supported in part by ContractAF-30(602)-3269 between the Rome Air DevelopmentCenter, Griffiss AFB, New York, and The Ohio StateUniversity Research Foundation, Columbus, Ohio.
The authors are with the Antenna Laboratory, De-partment of Electrical Engineering, The Ohio StateUniversity, Columbus, Ohio.*This particular boundary determined by the phase cen-ter of the feed and the edges of the reflector is knownas the shadow boundary. From optics it is known thatthe antenna pattern is approximately 6 dB below thefeed pattern at this angle.
The purpose of this report is, first, to demon-strate the manner in which the entire pattern of areflector antenna can be obtained from the charac-teristics of the feed and, second, to illustrate themanner in which undesired radiation and conse-quently radio-frequency interference would bereduced.
OFFSET PARABOLA
In order to simplify the experimental studies, asmall reflector surface is treated. Use of conven-tional center-fed reflector systems would, in thiscase, introduce significant aperture blocking. Con-sequently an offset feed system is used. Theantenna and its dimensions are shown in Fig. 1.The feed antenna is the small corrugated horn de-scribed in a previous report [2]. Its pattern at 13.2Gc/s is shown in Fig. 2. It has nearly identical E-and H-plane patterns. The reflector dimensionsare chosen so that the feed pattern is down 18 dB
PETERS AND KILCOYNE: REFLECTOR ANTENNA RADIATING MECHANISMS
/
to
/J
._lo
0)
0)/
/ E-Plone/_ -- H -Plane
-60 -45
-20
-30
-35
-30 -15 0Angle In Degrees
15 30 45 60
Fig. 2-Feed horn radiation patterns. Frequency 13.2 Gc/s.
at the reflector edge. These points are shown on
the pattern of Fig. 2. The slope of the pattern inthe vicinity of these points is large and the backlobes are low, thus the conditions stated in theIntroduction are satisfied. The larger corrugatedhorn treated in the previous report has a muchsharper slope at the 18dB points and far lowerback lobes. It would thus be a much better feedto be used with a larger reflector.
COMPOSITE PATTERN OF THEOFFSET PARABOLA
be described as a function f (r, 0 '), where r = p/aand is the normalized coordinate in the 0 = 90°plane, as illustrated in Fig. 3. Because of spatialattenuation, the amplitude of the source field at an
arbitrary point on the reflector a distance f fromthe feed is given by
f (r,o ') = F (f) f (r, '). (la)
where F (f) is the spatial attenuation factor [3]. Forthis configuration F (Q) = QO/Q, is the distance to thecenter of the reflector, as shown in Fig. 4. Substi-tuting in (la) yields
The aperture radiation pattern of this config- -O
uration can be obtained from the feed antenna f (r,4') =f f(r,4'). (lb)
pattern. First the aperture is obtained by means
of ray optics and the feed pattern. The amplitude The aperture radiation pattern is obtained from the
of the feed pattern between the -18 dB points can diffraction integral [4]
/
/I[I
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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
Reflector
II10
Feed
y
Fig. 3-Coordinate system for the circular aperture.
p
-jkRe fff (r,0t)eiurcose
¢~ rdrdo', (2)
where a is radius of the aperture, k = 27/X, u = kasin 0, and R is distance to the far field.
The diffraction integral can be evaluated for anyaperture distribution with the aid of a modern digi-tal computer. The validity of this method is wellknown, and consequently is not carried further.
The direct radiation is given by
0E R f (r,') (3)
Fig. 4-Geometry for spatial attenuation.
Denoting the principal-plane half-power beam-widths of the feed by
0 F l ' 0 F l2 2
and of the parabola by
0 , bP I P '
2 2
the directivity of the parabola relative to the feed is
DPD
DFF2 F 2
p1 p 12 2
(5)
From the measured patterns
0 = 22.50F 22
where ko is distance from the source to the centerof the reflector, and R is distance from the source
to the point of observation.The relation between the levels of the aperture
radiation and the direct feed radiation can be ob-tained by comparing (2) and (3). This would, ofcourse, require that the integral be evaluated. Therelative level of the two patterns may also be ob-tained by determining the directivity of the mainbeam caused by aperture radiation and the direc-tivity of the feed antenna. This is easily done bymeans of the approximate formula for the direc-tivity of a pencil beam antenna,
D= 41,2530' 1 '
2 2
(4)
where
= 20.40 = 4.502
Substitution of these values in (5) yields
DP = 21.3, or + 13.3 dB.
DF(6)
The diffraction of fields at the edges of the re-
flector is illustrated in Fig. 5(a). It is assumedthat the reflector can be replaced by infinite, per-fectly conducting half-planes, as shown in Fig. 5(b).Sommerfeld [5] obtained the diffracted field in theform
v (r4O) = e-j/4 [2
01, 12 2
are the principle-plane half-power beamwidths indegrees.
jkr cosC
0e cos 2
00 * 2
f e -J T dT, (7)
+ akr
R
z
0p 1
= 4.80
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PETERS AND KILCOYNE: REFLECTOR ANTENNA RADIATING MECHANISMS
-,V\ Diff ractedRays
Reflector
E Incident Rays
I --k Source
Fig. 5(a)-Edge diffraction.
In asymptotic form the diffracted field expressionfor a thin edge is
[27Tkr] -2 e-j (kr + )
vB(r, ) - 2. (8)cos 2
If p 1800, this yields a maximum component ofdiffracted radiation. It would be desirable to force
Point this maximum in the direction of the main beamwhere its contribution would be negligible.
Let u1 (0) and u2 (0) denote the diffracted fieldsfrom edges (1) and (2), respectively. Then
Pointu1(o) = vB(rl, ;61 - '01) + vB(rl, 1 + 01)/
(9)u2 (0) = vB(r2, ' '2 - iP02) + vB(r2) 1/2 + ?/02)The phase difference from edge (1) to edge (2) is ob-tained from Fig. 5(c) as
Fig. 5(b)-Geometry of edge diffraction.
Fig. 5(c)-Geometry of edge diffraction.
where
0 = 1'+ 'o [the (-) sign yields the incidentfields; the (+) sign yields the reflectedfields ]
a = 1 + cos 0
k = 2mu/X and 0, 00 are the angles shown in Fig.5(b).
The total diffracted field is the sum
U = VB(r,±+70) + vB(r, S 3-%0).
kd = 2mxo cos (?P2 - a2), (10)
where the distance xo from edge (1) to edge (2) ismeasured in wavelengths. The total diffracted fieldis
uT (0) = u1 (o) + [u2 (o)] ej27TxOcCos (t2- a2)
The computed diffracted field pattern is shown inFig. 6, and it should be noted that the appropriatephase factors have been included.
The total pattern of the reflector antenna may beobtained, approximately, simply by placing the com-ponent parts on a single pattern. No effort is madeto sum the phasor fields since it is the averagevalue that is of interest. The results are comparedwith the experimental pattern in Fig. 7. It is seenthat reasonable agreement is obtained for the com-ponent parts of the pattern, with the exception of theregion 1600 < 0 < 1800 in which the experimentalpattern is much lower than the computed pattern.This deviation appears because the main source orthroat of the horn is shielded from the edge by thewall of the horn, as shown in Fig. 8. The pattern ofthe horn in this region results from diffraction atthe horn edges and multiple reflections from thewall of the horn. The diffracted fields from thesevarious sources are not in phase, and consequentlythe total diffracted fields are lower than the pre-dicted values. This type of diffraction representsa new phenomenon and requires further study.
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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
Angle 9 In Degrees -*
Fig. 6-Diffraction pattem for the offset feed antenna.
La
z
-iw
w-J
LU
I-,
a.
ANGLE 6 IN DEGREES
Fig. 7-Experimental pattern compared with component parts. Note that the direct radiation for 1050< 0 < 1730 is shown only for clarity. This part of the direct radiation is intercepted by thereflector.
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'a:
c
z
:>la;
0f'
PETERS AND KILCOYNE: REFLECTOR ANTENNA RADIATING MECHANISMS
Corrugations
Fig. 8-Direct feed radiation.
It should also be noted that the actual pattern is7 dB below the antenna feed pattern at an angle of1050. Diffraction theory would predict this level tobe 6 dB below the feed pattern. This is anotherreasonably accurate, simple method of predictingthe level of this point on the pattern. Figure 7shows that angles V'1 and 002 can be selected so
that maximum edge diffraction is in the direction ofthe main beam, i.e., 900 for 0 = 00. Thus this
highest level diffracted energy does not contributeto any new sidelobes.
FURTHER REDUCTION OFUNDESIRED RADIATION
The major component of undesired radiation isthe lobe appearing at 0 = 95°. This lobe can beeliminated by extending the reflector by 9 inchesso that it subtends an additional angle of 150. Thiscould also be done by surrounding the reflector bya "tunnel' extending 6 inches from the edge of the
Feed
Fig. 9-"Tunnel" dish.
reflector, as shown in Fig. 9. Both of these ap-proaches require a significant increase in the sizeof the antenna structure.
A redesign of the feed structure could possiblyaccomplish the same goal without increasing thereflector size. The flare angle of the feed antennashould be reduced to eliminate the direct illumina-tion of the edge of the reflector from the throatregion of the feed antenna. It is expected that thiswould yield a radiation pattern in the vicinity of0 = 950 which is similar to that obtained at about1650.
CONCLUSIONS
Techniques have been given for determining thetotal radiation pattern of a reflector antenna fromthe properties of the feed antenna. The feed anten-na discussed in this report has the desirable prop-erties of relatively low back lobes and a relativelylarge slope in the vicinity of the shadow boundary.The average level of the back lobes is approximate-ly 50 dB. This is not an optimum, however, sincethe goal of this effort is to determine analyticallythe magnitude of the undesired radiation. Lowerback lobes should be obtainable by further consid-eration of these techniques.
Several guidelines for the expected levels of un-desired radiation have been given. First, the levelof the direct radiation is related by the gain of thereflector and of the feed antenna. Second, the dif-fracted radiation on the shadow boundary is 6 dBbelow the level of the feed antenna at this angle.Third, the maximum diffracted radiation can besuccessfully forced in the direction of the mainbeam by an appropriate choice of reflectorgeometry.
REFERENCES
[1] L. Peters, Jr., and R. C. Rudduck, "RFI reduc-tion by control of antenna sidelobes," Ohio StateUniversity Research Foundation, Antenna Lab.,Columbus, Ohio, Rept. 1423-4, ASTIA Doc. AD405 824, under Contract AF-30(602)-2711, RomeAir Development Center, Griffiss AFB, N. Y.,January 1, 1963.
[2] R. Lawrie, L. Peters, Jr., and C. Davis, "Modi-fication of horn antennas for low sidelobe levels,"Ohio State University Research Foundation, An-tenna Lab., Columbus, Ohio, Rept. 1767-2, underContract AF-30(602)-3269, Rome Air Develop-ment Center, Griffiss AFB, N. Y., February 22,1965.
1965 373
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
R. G. Kouyoumjian, L. Peters, Jr., and D. T.Thomas, 'A modified geometrical optics methodfor scattering by dielectric bodies," IEEE Trans.on Antennas and Propagation, vol. AP-li, pp. 690-703, November 1963.
