AD- A00O8 543

BROADBAND FERRITE TOROIDAL PHASESNHI FTE R

M. L. Reuss, Jr.

Naval Research LaboratoryWashington, D. C.

March 1975

DISTIBUTD BY

Natinal echicalInfomahn Sevic

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REPORT DOCUMENTATION PAGE B EAD INSTRUCTIONSREPORT NUMBER . GOVT ACCESSION NO. 3.ECIPIENT'S CATALOG NUMBERNRL Memorandum Report 3011 // '-'BEFrE___O______"_____ORM

4. TITLE (and Subtitle) S. TYPE OF REPORT A PERIOD COVEREDBROADBAND FERRITE rOROIDAL PHASE SHIFTER An interim report on a continuing

NRL problemA. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(o) 8. CONTRACT OR GRANT NUMUER(*)

M.L. Reuss, Jr.

s. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA A WORK UNIT NUMBERSNaval Research LAboratory NRL Problem R08-36

Washington, D.C. 20375 Project XF 54-545-007, Task K07

II. CONTROLLINS OFFICE NAME AND ADDRESS 12. REPORT OATaDepartment of the Navy March 1975Naval Electronic Systems Command 13. NUMNER Of PAGESWashington, D.C. 20360 23 %_14. MONITORING AGENCY NAME & ADDRESS(II dillerent from Controlling Ollice) 15. SEC 'RITY CLASS. (of te eort)

UnclassifiedIs& DEC ASSI FICATION/DOWNGRADING'

SCHEDULE

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Approved for public release; distribution unlimited. i

I?. OI4TRIBUTION STATEMENT (of the bstract entered In black 20, Itf diflerent Im Rose )

IS. SUPPLEMENTAWY NOTES lpfoducad byNATIONAL TECHNICAL APR 24 WSINFORMATION SERVICEUS Dopim~menI of coffler¢o

US pt~i nIgf.itd, VA. 2' 151 1 2It. KEY WORDS (Continu. on reverse aide, i neceeary and I dntil by block moe) )Mcrowave phase shifter

20. A TRACT (Continue an r vere aide If nece~ovwy end Imltity by block Rmsisr)uThere are applications requiring nonreciprocal phase shifters with flat differential phase

shift over waveguide bandwidths. This report covers the development of a X Band phaseroperating over the 8.2 to 12.4 GHz bandwidth of RG 52/U waveguide. The principal emphasisis placed on the matching procedure employed since computer analysis techniques for determining

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CONTENTS

SUMMARY ..... ........................................ 3

ACKNOWLEDGM.VENT .................................. 3

I

REFERENCES ... ....................................... 4

APPENDIX I -- Broadband Dielectric Rod Matching .............. 10

APPENDIX II - Broadband Fixed Phase DifferenceBetween Two Parallel Waveguides ................ 14

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BROADBAND FERRITE TOROIDAL PHASE SHIFTER

Toroidal ferrite loaded waveguide configurations producing fre-quency independent differential phase shift over waveguide bandwidthsare readily obtainable via use of the twin slab model such as reportedby Inue and Stern.[l] Figure 1 depicts the configuration employed andthe calculated performance of such a configuration capable of producinga flat differential phase shift from 8.2 to 12.4 GHz. Note that thisferrite loaded waveguide is reduced in width (0.500") relative to thenormal 0.900" width of RG 52/U1 waveguide. The dispersive character-istics of the loaded line differ, over the operating frequency band,from those of normal waveguide thereby resulting in a frequency depend-ent mismatch between these sections of transmission line, Principal -emphasis of this report will be the design approach employed to matchthese sections of line over the range of interest. j

The imapedance (Z TEof uniformly filled rectangular waveguide isgiven by:

Ex JUU uA

E _ wy Y

where w is the angular frequency, p the permeability and the propa-gation constant.[2J For two sections of transmission line filled withdifferent dielectric constant material,

Z and z2

where the subscripts indicate the characteristics of the respectiveregion. At a given frequency Z2/Z1 = 1ih2/ 2.i which for nonmagneticmaterials reduces to:

B21Z I II 2(I)L

since p2 = Ul -I

Note: Manuscript submitted February 10, 1975.

M___ If to a first approximation the assumption is made that equation

(I) is also valid for rectangular waveguide center loaded with a fullheight dielectric rod, computer generated curves of P vs. frequency canbe utilized to obtain dielectric loaded sections to serve as impedance

-~transformer sections. The propagation constant 0 can be determined over

a frequency range as a function of dielectric rod dimensions, dielectricconstant and waveguide "a" dimensions. The agreement between calcu-lation of A and experimentally determined P is quite good. Appendix Icontains preliminary data obtained for broadband matching of a dielectr~crod in rectangular waveguide.

When the waveguide is partially loaded with ferrite, the effectivepermeability is not unity. The computer analysis employed for thisregion is satisfactory for determining regions of flat differentialphase shift with frequency; however, due to approximations used to op-tamn the initial permeability, it does not predict the absoluteelectrical length with a high degree of accuracy or compute theeffective permeability of the ferrite loaded section. For these reasonsthe relative impedance is determined experimentally.

rk Experimentally the relative impedance of the ferrite loaded wave-guide to the standard waveguide can be determined as a function of Afrequency via use of a thin film resistance card attached to theferrite toroid as shown in Figure 2. This approach, when properlyimplemented, simulates a semi-infinite ferrite loaded region. Measure-ment of the signal reflected back into the standard waveguide can thusbe used to determine the relative impedance.

Analysis of the twin slab model of a toroidal phase shifter in-dicates a relatively small change in P and thus presumably theimpedance, as the "a" waveguide dimension is changed from 0.9 to 0.5inches. The deviation over this range appears greatest at the low endof the band where it is on che order of 2%. The relative impedance ofthe reduced width ferrite toroid loaded section was determined by:

1) determining the relative impedance of the toroid in standardwidth waveguide via use of thin film resistance material applied to theside of the toroid, and

2) assuming the ferrite loaded waveguide impedance is relativelyindependent of waveguide width as per the computer analysis.

After the impedance was determined as a function of frequency,

three-step Tchebycheff transformer impedances were calculated atseveral frequencies within the frequency band of interest. For con-venience, these relative impedances for the transformers over thedesired frequency range are expressed in terms of p (degrees per inch)

i to be compatible with computer printout for different dle!-vtric loadedsections which are to be used as the impedance transformers. In orderto minimize the reactive effects of changing the "a" waveguide dimension

2

IV-- -

between the standard and loaded waveguide, the "a" dimension of thetransformer sections was stepped in equal increments between the ferriteloaded section and the standard waveguide.

The next step was to find dielectric loaded waveguide sections withthe same impedance (expressed in terms of 0) vs. frequency character-istics as determined by the transformer calculations. Curve A ofFigure 3 denotes the experimentally determined impedance for the toroidloaded waveguide; the circles denote the experimental points used togenerate the curve. Curves 1, 11 and III denote the impedancecharacteristics for selected dielectric loaded waveguide configurationsto be used as transformers. The calculated values for the transformersat indicated frequencies are denoted by an "x". Curve C of Figure 3 isshown to illustrate that the proper impedance can 1e obtained at thecenter frequency but can have undesirable dispersion characteristics sothat the required transformer impodance is not present at the band edges.Table I shows the dimensions for the quarter wave transformers de-termined via this analysis approach.

These transformers were fabricated and attached to the toroid withcrude thin film mode suppressors employed. Figure 4 shows the in-sertion and return losses of the completed phaser as a function offrequency. The maximum VSWR over the band is 1.37:1. The differentialphase shift (Figure 5) is within +5 degrees of 239 degrees. No attemptwas made to improve this value via minor modification of the loadedsection "a" dimension. The relatively high insertion loss is primarilyattributed to nonoptimized suppression of modes.

This approach for achieving broadband matchiog was suggested by aprevious study aimed toward development of a broadband fixed phasedifference betwcen two parallel waveguides. Results of this study areincluded as Appendix II.

SUMMARY

A "flat" differential phase shift toroidal phaser was constructedto operate over the full bandwidth of RG 52/U waveguide. The maximumVSWR of less than 1.4:1 is obtained with a three-step transformerdesigned via a combination of experiment and analysis.

ACKNOWLEDGMENT I

The author expresses his appreciation to Mr.C.W.Young,Jr., whodeveloped the computer program utilized to calculate the relative im-pedances and to both Mr.Young and Pr.H.E.Spielman for stimulatingdiscussions. The offorts of Mr.M.Finnley and Mr.C.Banks 'ho ablyassisted in taking the experimental data are also greatly rppreciated.This report documents some of the tasks completed during Otte period1969 through 'Q73,

[3

TABLE I

Transformers for TT390 ToroidToroid outer dimensions: 0.172 x 0.400 x 2.000"Toroid hole dimensions: 0.052 x 0.280 x 2.00;"wCenter Loading: e = 10

LENGTH WAVEGUI DETRANSFORMER (IN) WIDTH WIDTH

I 9 0.125 0.170 0.6

11 6 0.200 0.100 0.7

III 4 0.310 0.050 0.8

REFERENCES

[11 William I. Ince and Ernest Stern, Nonreciprocal Remanence PhaseShifters it, Rectangular Waveguide, IEEE Transactions on MicrowaveTheory & Techniques, Vol.MTT-5, February 1967, pp.87-95

[21 Roger F. Harrington, Time-Harmonic Electromagnetic Fields, Mc(;raw-Hill Book Co., 1961, p.6 9

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APPENDIX I

Broadband Dielectric Rod Matching

An e 10 dielectric rod 0.225" wide filling the waveguide heightwas centered in RG 52/U waveguide. Thin film resistance material wasattached to the side of the rod as shown in Figure AI-I so thrtt

Seffectively only reflections from the front face of the dielectricwould be detected in the standard input waveguide. Table A-i comparesthese measurements with computations based on computer analysis of di-electric loaded waveguide. The relative impedance of the dielectricrod in reduced width waveguide was calculated at points over the

swaveguide band using the assumptions described in the preceding text.At each of these points the impedance of three-step Tchebycheff trans-former was calculated. Equal changes in waveguide width between thereduced width waveguide and standard waveguide were chosen for thetransformer waveguide section to reduce junction effects. Calculatedperformance of different dielectric constant and dimension rods wasused to determine the configuration whose performance characteristicsbest fit over the frequency band the points determined for each trans-former. Figure AI-2 shows the data obtained for the reflected signalfrom the 0.225" e = 10 rod centered in 0.5" wide waveguide with thethree-step transformer--determined by the above approach--in place.Considering tolerances on the physical dimensions and dielectricconstants, it was felt that this preliminary data justified applyingthis approach to ferrite loaded w %eguide.

10

10 S

TABLE A-!Return Loss (dB) for 0.225" Wide r,,=0Rod Located in Rectangular Waveguide

Frequency Calculations Measured

a =0.9 a -0.5 a =0.9

8.2 4.14 4.2 4.2

9.2 4.72 4.76 4.5

10.2 5.05 5.07 4.9

11.2 5.26 5.27 5.1

RE,12.2 5.40 5.39 5.2

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=1 13

APPENDIX II

Broadband Fixed Phase Difference BetweenTwo Parallel Waveguides

In certain applications, employment of a broadband fixed phase 7difference between parallel lines can be utilized to improve componentperforounce or to make a particular type of broadband waveguidecomponent feasible. An example of the first case can be seen in aferrite switch employing similar hybrids (either quadrature or 1800)and ferrite phasers (1800 differential phase shift required). Use of afixed phase difference between the two paths connecting the hybridsallows reduction of the required differential phase shift to 900 ineach arm. Phase errors associated with 900 differential phase shiftare generally ote-half of those associated with 1800, thus overall per-formance can be improved. Construction of a brodband waveguide ButlerEmatri can be a= example of the second case.

A feasibility model of one approach to obtaining a fixed phasediffereuce between two sections of G 52/U waveguide was constructedand evaluated. The design goal of 900 over the full waveguide band-vidth was met within 440 while the insertion loss was less than 0.5 dBand VSW better than 1.3:1.

a The approach utilized was that of determining dielectric loadedwaveguide configurations, that have similar changes of phase shift perunit length per change of frequency. The initial analysis employedcentered dielectric rectangular rods filling the waveguide height.Both width and dielectri constant were varied and phase shift per unitlength calculated as a function of frequency. Results of some of thesec41cultlons can be seen in Figure All-I where phase shift (degrees perinch) is plotted as a function of frequency for several configuration&.It is evident from this figure that there is essentially a constantdifference in phase shift over the frequency band when considering the

S, w - 0.25&', and t - 8, w - O.100" configuraticns. These con-figurations wver selected for experimental investigation. Whon usingveguide aR heavily loaded as these are, there 14 a strong probabilitythat hither order modes would be present, so resistive mode suppressorsorthaoenal tv the electric field were utlixed in each line.

Different i pedances relative to the enty waveguide are preventedby the tWo dielectric sectima, thu* the requred matching transformrswill differ, thereby affocting the phase difr betwen the twoload-ed waveguide sections. Wo section dielectric rod transforeers wereSelectd. The iv-- e of these trasformers reiative to the emptywvreguide was astiawd to be of the for%

Zlnmatvi ?L

where f.e and Ff refpr to the propagstimn constants of the empty and loaddv idr6 respertjvely. Using thv phase shift per unit length for the

tladed wsveid4e s,-ti ao plus the quarter tvlengh tansformers, the

5 H

-- 4

desired phase difference (in this case 900) was determined by considering i 17the difference in phase between two physically ec~ual length sections of 7-

waveguide; one fully loaded lengthwise and one partially loaded length- 2wise. If Bi represents the phase shift per unit length of a loadedsection and li represents the length of that section then

(Ljui T Lj+% e + a a)

n T~. 1 + i

k=l k Tk 2 12=

where 0 is the desired phase difference, the subscripts T, a, e refer tothe transformer, air and main dielectric regions respectively. Calcula-tions of this type are required at selected intervals over the frequencyband of interest.

An initial model was made using equal length (1.047) dielectricbo4ies (e - 6 and e = 8 rods) to determine general validity of the ap-proach since mechanical tolerances and dielectric constant tolerancescould significantly affect the results. The transformers employed forthe e - 6 rod were nominally (a) e = 4, w = 0.225" and A - 0.186" and(b) e - 2.5, w - 0.100" and 1 = 0.295" while the transformers employed

for the e = 8 rod were (a) e i 6, w = 0.090" and A = 0.198" and (b)e - 2.5, w - 0.075" and A - 0.311". Standard 0.900" x 0.400" i.d. RG 52/Uwaveguide was employed. Figure AII-2 is a sketch of the configurationused including the resistive mode suppressors. The calculated phasedifference over a 8.2 and 12.2 GHz band indicated a variation between95 and 102 degrees would be expected over this band. Using a Wiltron310B Phase Indicator and 311Z Resolver, a phase difference variation ofbetween 93 and 100 degrees was determined. Results of this measurementare found in Figure AII-3 along with the insertion loss and return lossfor each section: Over most of the band, the insertion loss was lessthan 1/2 dB and returv loss was greater than 15 dB. Agreement was con-

sidered satisfactory it, light of tolerances.

Emperically the lengths of the e - 6 and e = 8 rods were reduceduntil the data of Figure AII-4 was obtained. The £ a 6 rod was 0.965inches long while the e = 8 rod was 0.898 inches long. As can be seenfrom this figure, the extreme values of phase difference are with + 4degrees of the desired 90 degree difference over the full band of interest.Insertion loss was no greater than 1/2 dB while the VSWR was less than~1.5:1.

A fixed phase difference of 90 + 4 degrees has been maintainedbetween two waveguides over the bandwidth of RG 52/ waveguide. Insertion

4T

loss of less than 1/2 dB with VSWR of less than 1.5:1 was maintained.

These results indicate the feasibility of obtaining a broadband fixed

phase difference using dielectric rods of rectangular cross-section.

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