MICROSTRIP TO WAVEGUIDE COUPLING THROUGH HOLES

Wolfgang J. R. Hoefer* and David S. James**

1. Introduction

A significant limitation encountered in the design of microwave

integrated circuits (MIC's) is that of inadequate Q - factors and poor

temperature stability for currently available MIC reson~tor designs.

It is therefore iesirable that microwave integrated circuits be made

compatible with standard microwave waveguide components and subsystems.

The few transition designs presently available are empirical. This

paper describes a novel practical form of microstrip-to-waveguide transi-

tion whose properties may be readily predicted analytically.

In particular, we have analyzed and measured the coupling between

microstrip (dominant mode) and a circular-cylindrical cavity (TEo12 mode).

The configuration that we have studied has an aperture in the groundplane

of the microstrip. This groundplane also forms one of the walls of the

cavity. The micros trip line is terminated to reflect a short circuit at

the coupling aperture. (See Fig. 1)

1Wheeler's equivalent energy concept for coupling through small holes

forms the basis of analysis. In the experimental study, the coupling1

coefficient S and the loading power factor p (as defined by ~~eeler ) are

determined by measuring the power transfer from the cavity to the micro-

strip and the change in the bandwidth of the system, as a function of the

coupling hole diameter. The cavity is excited by a small loop in the

bottom wall.

**Communications Research Centre, Department of Communications, Ottawa,

Ontario, Canada.

*Department of Electrical Engineering, University of Ottawa, Ottawa,

Ontario, Canada. PROCEEDINGS OF THEFIFTH COLLOQUIUM

ON MICROWAVE COMMUNICATIONMT - 221

Budapest, 24-30 June, 1974

input

microstri p

to cavi ty

coupling

Figure 1 View of the coupling arrangement between

micros trip and TEo12 Cavity (loosely coupled input)

2. Analysis of the Coupling Arrangement

2Wheeler has shown that aperture coupling between a waveguide and a

resonant cavity can be evaluated by combining the solutions of two sym-

metrical coupling problems. The coupling between two cavities each iden-

tical to the resonant cavity in question must be found,as well as the

coupling between two waveguides, each identical to the waveguide in the1

original problem. Using Wheeler's nomenclature the coupling coefficient

k betwee~ two cavities and the normalized coupling reactance x between two

waveguides can be expressed in terms of effective volume ratios. Combina-

tion of one half of each symmetrical structure yields the circuit to be

analyzed (see Fig. 2) and the loading power factor p = l/Q of the1 ext.

cavity is given by

p = k . x + O«k'X)2) (1)

The coupling factor 8 defined by Montgomery4 is related to p, Q ,0

Qext'QL by Q08=-Qext

dp = 8 ..!.-= Q . p an 13+1 QL

0

MT - 222

In our study a circular TEO12 cavity has been chosen for the follow-

ing reasons:

a) It exhibits a maximum unloaded Q for a given ~vity volume. Thus,

critical coupling can be achieved through employmertt of relatively

small apertures.

b) Electrical contact between the main body artd the top and bottom

walls is not required. This guaranties unchanged electrical properties

after repeated assembly and disassembly of the cavity.

c) Magnetic coupling through holes in the top or bottom wall is

easily achieved.

a

...,-1--,

~ ,'

m

'~~.

i

' -"\~', I .-r"o,"

,

'" -

~ T '-:'", '-J I /,

1'0.~-,/

i

i

p

b c-Ft8ure 2

Combination of two

symmetrical coup-

ling problems (b

and c) to obtain

'-t(,((~((((J-'

~ ...,,---

the power loading

factor p of a

cavity coupled

to a microstrip

r t j

:

I

' :

I II I

WI,'!

. I , .

I

line.

-- k x

2.1 AE.e_r~_ureCoupling Between Two. Iden~i2al_TEu 2 Cavities

Since the normal component of electric field of the cylindrical

TEO12 mode is zero on the cavity wall containing the coupling aperture,

only magnetic coupling can be achieved between the ~wo identical resonators1

shown. According to Wheeler, the coupling coefficient k is given by

1k = _4 (V Iv)mc m(2)

MT ...;223

where Vmc is the effective volume of the coupling aperture, and Vm the

effective volume of the cavity. (The effective volume of the cavity !s

defined as the volume which, when filled with a field of uniform intensity

equal to the mag~etic field at the coupling hole, would contain the same

energy as the actual cavity.)

1From~fueeler , for a circular aperture of diameter d:

v = 2 d3/3mc (3)

The effective volume of the cavity is found as follows.

the tangential magnetic field in the cavity at the location of~

ling hole (before the hole was cut), and H the magnetic vector field func-

tion in the cavity at resonance. V is then defined by the expression:, m

~Let H becthe coup-

Thus

1:.~IH 12 . V = 1. ~ (IHI2dV2 c m 2 J I

cavity

JIHI2dVV = cavity

m IH 12c

(4)

(5)

The numerator of Equation (5) is integrated using Lommel's integrals (see2

for exampleAngot). We obtain

f ~ 'lTLR2

)]2

IHI2dv = ---r-' [J 0 (k1R(6)

cavity

where L = Length of the cavity; R = Radius of the caVity; k1 = xo1/R,

where XO1 is' the first root of the equation J1(X) = o.

The magnetic field at the coupling hole is given by

+ kgIH I = - J1 (k1s)

C y(7)

MT - 224

where s is the distance of the aperture from the cavity axis, k3 = 2n/L,

and y = [(XOl/R)2 + (2n/L)2] ~

In order to achieve maximum coupling, the aperture is located at the

maximum of the radial magnetic field.which occurs at s ... 0.481 R. The

coupling coefficient can now be expressed by combining equations (3), (6)

and. (7).

V 1 ,"2 3 k32 [k = 1.1!1.£...4" . '3 d (1) Jl(klS)]2

4 Vm 1TLRZ

Z- [Jo(klR)Y

which reduces to:

(8)

k = 8.7428 d3Ao'[2 L31)2

where Ao is the free space wavelength at resonance.

(9)

2.2 Aperture aoupli~g Between Two Identical Microstrips

Coupling holes in waveguide walls are discontinuities whose effect is

readily described in terms of lumped element equivalents. To simplify the

evaluation of the equivalent impedance of the coupling hole in the common3

groundplane, Wheeler's microstrip model is used. It is an idealized para-

parallel-platewaveguide with magnetic sidewalls. (Fig. 3)

(10 )2

feff = "Ag

Fig.3a Cross-section of a microstrip

line.

y

x

;A =.h.. ~

Zo~~

Fig.3b Equivalent parallel

plate model with mag-

netic sidewalls.

MT -: 225

3

Expressio~s for £eff and6z0 are given by'Wheeler, or more accurately byGetsinger and Schneider; AO and A are the free space and guide wave-glengths, respectively. The TEM fields in the model are simply:

H=H .1x(10)

+ +E = -1;; H jx

(11)

+ +where i and j are unit

~"].l0r; = .

£o£eff

vectors in x and y directions respectively and

In the case of Fig. 2c, the coupling impedance of the hole as seen

from either guide, is the same as that of an identical hole in a common

end wall (see Fig. 4). This can be shown by the following argument. In

the absen~e of the hole, the magnetic field at the endwall (Fig. 4b) is

the same as the field at the bottom wall at odd multiples of A /4 from thegstub. The electric field is zero because the open circuit termination

" ,

reflects a short circuit at the coupling hole and thus the coupling is

purely magnetic.

Z to-.Id

Z JI " i

r- 3A,/4~OPEN-1

CIRCUIT .

TdZ z

1 )~

'Fig. 4a Two identical waveguides

coupled through a hole in

the common bottomwall.

Fig.4b Two identical waveguides

coupled through a hole in

the coman endwall.

4Using the small hole approximation t the reactance of a small

circular hole in the common endwall can be expressed as

7TVx =~ 11 1

"2

2A So ng(12)

MT - 226

...-

where ~ is the transverse component of the unperturbed mode at the loca-

tion of the hole center, assumed uniform across the aperture. V. . 4 ~

is given by Equation (3), and the normalizing factor So is found to be

So = H2 .. A . hx (13)

Thus, the normalized reactance of the iris becomes

.'ITdx=- (14)3A Ahg

2.3 Coupling Between Cavity and Microstrip

The loading power factor of the cavity coupled to the microstrip can

noW be found by combining the results of Equations (9) and (14). We

obtain

l

p = k . x = 0.9276 d6A~L3D2A Ah

g .

(15)

This is the expression presented graphically as a function of the

hole diameter d in Fig. 5. This is easily generalized for finite wall

thickness t and TEOln cavity modes, to

0.2319Id6n2A~ -7.36t/dp = . e

L3d2AhAg

(16)

3. ~£erimental Results

We have measured the loading power factor p and the coupling coeffi~

cient S (the VSWR at resonance) of a TEo12 mode cavity coupled to a 50~

microstrip line. In order to minimize errors due to dimensional inaccura-

cies, measurements were made at a relatively low frequency

using oversize substrates (Rexolite, h - 5 rom, £ = 2.60).rmay be easily applied to ~uch higher frequencies by simply

(e.g. up to 33.4 GHz for h = 0.5 rom).

(3.343 GHz) ,

The result.s

resealing

MT - 227

7Previous measurements by Douville and James yielded an effective

dielectric constant E ff = 2.27 at 3.343 GH for 50~ lines on Rexolitee Z 3

substrates (h = 5 rom,w/h = 2.75). The width A of Wheeler's equivalent

parallel plate waveguide was calculated for h-. 5 mm to be 25 rom,and the

theoretical loading power factor p was calculated (Equation 15).

The groundplane of the microstrip which formed the top wall of the

resonator, was isolated from the body of the cavity by a 1/16" thick

teflon ring to suppress the unwanted TMl12 companion mode. This also

avoided the necessity of providing a reproducible electrical contact

between the cavity walls. The cavity was excited through a small loop in

the bottom wall (Fig. 1). The loading effect of the input was included

into the overall "unloaded Q" of the cavity, which was measured to be

2.31 x 10" :t1%.

The length of the open-circuited matching stub was 3A /4. The end8 g

effect was calculated using the results of James and Tse. The calculated

length of 42.1 mm provided a well-defined peak of coupling over the whole

range of hole diameters investigated in this study. The result is perhaps

somewhat surprising for the large hole diameters. Anomolous behaviour

does occur if the stub length is A /4 rather than 3A /4, SA /4...g g g

The diameter of the coupling hole was successively increased in steps

of about 1 rom, starting at 3 rom, The 3 dB bandwidth and the transmitted

power were measured at the matched output of the microstrip for each

value of d, yielding the loading power factor p and the coupling coeffi-

cient 6. Fig. 5 shows the measured values of the loading power factor

together with it's theoretical behavior (Equation ~). The crosses

represent values obtained with transmitted power measurements. The dots

were obtained from measurement of the bandwidth.

In Fig. 6, the hole diameter is presented as a function of the theo-

retical and measured values of the coupling coefficient. This figure

could be considered as a design chart to determine the coupling hole

diameter for a desired coupling coefficient.

MT - 228

11-]

10-8

+ ,..

t/G

/t/~/

~/

+//-- THEORY

+

: I MEASUREMENTS0

II 2 4 Ii . 18

Hole Diameter in mm

12 14 11

Fig. 5 External loading factor vs. coupling hole diameter for a TEI12

cavity coupled to 50Q microstrip line (E = 2.60; w/h = 2.75;rh - 5 mm; f = 3.343 GH~; L = 13.9 and D = 14.3 ems).

It is surprising how well the measurements agree with theoretical

results obtained from a rather idealized microstrip model and small hole

theory.

The accuracy of the measurements varies with the degree of coupling.

For weak coupling (p < lO-S), transmitted power measurements made with a

resolution of about 0.1 dB yield best results, wherea~ for stronger coup-

ling, measurements of the bandwidth (typically around 300 kHz) made with

an error of tl kHz are more accurate. The diameter of the coupling hole

was measured with an accuracy of about t 1%.

4. Conclusion

Microstrip to cavity coupling has been analyzed using Wheeler's

MT - 229

10-4Q.....eu.af 10-5

2>

110-6-'

. 10-7

6~"t" a

,,~

""~

+"'+>-0::0'wJ:I-

V)I-2w:Ew0::::>V)«w:E

++

0

0

...... ..,..... or........ a.... ..-

CI....

...,Ia....

....

ww U! P JG~.WD!a GIOH

Coupling hole diameter vs. coupling coefficient for a TEo12

cavity coupled to a 50~ microstrip line (8 = 2.60;r

w/h = 2.75; h = 5 rom; f = 3.343 GHz; L = l3.9cms;

D = 14.3 ems).

Fig. 6

equivalent energy concept for coupling through small hol.es. Th~ micro-

strip was represented by an equivalent parallel-plate waveguide. Measure-

ments of the loading power factor and the coupling coefficient agree well

with the theoretical results obtained from this simple model over a wide

range of hole diameters. As an example, the hole diameter, as calculated

for critical coupling between a circular cylindrica~TEo12 cavity and a

50~ micros trip line, is only 2% greater than the measured value. This

percentage corresponds to the estimated overall accuracy of the measure-

ment itself. Microstrip coupling to a waveguide rather than to a cavity

can be readily achieved in the same manner, with a corresponding simplified

analysis.

The analysis presented above may be trivially extended for more

seGeral aperture shape~and other cavity configurations.

MT - 230

-I -a C.... .!!

v--=....GI0

t'4 UID

m....c

a..0

C"I UID....

The coupling arrangement described is especially attractive for

narrowband filter and oscillator applications. It shows great potential

in overcoming several of the more serious problems associated with existing

MITC design techniques.

5. Bibliography ~

~ee1er, H. - Coupling holes between resonant cavities or waveguides

evaluated in cerms of volume ratios, IEEE Trans. on Microwave Theory and

Techniques, Vol~ MTT-12, March 1964, pp. 231 - 244.

2Angot, A. - Complements de Mathematiques, Editions de 1a Revue

d'Optique, Paris, 1965, p. 370.

3Wheeler, H. - Transmission line properties of parallel strips

separated by a dielectric sheed, IEEE Trans. on Microwave Theory and

Techniques, Vol. MTT-13, March 1965, pp. 172 - 185.

4Montgomery, C. G. - Principles of Microwave Measurements, Boston

Technical Publishers, 1964, p. 176.

5Getsinger,W.J. - Microstrip Dispersion Model, Trans. IEEE,

Vol. MTT-21, January 1973,00.34 - 39.

6Schneider, M. V. - Microstrip Dispersion, Proc. IEEE, Vol. 60, No.1,

January 1972,.pp. 144 - 146.

7 .Douville, R. J. P. and James, D. S. - Experimental characterization

of microstrip bends and their frequency dependent behaviour, International

Electrical, Electronics Conf., October 1973, Toronto, Ontario, Canada.

8James, D. S. and Tse, S. H. - Microstrip end effects, Electronics

Letters, Vol. 8, No.2, 1972, pp. 46 - 47.

MT - 231