Mode CAD

Rigorous CAD of Rectangular Aperture Coupled Circular Waveguide Multi Mode Filters

Reinlhard Keller

*

and Fritz Amdt

**

AANTNachrichtentechnik GmbH, AN/EV036, Gerberstr. 33, D-71522Backnang, Germany;

tel. 49-7191-133679, fax: 49-7191-133044

N*icrowave Department, University ofBremen, Kufsteiner Str. NW1, D-28334 Bremen Germany

Abstract-A rigorous field theory analysis ispresented for the accuratedesign of rectangular iris,coupled circularwaveguide single,double andtriple modefilters. The multi modecoupling between the orthogonal modes is achieved bya new technique using additional asymmetricslots in theAperture plane by multiport coupling

techniques. This avoids the traditional 450coupling screws. Thetheorie is based onthe full-wave mode-matching method for thekey-building blockdiscontinuitycircular waveguide to smaller rectangular waveguide. Arbitrary iris location, differentcross sections, unequal E- and H-plane crosssizeand finitethickness arerigorouslytaken into account. The efficency of the design methodis demonstrated at two new filterexamples;

onerectangular-iris coupled one-resonator dual mode and onetriple mode circularfilter in the P-band (10-15 GHz). The theorieis verified by comparison with mesurements.

I. INTRODUCTION

Multi-mode circularwaveguidefilters arecommonlyused in manymicrowave applications, i.e.

narrowbandpass multimode filterstI]. The t-raditional waytocouple the orthogonal modesin suchFilters is by wayofcoupling screws. Inthe absence ofgood designtoolsnumerous,

redesigns andadditional tuning elements arenecessary. Low-costandmass-production requirements ofmodernfilter design has ledto this alternative solution, which allows the overall CAD of multi-mode filterswithout,thenecessity of tunable couplingelements.

Forrectangular structures, theanalysis of irises [2], [4] andL-shaped waveguide sections for providing the required orthomodecoupling have been investigated

[4-].

^{For circular} structures, therigorous analysis of centered [3]-[5] andasymmetric [6] rectangular irises aswell as circularirises [4] iswell-known.

The purposeofthis paperis to combine these methodsto come to a easy-to-manufacture coupling technique, which avoids the usual couplingelements and post assemblytuning procedures. These filters arerigorously designed bya mode-matchingmethodbased, fast and reliable design tool. The efficiency of this method is demonstratedat adual-mode and a triple- mode filterat 12 GHz.

II. THEORY

The multi-mode filter (Fig. Ia) with the iris element offinite

thickness

andadditional stub holes is decomposed into the key-building block discontinuity asymmetric waveguidetransition

These stub-waveguides maybe shortened oropen, ifthe

electromagnetic

fieldsare

sufficiently

decayed.

Fig. 1 a)Multi-mode filterstructure b)Furcation circularto circularand circulartorectangularwaveguide

Themode-matching solution forthe

single key-building

blockdiscontinuitiescircularto smaller rectangular andcircularwaveguidehavebeen

presented

in

[6]

and 141 so

merely

the basic steps aredescribed hereusingthe present

notation.e

^-

Inthe circularregionIand the circular or

rectangular region II,

thefields

C =Vx(4A+

ⁱ

Vxvx(ie")

ft =Vx(2jA+ 1Vxvx(Av}')

J041l

v1= I, II (1)

are derived

from

the z-components ofthe electric

(index e)

and

magnetic (index h) Hertzian

vectorpotentials:

A-V_e 1 _em

_kaem

^a exp(

-v' _'em'

^{1 bv}_em

_rm exn(+ _ue,nIK

^v

zYi

m

fe

m

v5ghV

ahm

^ex

+bv

^{ex + v z z}

m

(2)

with thewave impedances

z-'-Yemnv

Zfi e=E

Pa

'Nm

h^v

⁽³⁾

and thepropagation ^constants

y,,v, yhv1

ofthe TM- andTE-modes

respectively. T7J

,

T,,,

^arethe

normalized cross-section

eigenfunctions

of the

corresponding

^circular

(index c)

^or

rectangular

(index r) waveguide regions v =I, II.

2

cos(krx)cos(k§y)

Tr

_ _

h'qV kC

'fa

^{b 7I16O}

Jfl(kgchP)-Cos(

^{' (}

jPP))

h vXnv fJeXnvI

2.sin(k>)

sin(k;y)

e4- krv

^r

Tc ^- e)sn I

Te_C---J

Jct

x4,

^Jlx,)

sxc

(4)

r(1

⁺28oi

)

Matching thefieldsat thestep discontinuityatz= 0

leads

^tothecoupling

matrix

vfqr^a waveguidetransition of anytwowaveguidecross sections, rectangularor circular

[21, [6].

Withthe normalizedvoltage andcurrent coefficient vectors u v=av+b iv= a

-b

^we get the matrix

equations:

U1 ⁼

V*U2

^{12 V}

-Il

⁽⁵⁾

Together with the normalized modal admittance diagonal submatrices y> vof the

homogenious

circularwaveguideoffinite

length 1,

wearriveat the desiredmodal admittance matrix ofthe (P-1)-furcation circular to anyof circularorrectangular waveguide (Fig.

lb):

ilI i2

13

KI

^P

yi1I

V12Y21

T1l3Y2I alP2

YI'2VI2

V12Y22VI2 V13y22V12

v TV1 2

2VI

YIf2fI3

V12Y22V13 V13Y22VI3

P

V1IPY22VI3

T _,

Y12VIPI

1V2Y2'2VI

^P

V13Y2'2VIP

I

PY2'2VI

^PJ

I,

U1

U2

U3

tUp

(6)

Thematrices

vij.describe

^thevarioustransitions from circularto circularorcircularto

rectangular waveguide

accordingto

equation (5)3

Thederivation ofthis

equation

^is

given

in [9]. Insertingthe

coupling

matrices

vj

forthe

rectangular

to

rectangular waveguide transition

leadsto thewell knownrectangular

wageuide

N- furcation [9,10,11]. However

equation (6)

may beused for anarbitrary set ofdifferent

waveguide

tr&insitions, i. e. for the circularto

rectangular and the circularto circular step.

Togetherwith shortened oropen

waveguide

sections for the

coupling

holes, some

examples

of multimodefilters werecalculatedusingthe GAMformulation. Toget

good

convergence, the numberofTE-and TM-modes takeninto account inthe several

regions

^areestimatedbythe ratio ofthe

geometrie

^onthetwo sides ofthediscontiunuity. Forthe circularto

rectangular

step the ratio 2r/a=2 means double number of modes in the circular

waveguide

than inthe rectangular section. For abreefresultorfor

optimization

40 modes

(TE-,

TM-modes, both cosine- and sine-types) in the circular

waveguide

maybe sufficent.

I 1.

III. RESULTS

To

verify

the theory, firstavery simplestructure wasfabricated and compared with the theory.

Fig. 2 shows the insertion and returnlossversusfrequencyofarectangular-iris coupled one- resonator circular filter with two rectangular ports in the P-band. Excelent agreement may be stated.

v;10 X'

-20.~~~~~~~~~~~~~.

-20.~~~~~~~~~2

30e _ ~~~- r^-- dt ~1X,5 11'.7 118 12.e -30.

10. 12. 13. 15

frequency

^{/GHz - -}

Fig. 2 One-resonator filter: measuredand computed scatteringparameters.

a=19.05mm, b=9.52, 1=45.0mm; al=9.53mm, bl=2.95mm,

11=1.Omm

Fig. 3 shows a one resonatordual-mode filter withrectangular irisesand circularstubsfor mode conversion. Input and output couplingis donebytwo orthogonal rectangular

irises,

which arecoupling the

TEl

13 -cosine modeandtheTE1 13 - sine modeto the TE0 -mode in the rectangularinput and outputwaveguides respectiveley. Toachievethedesired coupling between theorthogonal modes andto omitexitation ofthe TMO1 - modeinthe

Filter,

two stubs arerequired in the inputiris plane, located450 and2250 referringto theinput

iris,

These stubscause amagnetic current distortion in the wall and so provide magneticfieldcoupling of the two modes.

11,86 11,88

11,90 f/GHz->

11,92

Fig. 3 Dual-mode filterwith stub-coupling: a-19.05mm, b=9.52, 1=45.0mm;

al19.53mm,blh2.95mm, 11=3.0mm; r2=2.75mm, 12=2. 1mm

Afirst result ofa newtypeoftriple-modefilterwithasimiilar coupling mechanismas shown aboveispresentedinFig. 4. The TEl 13 - cosine and - sine mode represent thefirst andthird resonancie respectively. Rectangular slotsin the irisplanes causemagnetic couplingtothe TMO12 mode, beeingthe second resonanceofthe filter. The coupling slots may be fabricated bymilling techniques.

I

S1i's21

*dB -50-

-100-

f/GHz & ^15.00

IV. CONCLUSIONS

A new and complete formulationforarbitraryN- furcationsfrom circular toboth circular and rectangular waveguides was found. Bythis, a rigorous and efficient method fordesigningmulti modecircular waveguidefilters has been developed and appliedto dual- andtriple- mode resonators. All relevant design parameters, suchasfinite thickness ofirises, higher order mode interaction,

arbitrary

position of irises and coupling structures, and multiple apperture irises are taken into account. Post assembly tuningis no morenecessary.

V. REFERENCES

[1] A.E. Atiaand A.E. Williams, "Narrowbandpass waveguide

filters",

IEEETrans.

MicrowaveTheory Tech., volMTT-20, pp. 258-265, Apr. 1972.

[2] H. Patzelt andF. Arndt "Double-Plane StepsinRectangular Waveguides and their Application for Transformers, Irises and Filters," IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 771-776, May 1982.

[3] J.D. Wade, andR. H. MacPhie, "Scattering atcircular-to-rectangular waveguide junctions", IEEE Trans. MicrowaveTheory Tech., volMTT-34, pp. 1085-1090,

Nov. 1986.

[4] F. Arndt, andU. Papziner, "Modal-S-matrix design ofmicrowave filterscomposed of rectangular and circular waveguide elements", in IEEEMTT-S Int. Symp. Digest, pp. 535-538, 1992.

[5] R. H. MacPhie R. Delewil et al., "Full Wave Scattering Analysis of

aCircularWaveguide and asmallerRectangular Waveguide" in URSIRadio Science Digest, p. 216, Chicago, July 1992.

[6] R. Keller, andF. Arndt, "Rigorous modal analysis of the junction ofacircular

waveguideanda smallerrectangularwaveguide", IEEEMicrowave and GuidedWave Letters, vol. 3, pp 185-187, June 1993.

[7] X.-P. Liang, K.A. Zaki, and A.E. Atia, "Dual-mode couplingbysquare cornercutin resonators and filters", inIEEE MTT-S Int. Symp. Digest, pp. 1327-13330, 1992, andIEEE Trans. Microwave Theory Tech., vol MTT-40, pp. 2294-2302, Dec. 1992.

[9] W. Hauth, R. Keller, U. Papziner, R. Ihmels, T. Sieverding, F. Arndt, "Rigorous CAD ofmultiport coupled rectangularwaveguide components", inProc. 23rdEurepean Microwave Conf., Madrid, Sept. 1993.

/10/ Dittloff, J.; Arndt, F.: Rigorous Field Theory Design ofMillimeter- WaveE-Plane Integrated Circuit Multiplexers. IEEETransactions onMicrowave Theory and Techniques MTT-37, pp.

340-35Q,

February 1989

/11/ Rebollar, J. M.;Encinar, J. A.: Field theory analysis of multiport-multidiscontinuity struktures: Applicationto short-circuitedE-plane septum.. Proc. Inst. Elec. Eng., Vol.