AD/A-002 601

A BROADBAND QUADRUPLE-RIDGEDWAVEGUIDE RADIATOR

Fan King, et al

Army Missile Research, Development andEngineering Laboratory

Prepared for:

Boeing Aerospace Company

30 June 1974

DISTRIBUTED BY:

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE

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SA BROADBAMN QUADRUPLE-RIDGED WAVEGUIDE RADIATOR Technical Report

S~6 PERFORMING ORG. REPORT NUMBER

___RE-74-7S7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(*)

Fan King, James S. Yee, Dorald R. grbach

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US Army Missile Research, Development and AREA 6 WORK UNIT NUNBEfS

SEngineering Laboratory AC de 62303.1 0US Army Missile Command AMCMS Code 632303.11.21401

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30 June 197413. NUMBER ^I' -AGFS

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20 ABSTRACT (Continue on rever.. aid. It neceezi.,) end Identify by block nu.ber)

This report presents the results of an investigation in the design of abroadband quadruple-r.dged waveguids radiator. It covers the theoretical andpractical aspeccs in the design of the ridged waveguide parameters, the designof the ridges in the flared section, and the design of the coaxial to ridgedwaveguide trans former.

71-P result of the investigation is a 2 - 12 GHz bandwidth, dual-

polarizatio-,, quadruple-ridged horn which is an advancement in the state-j of-the-art. .....

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II

CONTENTS

Section Page

I INTRODUrITION .*. . . . . . . . . . . . . . . . . . . 3

II STATEEIN'; OF THE DESIGN PROBLEM. . . . . . *....

III RIDGED WAVEGUIDE PARA•JTERS . . . . * . . . . . . . . i

IV DESIGN OF THE RIDGES IN THE FLA-RED SECTION ..... 22

V DESIGN OF THE COAXIAL TO RIDGED WAVEGUIDETRANSFORMER. . ... . 24

VI EXPERMINTAL RESULTS . ................ 28

VII CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . 35

ii

ACKNOWLEDGEMENTS

My thanks are expressed to Mr. William L. Low, Chief, RadarTechnology Branch, Advanced Sensors Directorate, and Mr. William J.Lindberg, Director, Advanced Sensors Directorate, US Army MissileResearch. Developm Mt and Engineering Laboratory, US Army MissileCommand, for their encouragement and cooperation in tbis work.

I also wish to acknowledge that without the full cooperation ofpersonnel of the Boeing Aerospace Company, Research and EngineeringDivision, Seattle, Washington, this report could not have been wcitten.

2

Section I. INTRODUCTION

This report presents the results of an investigation in the design"of a broadband quadruple-ridged waveguide radiator. Since a quad-ridgedI horn element is used in the US Army Radio Frequency Simulation System(RFSS) target array, the design was undertaken to reduce the developmentrisk in achieving a horn which would meet the RFSS antenna requirement.

The electrical performance characteristics for the horn are shownin Table 1. These characteristics are to meet the test conditions andlimits so specified in Table 2. The desired antenna recuaires highspatial volume efficiency over a wide frequency range. Considerationof broadband antennas naturally leads to corsideration of psuedo-infinitelog-periodic antennas which have proven useful on so many applications.Log-periodic antennas, however, are limited to a geiu of approximately10 dB independent of the frequency. This means that Twhile the antennamay have a very high volume efficiency at the low frequencies, theefficiency at the higher frequencies may not be all chat is desired.

Horn antennas have high aperture efficiencies b.it have beencapable of operating over only liited bandwidths. -o extend thelimited bandwidth4, ridges have been added in recent years to thewaveguide and flared sections of the horns. Since tha design requiresan antenna capable of producing circular polarizqtion with two ports,a square geometry would be necessary. Another itrpoi tant designparameter was the cross-polarization coupling oi-. bearin axis between thetwo ports. It was this parameter that eliminated i -onsderation oflog-periodic antennas, since tescs of suitable a-vte. -s revealed resulcson the order of -12 dB rather than the -20 dB d ! ;oecification.Narrow band quad-ridged horns had been tested and ha- cross-polarizationcouplings of the desired magnitude.

3

TABLE 1. ELECTRICAL PERFORMANCE CHARACTERISTICS

LVr.it

Parameter Minimum Maximum Units

Frequency range (continuous) 2.0 12 GHz

Number of ports 2 2

Gain on beam ax).s (at each port) 6.0 dBI

Pattern characteristics

Symmetrical beam with

mr-ximum on ax'.

Front-to-back lobe ratio 10 dB

Cross-polarization coupling on -20beam axis

Port isolation 25 dB

Amplitude imbalance between 0.5 dB

ports

Phase i-tibalance betw'een ports 10 degrees

VSWPR at each port 2.0:1

Port connectors (2) female type SMA

Gain spread among antennas (at I dBany frequency withii,: band)

Power handling capability

Peak power 10 100 Wattduty factor (averagepower) 25% 2._ 25 Watt

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Section Ii. STATEMENT OF THE DESIGN PROBLEMI

It is the goal of this paper to dwell on the theoretical andpractical aspects of designing a quadruple-ridged waveguide radiatorrather than on the aspects of pyramidal horn design. The exteriordimensions of the born were selected consistent with the dimensions ofthe feeding waveguide, the 6 dBI minimum gain requirement at the lowerend of the frequency band, and minimization of phase errors across theaperture. This later constraint is especially true when extremely widebandwidtns are considered. Since the ridges must be terminated withinthe flared section, the horn aperture must be half a wavelength or morein width (H-plane) at the lowest frequency to permit propagation of theTEl0 mode.

However, an aperture more than a half wavelength wide at thelowest frequency is many wavelengths wide at the highest frequency.This means that large phase errors will be present acrGis the apertureunless the horn is extremely long. This can be a limiting factor atthe high end of the frequency band of operation of ridged horns. Some-times a dielectric lens is used to reduce the phase error to a minimum.

Figure I shows the broadband quadruple-ridged waveguide radiator.It looks like an ordinaty pyramidal horn. An open view is depicted inFigure 2, and Figure 3 ,,ives an open view on a coax feed-side of thehorn, The basic horn zcnfiguration, as seen from the three figures,consists of quadruple-ridged waveguide terminated at one end in a wave-guide to coax transformer and at the other end in the fl.red horn sec-tion. Selectisn of the ridged 4aveguide parameters will be discussedin Section III. Design of the ridges in the flared section is coveredin Section IV and the coaxial to ridged waveguide transformer designis in Section V.

7

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Section III. RIDGED WAVEGUIDE PARAMETERS

Ridged waveguides have been useLul for several years in microwavesystems requiring broadband operation. Much theoretical and practicalwork has been done. In 1947 Cohn [1] published waveguide eigenvaluesobtained by using transverse resonance to formulate transcendentalequations. The discontinuity susceptance between parallel plate wave-guides obtained by Whinnery and Jamieson [2] was employed in the calcu-lations. In 1955 Hopfer [3] extended Cohn's work to other aspect ratiosby inclusion of a first-order correction factor. Hopfer used a quasi-static solution for the discontinuity susceptance between parallel platesobtained from Marcuvit=: [4]. In 1964 Walton and Sundberg [5] extendedthe analysis to cover a broad range of aspect ratio's and applied theseresults to the design of broadband, linearly polarized horns. Hopfer'swork was further extended in 1966 by Pyle [61 to accurate data for anyaspect ratio. Additionally, Pyle included an analysis of error effects.

Each of these previous investigations was primarily aimed at thesolution for the TEno eigenvalues. Little was said about the fieldsof ridged guide until 1961 when Getsinger [7] formulated approximatefield equations by assuming a TEM mode at the gap and matching onlythe electric field. Getsinger used the eigenvalues obtained by Hopfer.A more complete analysis was presented by Montgomery [81 in 1971. Thesolution is obtained by the formulation of an integral eigenvalueequation which is subsequently solved numerically by application of theRitz-Galerkin method.

All of the previously mentioned papers concern themselves with thesingle oi acuble-ridged waveguide problem. Sexson [91 in 1966 did someanalysis on the quadruply-ridged horn. A perturbation technique isused to determine the TEno cutoff frequencies when the ridges are small,and a transverse resonance technique is used when the ridges are large.More recently, with the increased interest in wideband, circularlypolarized radiators in phased array antennas, additional work has beendone in 1973. C. C. Chen [10] et al. designed some radiators with fourridges, while M. H. Chen and Tsandoulas [11,12] determined the modal

characteristics of quadruple-ridged circular and square waveguide.Their analytical study is based on a computer program that calculat-qthe eigenvalues and scalar potentials for an arbitrarily-shaped wave-guide. The analysis was developed by Koi.• - and Sylvester [13] usingthe triangular-finite-element method.

In the actual design of the ridged waveguide parameters, it wasassumed that a simpler two-ridge analysis could be carried directly tothe four-ridge geometry. Once the actual geometry was settled uponbased on a parametric study of the simpler equations and curves for atwo-ridge geometry, a final verification for the four-ridge geometry wasobtained by the computer work of Chen and Tsandoulas.

11

The geometry selected is shown in Figure 4, with the letter notationthat used by Chen and Tsandoulas. Figure 5 shows Cohn's [1] single-ridged geometry with the shaded portion indicating that use of his equa-tions would be an approximat_ .n to the pointed ridges. This is truealso for Walton and Sundberg's [51 geometry shown in Figure 6. They

consider flat ridges only. Locating the feed probe in the center of theawaveguide using a short straight section of ridged waveguide, as the

wave launcher, precludes exciting the TE 2 0 mode so that the maximum

usable bandwidth is the ratio of TE to TE30 mode cutoff oavelengths(0/%3 ) rather than (%10 /10 2

C C* C

The simpler equations for the cutoff wavelt-gths of the variousmodes are as follows:

B BCStan 02 - cot eI +-- 0 (I)D 2 1 Y

B BC-cot O2 + cot eI --- = 0 (2)

where all notation is that for Figure 6 and

36G /A - S\@I = •jYk) degrees

X (-) degrees.Ce 360 d-es

The value of the discontinuity susceptance term (BC/YIO) is derived

by WIninnery and Jamieson [21, and Equation (1) applies to T%1O modes

where M is odd while Equation (2) applies where M is even.

Hopfer [3] has derived an expression for the characteristic impedance

of ridged waveguides for the TE10 mode at infinite frequency which is asfollows:

I2

12

VJ

I I

1.i

Figure 4. Ridged waveguide parameters.

b2

b1

I I

Fig-ire 5. Cohn's wavguide parameters.

D

A

Figure 6. Walton and Sundberg's

waveguide parameters.

13

where

60 %C 2D 2 (jiShrDYOO 2 L 2 D3-Cos in C 123

S~Cos/

S 21S + C• k"S+ - si+ sin

z =1 7 U sin (4)

to Previously published curves of XI ax'd *kC may prove to be adequate

addtinalcacultinswill nedt eperformed. Figure 7 presentsS Fi g re . U ing act al alu s de ive fr m F gur 4) thewaveguidei

Thpcarame teriratios bempe:Vea rqec sgvnb

$-b2 82b

Noting that XC = 2a1 , these ratios give the TE0 cutoff frequency

C0 10

at approximately 1.2 G-z. Cohn's curves also give Z• at approximately

68 ohms. An actual calculation of be for a cutoff frequency of 1.2 Gt z

using Cohn's impedance formula gives ZO =63.5 ohms for double-ridgedwaveguide. Cohn also calculated the cutoff ratios for the TB3 0 modes

as shown in Figure 8. Using previously calculated waveguide parameterratios, the Te 0 cutoff frequency lies between 11.2 GHz and 11.3 Gboz.

Walton and Sundberg calculated the curves shown in Figure 9. The3/A = 0.9 is fairly close to the actual B/A = 1.0 ratio. The otheri ratios a-e S/A b 0.1923 and D/B 2 0.0354. Therefore one can obtain

from Figure 9 the TE1 o cutoff at approximately 1.2 Glz, the TB30 cutoff

at approximately 11.5 GHz, and c0v at approximately 40 ohms. An actual

•14

waeud.Ch als cacuated th cuof raio for• th TE 30 • m odes• mwwm~nmma

1b2 T2 b

II.. a2*. I

I"/_I 2

00

22b

5- ZO-15a 09

2O 0.03

0.75

0.75

1 I 96 i 1.00.2 0.4 0.6 0.8 1.0

a21a1

Figure 7. Chatracteristic impedance and cutoffw.,-:elengt~h of ridge waveguide (bl/a 1 = 0.5).

i5

S"t.4

-.---0.1

1.2 1 -0 0.2

11.0 000- .1.00 T

1.TE3 0 MODE0.8 -

_ g 0.60

80.4 0-

:• ~0.21-

Io_ w i .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0a2/a1

SFigure 8. Cutoff-frequency ratios for the TE 30modes in ridge waveguide.

11.0 B/A= 0.075 D/B 0.15 1.1

o 0.10 TE0.310° .0 -i" TE1 201 I10. °

3.0 0 -7 0..<3 R. 0 .6 "-

8.0 - 0.0. , 0.5

51 0..7

2.0 - 0.20 0.1 0.2 0.4 0.5 0.6 0.7 0.8 0.9

SIA

Figure 9. TEo and TE0 mode cutoff wavelengths

15 0 30ZI-

in doubly-ridg'ed waveguide. ZO• is also shown.

B/A = 0.9.

16

calculation of Z 0- using Hopfer's more accurate impedance equation,

Equation (4), and TE 1 0 cutoff at 1.2 GHz gives Z07 = 50.11 ohms.

These results indicate that the geometry selected for the quadruptyAridged waveguide seems fairly sufficient in bandwidth and impedance.Some concern was given to the possibility of TE 3 0 modes at approximatel:

11.5 GHz but it was hoped that these modes would not be excited. As averification of the approximations made in going from two flat-ridgedwaveguide to the pointed-ridged waveguide, correspondence was made wittH. H. Chen for use of his computer program. His program solves thescalar, two-dimensional Helmholtz equation,

(V2 + k"J O(x,y) = 0 (5)

c

subject to proper boundary conditions. Since the scalar potentialrepresents either the longitudinal magnetic field, Hz, for the TE mod .s

or the longitudinal electric field, Ez, for the TM modes, the boundai

conditions for these modes are respectively O/ýn = 0 and 0 = 0. Th.1solutions of Equation (5) are eigenvalues, k , and eigenfunctions,

ciI

Di (x,y). The k may be related to the modal cutoff frequency and tie

0 (x,y) may be related to the field distribution for mode i in the

iIS~waveguide.

The actual geometry as shown in Figure 4 was utilized in thecalculations by Chen and Tsandoulas. Results are shown in Figure Ipfor W/a = 0.1923. The actual H = 0.627 inch, a = 1.3 Inches givesratio H/a of about 0.48 and readirg from Figure 10 gives the TEl 0

cutoff frequency at 1.36 GHz and 11.36 GHz as the cutoff frequency 5orTE mode. Thus the assumption of utilizing double-ridge analysis -1cr

quadruple-ridge geometry seems to be a good one. Figure 10 also s>wsthat the geometry selected can support several other propagatingat frequencies lower than the TE3 0 mode cutoff frequency of 11.36

30IThese modes will not be excited with tbc selection of the feed at h-ecenter of the ridges.

Figure 11 -hows the bandwidth (TE1 0 - TE30) versus H/a character-

istics for the W/a = 0,1923 ratio. The bandwidth is computed from Arhe

relation,I

S= xl°- X3° oo

X 200%.10 + 30

17

1.5

T530S0TE31 L

TM12

o TE21

S1.0WETE20UJ

~TE20L

TEll "

TE1O

S0 0.1 0.2 0.3 0.4 0.5 0,.6

H/a

1Figure I0. Modal cutoffs versus H!a characteristics forquadruple-ridged square waveguide.

18

r

1 ~150I?

501-

03

0.1 0.2 0.3 0.4 0.5 0.6S~H/a

Figure 11. Bandwidth (TE 10 -. TE 30 ) versus 11/a characteristics for

quadruple-ridged square liaveguide.

19

where 10 and X30 are the TE10 and TE cutoff wavelengths, respectively.

The value of BW thus obtained is as a percentage of the center frequencybetween the two modal cutoffs.

The transverse field distribution for quadruple-ridged square andcircular waveguides can be obtained from the computed scalar potentialS•(x,y). The scalar potential represents the longitudinal componentof the magnetic field for TE modes and of the electric field for TMmodes. Therefore, the transverse electric and magnetic fields can bederived f rom

Hj(x,y) "- Vt TE m(X,y)

E (XY) -z x 0 (,Y) TE modesEt~xy = • t •TE(X

(7)

Sy)4

modes

H t(x,y) -to 0 7 t T TMd(XY) T

Accordingly, the equipotential lines represent electric field lines forthe TE modes and magnetic field lines for the TM modes.

Figures 12 and 13 show the electric field patterns for the TEIo-,d the TE 30 modes, respectively. The figures represen, one-fourth of

the actual geometry. The other three-fourths is symmetric with theportion shown. The field patterns for the dominant TE10 mode indicate

that most of the electric field is maintained within the ridges as seenin Figure 12. For the TE-0 mode field patterns there are two maxinums

with a change in sign. This is one way to represent the T-E 30 moding,

and indicate that there is more field intensity outside of the ridgegaps than for tbe TE mode case.

20

0

Figure 12. Electric field lines for TE mode.

0

Figure 13. Electric field lines for TE30 mode.

21

Section IV. DESIGN OF THE RIDGES IN THE FLARED SECTION

In the design of the ridges in the flared section one notes thatthe ridges must be extended into the flared horn section past the pointwhere the flared section becomes sufficiently wide to support the TE10mode at the lowest. operating frequency. It is desired that the ridgeheight and width taper must also be such that the associated impedancetaper is a smooth transition from the ridge impedance of 50 ohms orless to the impedance of free space, 377 ohms.

Walton and Sundberg [5] found that an exponential impedance taperof the form

Zz e ; 0 :x< (8)

Z = 377 +Z0. (I- ek(i x)) Lx:1(92x 2 (9)

is quite satisfactory. Here Z 0 is the characteristic impedance of the

waveguide and K is a constant such that the impedance of the midpointof the flared section is -he average of the end point impedances.

Kerr [14,15,16] superimposes an additional linear taper on alogarithmic curve. The amount of this additional linear taper hasbeen deteimined experimentally in the design of double-ridged horns.They have ranged from 0.008 X inch to 0.020 X inch where the X-coordinatesare axial distances measured along the center line of the antenna,beginning at the aperture plane of the launcher. He uses the Y-coordinates as perpendicular distances from the center line of theantenna to the radiating element surface.

The taper used in the actual horn design is shown in Figure 14.Constants of the horn taper design were calculated to be derived fromthe following formula for a 4.50 inch square aperture horn:

Y = 100.192543 X - 1.63827 + 0.020 X (10)

where the X and Y coordinates are depicted previously, and the 0.020 Xadditional linear taper is used. Kerr found that this additional lineartaper serves to provide a significant improvement in the VSWR over thefirst octave of the bandwidth and has little effect elsewhere in therange of interest.

22

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CEIlot 0

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2--4

Section V. DESIGN OF THE COAXIAL TO RIDGED WAVEGUIDE TRANSFORMER

The previous sections have dealt with the design of the ridgedwwveguide and the design of the ridges in the flared section of thehorn. This section will deal with the design of the coaxial to ridgedwaveguide transformer. The basic problem is to provide for a transitionbetween the principal coaxial TEM mode and the dominant TE 1 0 mode in

the ridged waveguide. The fundamental way of establishing a desiredmode in a waveguide is the excitation of either the electric or themagntetic field intensity with that mode. This is done either by meansof an "antenna" element parallel to the electric field or by means ofa loop, the plane of which is normal to the magnetic field. Althougheach type has had some application, transitions based on the waveguide"antenna" for electric coupling are much more widely used and is themethod selected,

The crossed transition from coaxial line to waveguide is treatedtheoretically by Slater [171 who has shown that a transition of thistype can be matched by variation of the end-plate and coaxial-plungerpositions, dimensions D and S of Figure 15. In particular, the coaxialstub constitutes a variable reactance in series with the waveguide"antenna" (that portion of the coaxial center conductor which extendsacross the guide), and by means of variations in the length of theshort-circuitsd section of guide, it is possible to adjust the radiationresistance of this "antenna." It has been found, however, by Ragan [181,Cohn [19], Walton and Sundberg [51, and Kerr [14-16] that an exper:Lmentalapproach to the design seems more expedient.

The approach taken in the design of the quadruple-ridged wave-guide radiator was to construct two identical horns as shown previouslyin Figures 1, 2, and 3. These two horns had a movable piston in theback or short-circuited section of the guide. This allowed a movableD dimension. Once the horns were constructed, the design of the coaxialto ridged waveguide transformer was accomplished experimentally. Workwas performed at Boeing, Seattle, and Redstone Arsenal, Alabama,simultaneously.

The final horn dimensions are shown in Figures 14, 16, and 17.Figures 14 and 16 show the side and front dimensions of the radiator,while Figure 17 shows the coaxial to ridged waveguide transformer. Thecoaxial connector is an OSM 206-2 flange mount connector for 0.085-inchsemi-rigid cable. The center conductor or "antenna" of the coaxialcable is 0.020 inch in diameter.

Initially, the ridges did not have the angle e cut into them. Thetwo "steps" shown in Figure 17 also were not initially constructed.Measurements were made utilizing only the "piston" movement as a var-iable. Results indicated good characteristics up to approximately 8Gllz for an optimum setting of the "piston" or "plunger." The addition

24

F

COAXIAL LINEI

Figure 15. Slater's crossed transition "orexcitation of the ele..tric field.

4.625 in.

_ I

Figure 16. Quadruple-ridged waveguideradiator dimensions (front).

25

i JUST TWO

:: RIDGES SHOWN

j -,N' ] 5/16W.n.

TOP VIEW OFRIDGE END /8 ii,

.125 in.

RADIUS

STE

Figure 17. Coaxial to ridged waveguide transformer.

26

of the proper "steps" extended the antenna bandwidth up to approximately10.5 GHz. Later the angle e of approximately 30 degrees was cut intothe ridges, and a metal sleeve was added to the antenna. The sleevewas 0.032 inch in dimmeter.

Only one pair of ridges is shown in Figure 17. Another pair existswith another feed orthogonal to the first antenna. Metal to metalseparation is 0.020 inch or 0.030 inch. One antenna had the 0.020 inchseparation and another the 0.030 inch separation. The only parameterthat was noticeably affected by this difference in antenna separationwas the phase imbalance between portA. The closer the separation, thebetter the phase imbalance between ports. This phase imbalance is noca critical consideration aa one can cfftset the coaxial cable flangemount from the surface of the radiator to "rake up" for the phaseimbalance. A 0.020 inch offset for a 0.020 inch separation seemsadequate to meet the design specification. Likewise for the 0.030 inchseparstion case, an oifset of 0.030 inch is adequate.

Since the second feed or anterna is further away from the short-circuited part of the transformer, it was found that a deeper ridge cutwas necessary than indicated for the first feed pair of ridges. Theangle e is approximately 42 degrees for the 0.030 inch separationantenna. These deeper cuts are necessary for fine tuning the design forthe VSWR parameter in the specifications, but the actual dimensions arenot critical in the precision machining sense. Only the gap separationbetween ridges require precision machining.

Care must also be taken in the construction of the coaxial feeds.As shown in Figure 17, Che coaxial feed is inserted into a hole in thebottom ridge, and the center conductor (sleeve not shown) continuesacross the gap between the ridges into a hole in the top ridge. A setscrew anchors the center conductor in the top ridge for good electricalcontact. The hole in the bottom ridge may be drilled for either thedielectric portion of the coaxial cable or the outer conductor of thecoaxial cable. Although both antenna horns constructed had holes drilledfor the entire coaxial cables, it is recommended that holes be drilledfor the smaller dielectric diameter. The reason for this is that theridges are pointed. A dielectric entrance into the gaps between th-ridges creates less of a perturbation than one with both metal outerconduc6or and dielectric. In the latter case, the outer conductor mustnot protrude into the gap regions. In both cases, the dielectric stopsat the apex of the ridge point.

27

Section VI. EXPERIMENTAL RESULTS

The electrical performance characteristics for the broadbandquadruple-ridged waveguide radiator are shown in Table 1. Actual exper-imental results of the horns designed are compared to these desiredspecification values.

Figure 18 shows the gain characteristics of the MICOM horn. Thevalues used in the plot of Figure 18 are derived from a comparison ofthe measured patterns with that of a standard gain horn. Patterns ofthe E-plane and H-plane are taken at 2, 4, 5.5, 8, 10, and 12 GHz. Ineach pattern, the amplitude or gain on main beam axis of the standardgain horn is indicated by a marker. These patterns also give theamplitude imbalance between the two ports of the horn. The solid pat-tern is for one port (Port No. 1) while the dotted pattern is for thecorresponding port (Port No. 2). The results indicate that the patternsare symmetrical with the maximum on the main axis. Gain is well abovethe specified values, while amplitude imbalance is near the 0.5 dBspecification. These patterns are found in che appendix.

The appendix also contain plots of the on-axis-polarization patternsat 2, 4, 5.5, 8, 10, and 12 GHz. In Figure A-3 of the appendix, across-polarization of 18.5 dB is indicated. Actually, one should readthe difference between a peak and a null of the same pattern, ratherthan a null from the pattern of one port and a peak from the pattern ofthe corresponding port. However, reading the cross-polarization asindicated in Figure A-3 is good enough as patterns are within one-halfdB of each other. The value of 18.5 dB is the only value out of thespecification value of 20 dB. It should be noted that the other porthas a cross-polarization value of approximately 30 dB at 2 GHz.

It should be noted that swept frequency measurements of gain,amplitude-imbalance, and cross-polarization coupling were taken asspecified in Table 2, but only a representative part of the data isshown in this report.

Figure 19 presents consolidation of the isolation characteristicsof the MICOM horn, and Figure 20 shows the phase imbalance between ports.Tigure 20 is shonm only to indicate what the phase imbalance is withoutany coaxial-line adjustments in the feed probes. The two probes orantennas inside the gap of the ridges are 0.030 inch apart. As discussedearlier, an offset of the coaxial cable flange mount from the surfaceof the radiator can "make up" for the phase imbalance shown in Figure 20.Values of approximately 5 degrees were achieved.

The VSWR characteristics of the MICOM horn with two gap widths areshown in Figures 21 and 22. All data previously indicated were for theMICOM horn with the 0.030 inch probe separation and 0.033 gap width.By reducing the gap width to 0.026 inch, one improves the VSWR withoutchanging the other characteristics very much. This lowers the peak VSWRpoints from 2,5:1 to 2.3:1 in the 2 - 12 GHz frequency band.

28

(.400

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to $4S0 .z ,

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All results previously discussed were for the MICOM-30 horn or thehorn •ith the 0.030 inch probe separation. Results for the MICOM-20horn or the horn with t.he 0.020 inch probe separation generally wereslightly better in the VSWR and cross-polarization characteristics.Work on the design of the two MICOM horns were redirected from the 2 -12 GHz frequency band to a broader frequency band of 2 - 18 GHz. Manyspecifications were relaxed with this redirection.

34

ISection VII. CONCLUSIONS

This report presents the results of an investigation in the designof a broadband quadruple-ridged waveguide radiator. It covers thetheoretical and practical aspects in the design of the ridged waveguideL 1 parameters, the desiga of the ridges in the flared section, and thedesign of the coaxial to ridged waveguide transformer.IU

The result of the investigation is a usable 2 - 12 G~z bandwidth$dual-polarization, quadruple-ridged horn which is an advancement in thestate-of-the-art. It is felt that further refinement in the design ofthe two constructed engineering models would have corrected the mar-ginal VSWR and cross-polarization characteristics at the extreme lower

L end of the frequency band. The difference in characteristics betweenthe two horns can be attributed to construction differences and givessome indication as to what tolerance controls are needed in the pro-duction of a large number of antennae of this design.

35

REFERENCES

1. Cohn, Seymour B., "Properties of Ridged Wave Guide," Proc. IRE,Vol. 35, August 1947, pp. 783-788.

2. Whinnery, J. R. and Jamieson, H. W.4, "Equivalent Circuits forDiscontinuities in Transmission Lines," Proc. IRE, Vol. 32,February 1944, pp. 98-116.

3. Hopfer, Samuel W., "The Design of Ridged Waveguides," IRETrans. MTT, Vol. MTT-3, October 1955, pp. 20-29.

4. Marcuvitz, N., Waveguide Handbook, M.I.T. Rad. Lab. Ser.,Vol. 10, N.Y.: McGraw-Hill, 1951, pp. 399-402.

5. Walton, K. L. and Sundberg, V. C., "Broadband Ridged HornDesign," Microwave J., March 1964, pp. 96-101.

""The Cutoff Wavelength of the TE Mode in

Ridged Rectangular Waveguide of Any Aspect Ratio," IEEE Trans.zIcrowave Theory Tech., Vol. MTT-14, April 1966, pp. 175-183.Getsnger, W. J. "Ridged Waveguide Field Descripionan7.~C GesneW-. Rde WvgieFedDsrpion and

Application to Directional Couplers," IRE Trans. MicrowaveTheor' Tech., Vul. MTT-lO, January 1962, pp. 41-50.

8. Montgomery, James P., "On the Complete Eigenvalue Solution ofRidged Waveguide," IEEE Trans. Microwave Theory Tech., Vol. MTT-19,June 1971, pp. 547-555.

9. Sexson, T., Quadruply Ridged Horn, TR ECOM-0181-MI160, March 1968,Sylvania Electronic Defense Laboratories, DAAB07-67-C-0181.

10. Chen, C. C., Wong, N. S., and Tang, R., Ultra-Wideband PhasedArrays, Final Report AFCRL-TR-73-0569, July 1973, Hughes AircraftCompany, F19628-72-C-0224.

11. Chen, M. H. and 'Tsandoulas, G. N., "Bandwidth Properties ofQuadruple-Ridged Circular and Square Waveguide Radiators,"PGAP Symposium Record, August 1973.

12. Chen, M. H., Tsendoulas, G. N., and Willwerth, F. G., "ModalCharacteristics of Quadr:,ple-Ridged Circular and Square Waveguides,"to be published in IEEE Trans. Microwave Theory Tech., Vol. MTT-12,August 1974.

13. Konrod, A., and Sylvester, P., "Scalar Finite-Element ProgramPackage for Two-Dimensional Field Problems," IEEE Trans.Microwave Theory Tech., Vol. MTT-19, December 1971, pp. 962-954.

36

14. Kerr, John L., A Very Broad Band Low Silhouette Antenna,TR ECOM-3087, January 1969, US Army Electronics Command.

15. Kerr, John L., Short Axial Length Broadband Horns,TR ECOM-3344, October 1970, US Army Electronics Command.

16. Kerr, John L., Broadband Horns, TR ECOM-3319, August 1970,US Army Electronics CoWmmand.

17. Slater, J. C., Microwave Transmission, McGraw-Hill, New York,1942, Chapter VII, pp. 280-304.

18. Ragan, George L., Microwave Transmdssion Circuits, M.I.T.Rad. Lab. Ser., Vol. 9, N.Y.: McGraw-Hill, 1948, pp. 314-361.

19. Cohn, Seymour B., "Design of Simple Broad-Band Wave-Guide.-to-Coaxial-Line Junctions," Proc. IRE, Vol. 35, September 1947,pp. 920-926.

37

AKPnND IX

Precedinlg P3ge blank 3

121

400

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310 •S~310"

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Figure A-3o On-axis-polarization patterns at 2 GHz

(Top pattern is for Port 1. and other pattern is

for Port 2).

42

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Figure A-8. H-plane patterns at 5.5 GHz (standard gain, 14 db).

47

ISO V 10,10*

340

330 30

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300

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Figure A-9. On-axis-polarization patterns at r.5 Gliz(Top pattern is for Port 1).

48

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350 00 10,340 10, 35-) 20

333' 3030, 330

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50

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180 320

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Figure A-13. E-plane patterns at 10 GHz (standard gain, 18.5 db).

52

3202

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1380

Figur ACo-1paeptersa 0Gz(tndr an 85d)I0 0290 50

En

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/ "---! : 0' I -i-t \--V • -"•i , . --. is'- + ... • ,

Fi~gure A-].6, E-pi~ane pat~terns at 1.2 Gltz (standard gain, 1.8 db).

55

/ . ,.-" 'S \/ ..> '.LI '0

•A . M , "

"- - 5 i

Fiur A1. H-ln paten at1\z(tnadgi n, 18- db

./ , -6 , " '

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Figure A-18, On axis- polarization patterns at 12 GRz(Top pattern is for Port: 1).

57