THE MATCHED SYMMETRICAL FIVE-PORT JUNCTION AS THE ESSENTIAL PART OF ANIDEAL SIX-PORT NETWORK

E.R.Bertil Hansson* and Gordon P. Riblet**

ABSTRACT

The basic properties of a novel configuration for six-port measurements,consisting of a matched symmetrical five-port junction and a directionalcoupler,are described. The proposed six-port is shown to possess severaladvantageous properties for accurate determination of complex signal ratios.The basis for analysis of planar symmetrical five-port junctions is givenand it is demonstrated that stripline junctions can be matched over broadfrequency bands by the use of short line segments. An experimental strip-line five-port shows a performance in good correspondence with the theore-tically predicted one. Results are given of six-port impedance standardmeasurements made with the stripline five-port junction.

INTRODUCTION

As an aid in determining what properties a six-port should have to enableaccurate measurement of the reflection coefficient, r , Engen introduced auseful diagram in the complex r-plane [li. Engen showed that, ideally,onepower detector should be used to measure the power incident to the unknownload, and that the complex numbers q1 , q2 and q3 associated with the re-maining three power detectors should be symmetrically distributed aroundthe origin , i.e. separated by 1200 , Fig.l. A six-port network accom-plishing these features consists of a matched, reciprocal, symmetricallossless five-port junction and a perfect directional coupler, Fig.2 [2].

PROPERTIES OF THE PROPOSED SIX-PORT NETWORK

Applying the conditions of losslessness and matching to the scatteringmatrix element-eigenvalue relations for a symmetrical, reciprocal five-port it can be shown that the transmission coefficients for the five-port,S12 and S13 ,are given by [3]:

1S121 IS131 = .5

L 13

(1)

(2)= L2 + 1200

Such a five-port junction thus works as a four-way equal power divider.With reference to Fig.2 the complex amplitudes of waves entering into,andemerging from the five-port junction, assuming matched detectors, arerelated as

*Chalmers University of Technology, Division of Network Theory, S-41296 Gothenburg, Sweden

**Microwave Development Laboratories,Inc., 11 Michigan Drive, Natick,Massachusetts 01760, USA

501

b =S a + S a (3)2 12 3 12 1

b =S a (4)3 13 1

b =S a + S a (5)4 12 3 13 1

b =S a + S a (6)5 13 3 12 1

with a according to (4) the powers entering the detectors 1-3 are1

P = 1S jlb I lr-(-9S1 2 (7)

p2 = jS12 jb 2 12) (8)

p = Is I lb I I r-(- v)| (9)2 12 3 S12

S 2121'lb 12 jr-(- -S12 (9)

where r =a31/b3 In (7)-(9) we identify, [1i, ql = -l/Sl3 q2 -1/S12 and

q= -S12/S1f or with (1) and (2):

q 1= jq = iq I = 2 (10)

b= ±+ 1200 (11)

= [2i + 1200 (12)

A more detailed study would show that for a physical five-port junctiononly one combination of signs in (11) and (12) is possible. Hence theq-points are ideally situated for six-port measurements, see Fig.l.

An important consequence of these results is that the problem of obtaininga preferable distribution of the q-points is , for the proposed six-port,essentially reduced to the problem of matching the five-port junction. Thereciprocal five-port junction thu-s exhibits an analogy with the non-reciprocal three-port junction , where similarly, the desired functionmode, namely circulation, can be obtained by simply matching the junction.The scattering matrix eigenvalues of these junctions, when matched, areshown in Fig.3. The arbitrary phase of the even mode eigenvalue has beenset to 1800.

DESIGN OF A MATCHED STRIPLINE FIVE-PORT JUNCTION

A symmetrical stripline five-port junction can be analyzed based on aseries expansion of the fields in the junction subject to proper boundaryconditions [4]. The analysis results in computed values of the elementsor eigenvalues of one of the matrix representations of the five-port. Byfollowing a procedure similar to the one developed for the non-reciprocalthree-port junction [5j analytic expressions for the equivalent admittance,Y , have been derived:eq

502

(l+Y02)G+j[G2Y0-(1-BY0)(B+Y0)] (13)

where

G = y Oy|(14)

Yoy2+1 Y Y0+1l (B= ± j + Yo~ J (15)

and YO , Y1 and Y2 are the three different eigensusceptances of thesymmetrical five-port junction. The equivalent admittance has the propertythat if a two-port matching network matches into this admittance, then thesame network connected in each five-port arm will match the five-port. Aparticularly simple configuration results for Yeq = .02'-1. Then thefive-port matches directly into a 50Q network. After computer optimiza-tions it was found that the restrictions imposed by the stripline config-uration prevented the design of a broadband, direct coupled five-portjunction. (Broadband, direct coupled five-port junctions with a lessrestrictive planar configuration have been designed[2f). However, byextracting low impedance line sections, shorter than a quarter wavelengthat the center frequency, see Fig.4 , a design was obtained with thetheoretical performance of Fig.5a. The measured performance of thecorresponding experimental five-port junction is shown in Fig.5b. Therelatively large bandwidth obtained for the coupling angle ' = 400 and withthe very simple matching sections used is remarkable.

An experimental stripline five-port junction has been used, together witha directional coupler, in a system for six-port measurements , Fig.6.Results of measurements of some impedance standards, not used in thecalibration of th-e six-port , are shown in FigS7 and Table I. It isnoteworthy that high accuracy measurements can be made over a frequencyband considerably larger than that where the five-port is well matched.

CONCLUSION

A compact and simple six-port configuration with virtually ideal propertiesfor precision measurements consisting of a symmetrical five-port junctionand a directional coupler has been presented. A theoretical basis for thedesign of matched stripline five-port junctions has been developed, con-firmed by demonstrated correspondence between computed and measuredperformance of an experimental model. The accuracy of measurements ofstandards has demonstrated the applicability of the proposed six-portconcept.

REFERENCES

[1] G.F.Engen,"The six-port reflectometer: An alternative networkanalyzert, IEEE Trans.on Microwave Theory and Techniques,Vol.MTT-25,pp. 1075-1080, Dec.1977.

-[2] G.P.Riblet,E.R.B.Hansson,"The use of a matched symmetrical five-portjunction to make six-port measurements", 1981 IEEE_MTT-S InternationalMicrowave Symposium Digest, Paper GI-2, June 1981.

503

[3] C.G.Montgomery, R.H.Dicke, E.M.Purcell, "Principles of MicrowaveCircuits", McGraw-Hill , New York, 1948.

[41 J.B.Davies, P.Cohen, "Theoretical design of symmetrical junctionstripline circulators" , IEEE Trans.on Microwave Theory andTechniques, Vol.MTT-ll, pp. 506-512, Nov.1963.

[5] G.P.Riblet, "The measurement of the equivalent admittance of 3-portcirculators via an automated measurement system", IEEE Trans. onMicrowave Theory and Techniques, Vol.MTT-25, pp.401-405, May 1977.

TABLE IMeasurement of open circuits

Freqy(MHz)5000550060006500700075008000850090009500

100001050011000115001200012500

OffsetIii

0.9190.9730.9690.9920.9890.9911.0171.0110.9890.9781 .0141.0081.0030.9801 .0061.025

1 .892mmLr(o)

"-1 .7-1.9-1.8-1 .0-0.7-1.8-0.40.00.5

-1 . 1-2.6-0.40.30.0-3.0-1 .0

Offset

0.9450.9950.9840.9901.0041.0181 .0050.9870.9961.0261.0351 .0090.9851.0041.0181.019

-2.057mm[PA(0)0.4-1.6-0.2-0.8-1.7-0.60.2-0.7-2.0-2.4-0.10.1-0.8-2.2-2.0-0.7

a1)jy

N-

Fig.l Optimum location of q-points for six-port measurements.

504

Fig.2 Six-port configuration.

Fig.4 Experimental stripline five-portjunction with low impedance linesections for broadband matching.

52

Fig.3 -Scattering matrix eigenvalue configuration formatched,lossless,symmetrical junctions:a. Nonreciprocal three-port,e1=2cosCI(.5)=120.b. Reciprocal five-port,®2=2cos-'(.25)=1510.

(GH)s

le - --

,12

Id8)

Fig.5a Computed performance of experimental stripline five-port.

505

a.

b.

sot

-10I

-20O

- 304

i a I

-10 I

-20+

(dB8)

Fig.5b Measured

Ir'.?I

.II

6 i~~~ 0II12

131~~~~~A

--- I i NNW~~~~~~~~~~~~3

(GHz)

performance of experimental stripline five-port.

Fig.6 Experimental six-port.

~~9.0 10.0 11.0 12.04.0 5.06.0 70 8.0 W~~~~~~~(HO)

Fig.7 Measurement of

4 to 12.5 GHz.

impedance standard, Irj. = .2 nominally, over

506

I i I~ ~~~~~a I**.*