Systematic Design of Reconfigurable Quadrature Directional Couplers Henning Mextorf, Thomas Lehmann and Reinhard Knoechel

Institute of Electrical and Information Engineering, Microwave Laboratory, University of Kiel, Kaiserstrasse 2, 24143 Kiel, Germany

Abstract — This paper presents an approach for the

systematic design of reconfigurable quadrature directional couplers. From even-odd-analysis of four-ports with two-fold symmetry four eigenreflections are derived. The scattering-parameters are linear combinations of them. The eigenreflections can be positioned deliberately with tuning reactances to create directional couplers which are reconfigurable in coupling ratio, operating frequency or the arrangement of the output ports. Two exemplary couplers, a LC-bridge and a modified branchline-coupler, are presented and measurement results are shown.

Directional couplers with adjustable coupling ratio can also be created with cascaded couplers and additional phase shifters or discontinuities. A compact directional coupler using this principle is presented together with measurement results.

Index Terms — directional coupler, reconfigurable, tunable, variable

I. INTRODUCTION

Reconfigurable quadrature directional couplers find applications in e.g. multi-standard systems, reconfigurable antenna arrays or sequential amplifiers. Various directional couplers with tunable coupling ratio [1]-[8] and with adjustable operating frequency [9]-[15] were already presented in the literature. A directional coupler tunable in coupling ratio, operating frequency and being switchable between forward and transverse operation was introduced in [16]. Previously suggested reconfigurable couplers, however, were often designed intuitively. In this work a systematic design approach for reconfigurable quadrature directional couplers based on the analysis of two-fold symmetrical four-ports will be introduced.

II. ANALYSIS OF TWO-FOLD SYMMETRICAL FOUR-PORTS

The scattering-parameters of a two-fold symmetrical four-port as shown in Figure 1 with the symmetry planes A and B can be determined using an even-odd-analysis.

Fig. 1. Two-fold symmetrical four-port

An extension of the method of Reed and Wheeler [17] with

even and odd excitations in both symmetry planes leads to a decomposition of the four-port into one-ports. Four one-ports terminated with electric (ew) and magnetic walls (mw) occur as shown in Figure 2.

Fig. 2. Equivalent one-ports with even- and odd-mode excitations

The matrix of excitations [ consists of the four excitation-vectors:

]E

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−−−

−−=

111111111111

1111

41E . (1)

The corresponding matrix of eigenreflections can be written as

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

dd

ed

de

ee

rr

rr

R

000000000000

, (2)

comprising the four eigenreflections in the diagonal. The scattering-matrix can be calculated from (1) and (2):

[ ] [ ] [ ] [ ] 1−⋅⋅= ERES . (3) The scattering-parameters are linear combinations of the

four eigenreflections:

( )ddeddeee rrrrSSSS +++====41

44332211 , (4)

( )ddeddeee rrrrSSSS −−+====41

34431221 , (5)

( )ddeddeee rrrrSSSS +−−====41

24421331 , (6)

( )ddeddeee rrrrSSSS −+−====41

23321441 . (7)

978-1-4244-2804-5/09/$25.00 © 2009 IEEE IMS 20091009

III. QUADRATURE DIRECTIONAL COUPLERS

If the four-port with two-fold symmetry is lossless, the absolute values of the eigenreflections are one. In order to match the circuit the positions of the eigenreflections in the complex plane have to be chosen so that they form two antiparallel oriented pairs. If the three criteria (two-fold symmetry, lossless, port-matching) are fulfilled, the four-port will be a quadrature directional coupler, i.e. one port will be decoupled and the phase difference between the output ports will be 90 degrees. There are three different types of couplers in general, the forward coupler, the transverse coupler and the backward coupler. The type and the coupling level depends on the positions of the eigenreflections.

IV. RECONFIGURABLE QUADRATURE DIRECTIONAL COUPLERS

A. Variable coupling ratio

The basic idea to realize a quadrature directional coupler with variable coupling ratio is to deliberately rotate the eigenreflections in the complex plane. They have to form two antiparallel pairs to ensure perfect matching. Figure 3 shows an example of a constellation of eigenreflections for a 3dB forward coupler.

Fig. 3. Constellation of the eigenreflections of a 3dB forward coupler

eer and as well as and are antiparallel. The scattering-parameters can be calculated from (4)-(7). The four-port is matched and one port is decoupled. The magnitude of the output scattering-parameters depends on the angle between the two pairs of antiparallel eigenreflections, described by (8) and (9):

edr der ddr

α

2cos21

α=S , (8)

2sin31

α=S . (9)

If it is possible to vary , the coupler will be variable in coupling ratio. For any constellation of eigenreflections in the complex plane one has to rotate at least two eigenreflections to meet the matching criterion for different configurations.

α

B. Variable operating frequency

To create a quadrature directional coupler with constant coupling ratio over a frequency bandwidth one either has to keep all eigenreflections constant over frequency or rotate the whole constellation with a constant angle over frequency. α

C. Switching between forward and transversal operation

The transposition of the symmetry planes A and B leads to a transposition of the eigenreflections and and therefore to a permutation of forward and transversal coupling. Figure 4 shows the constellation of eigenreflections of a transversal coupler. In relation to the constellation in Figure 3, port 2 is decoupled and port 4 is an output port.

der edr

Fig. 4. Constellation of eigenreflections of a 3dB transversal coupler

V. IMPLEMENTATIONS

The implementation of reconfigurable quadrature directional couplers requires reconfigurable circuit elements, e.g. tunable capacitors, inductors or switches. These elements have to be placed suitably in the coupling structure.

A. LC-coupler

The LC-coupler, also known as the Maxwell-bridge, is a bridge circuit consisting of an inductor and a capacitor. It is depicted in Figure 5. It can be analyzed with an even-odd-analysis as mentioned previously.

Fig. 5. LC-coupler equivalent circuit

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The normalized eigenimpedances are

∞→eez , (10)

0CZjzde ω

−= , (11)

0ZLjzed

ω= , (12)

0=ddz . (13)

The eigenreflections can be calculated from

{ }oddevenbazzr

ab

abab ,,,

11

∈+−

= . (14)

The eigenreflections and are frequency independent. and r can be adjusted independent of each other by tuning of the capacitor and the inductor. In principle the coupler is able to work at arbitrary frequencies with arbitrary coupling ratios. Perfect matching and directivity are given for all frequencies. The circuit can be implemented at microwave frequencies as shown in figure 6.

1=eered

1−=ddrder

Fig. 6. LC-coupler at microwave frequencies

The structure consists of two microstrip-lines which are connected by the variable capacitance 1 on the upper site. A slotline loaded with two variable capacitances is defined in the ground plane. and can be adjusted independently of each other by tuning of capacitors. The coupler theoretically works at arbitrary frequencies with an arbitrary coupling ratio, however matching and directivity are no longer frequency independent. The variable capacitors are realized by varactor diodes. In fig. 6 the DC-supply is omitted. The range of operating frequency and coupling ratio change mainly depends on the capacitance ratio of the varactors. The realized coupler is able to work with 3dB coupling between 1.5GHz to 2.4GHz. At 2GHz can be changed between -1.8dB and -19.8dB and accordingly between -6.5dB and -1.1dB. Figure 9 and Figure 10 show the measured scattering-parameters of the 3dB configuration at 2GHz and 2.4GHz.

C

edr

41S

2Cder

21S

B. Modified branchline-coupler

The modified branchline-coupler is a structure with two crossed 2/λ -lines which each connect two opposite ports. The characteristic impedance of all lines is Ω100 .

Fig. 7. Modified branchline-coupler

eer and are independent of the capacitances. can be adjusted as required by tuning the capacitors 1C . will be influenced by this tuning so that it has to be adjusted to the desired position via tuning of . The realized coupler is variable in coupling: can be varied between -3.6dB and -8.6dB and the corresponding between -3.6dB and -2.9dB at 950MHz. It shows an excess loss of 1.4dB due to the series resistance of the used varactors and the complex DC bias network.

edr ddrder

2C

3121S

S

VI. CASCADED COUPLERS

Directional couplers with variable coupling ratio can be created by cascading two directional couplers having a phase shifter in one connection branch [18] or discontinuities in both branches [19], [20]. There are several possibilities to design directional couplers with one-fold and two-fold symmetry.

Fig. 8. Combined two-fold symmetrical coupler

Figure 8 shows a cascade of two 3 dB forward directional couplers and two capacitive discontinuities. Each coupler consists of two Ω50 -lines with an electrical length of 45 degrees and two capacitors with an impedance of Ω− 50j

S

at the desired operating frequency. Two tunable capacitors are connected to ground. Varactors are used in practice. The realized coupler achieves a tuning range from -1.5dB to -12.2dB for 21 and from -11.1dB to 0.76dB for 31 at 1.97GHz. Figure 11 and Figure 12 show measured scattering-parameters of the coupler.

S

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[17] J. Reed, G. J. Wheeler, “A method of analysis of symmetrical four port networks,” IRE Trans. Microw. Theory Tech., vol. 4, pp. 246-252, 1956.

VII. CONCLUSION

This paper presents a systematic approach for the design of reconfigurable quadrature directional couplers. It is based on the analysis of eigenreflections and their deliberate positioning in the Smith chart using tuning reactances. For the realization of variable coupling ratios cascaded couplers appear to be a convenient solution because of their simple separation into ordinary couplers and additional discontinuities or phase shifters. Couplers with tunable operating frequency or being capable of switching the output ports can be readily realized using lumped element networks. The constellation of eigenreflections can be kept constant over frequency by adapting capacitors and inductors. Port switching by transposition of symmetry planes can be achieved by transposing capacitance- and inductance-values.

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Fig. 10. S-parameters, LC-coupler, 3dB, 2.4Ghz

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Fig. 11. S-parameters, cascaded coupler, 3dB

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Fig. 12. S-parameters, cascaded coupler, S31 max

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