Tunable Impedance Matching Network

Karolinne Brito and Robson Nunes de Lima

Universidade Federal da Bahia � UFBA, Salvador, BA, 40210-630, Brazil / Universidade Federal do Recôncavo da Bahia � UFRB, Amargosa, BA, 45300-000, Brazil

Abstract � This work presents a RF tunable impedancematching circuit. It uses a quarter-wavelength (�/4) transmissionline loaded by a combination of switches, capacitors andinductors. With MEMS-based switches and inductors, thesimulation results show that this circuit is capable of correctionload reflection coefficients of up 0.5 to better than 0.38 withinsertion loss between 0.74-2.11 dB at 2GHz.

Index Terms � Impedance matching; MEMS; MicrowaveSwitches.

I. INTRODUCTION

The antenna, in a mobile telephone handset, is connected tothe power amplifier and to the low noise amplifier (LNA)through a duplexer or a switch. Its input impedance variationwas already demonstrated in different works [1] - [2], as wellas the effects in the output power and in the phase distortion ofthe power amplifiers [3]. It was shown that the antennareflection coefficient can vary from 0 to 0.5 according to thedistance between the antenna and the user [2]. An automaticimpedance matching system can reduce this variation.

An automatic impedance matching system is basicallycomposed of an impedance measurement circuit, a tunableimpedance matching network and a digital processor, whichthrough an algorithm operates on the impedance matchingnetwork in order to minimize the reflection coefficient. In [4],an MMIC automatic impedance matching system at 5 GHz ispresented, whose matching network is based on a �/2-transmission line loaded by 12 capacitors and 12 pHEMT-switches.

In this paper a new tunable impedance matching network isproposed, based on a �/4-transmission line loaded by sixswitches, capacitors and inductors for a future conception ofan automatic impedance matching system in integrated circuittechnology.

II. FUNDAMENTAL THEORY

A lossless impedance matching network (Q) transforms thevariable reflection coefficient �L into a coefficient �M. Whenthe match is perfect, �M equals zero (Fig. 1), and the poweravailable from the source is delivered to the load.

In practical circuits, it is difficult to achieve such a condition(�M= 0), especially when the reflection coefficient isarbitrarily variable. Therefore a non-zero reflection coefficientsmaller than a predetermined value �min is usually accepted.

Fig. 1. Transmission line connected to a variable load through amatching network

Considering a Q lossless two-port network represented by itsscattering matrix [S], being a1 and a2 the incident waves and b1

and b2 reflected ones at its ports, the reflection coefficient afterthe matching (�M) is given by (1).

L

LM S

SSS

a

aSaS

a

b

���

���

���22

211211

1

212111

1

1

1(1)

To find the load impedances that are matchable by the Q-network, one firstly consider the following inequation:

min22

211211min 1

�����

�����L

LM S

SSS (2)

Assuming a symmetrical and lossless Q-two-port network,one can manipulate (2) to obtain (3) [5].

22

22min

2222

2min

222min

2min*

22

1

1

1

1

S

S

SSL

��

���

���

�

���

�

�

��

�

��

�

�

��

���� (3)

The solution of (3), in the �L plane, is bounded by a circleon the Smith chart, whose center c and radius r are given by:

��

�

��

�

�

��

���

222min

2min*

221

1

SSc (4)

2

22min

2

22min

1

1

S

Sr

��

��� (5)

117

1-4244-0661-7/07/$20.00 c© 2007 IEEE

Fig. 2. ZL matchable region (grey);

Thus, with a lossless two-port network it is possible tomatch the impedances lied on this circle. Varying the phase ofthe center of this circle and keeping constant the magnitude ofcenter c and radius r, one obtain a tunable matchable ZL

impedance region, located between two circles of radii ��min�and ��max�. This phase variation can be achieved by cascadingthe Q-network and a phase shifter �m.

Thus, the new matchable region is represented by a circle,whose radius rm and center cm are given by (6) and (7),respectively.

2

22min

2

22min

1

1

S

Srm

��

��� (6)

mjmjm ce

SeSc �� 2

222min

2min2*

221

1��

�

�

��

�

�

��

��� (7)

As it is shown by (6) and (7), the new matchable region ismodified simply by the center phase. And varying �m, one canmatch the impedance locus between the circles �min and �max.

Assuming as acceptable a load reflection coefficient lessthan ��min�, the region delimited by a circle centered at theorigin, whose radius is equals to ��min�, is thus consideredmatched. In this case, it is necessary a procedure to disable theQ-network, what can be done through the switches. By sodoing, when the magnitude of the reflection coefficient isbetween ��min� and ��max�, the switch (S) is set on and the phaseshift �m is properly changed in order to get the matchedcondition. When �L is smaller than �min, the switch is set off,altering only the phase of �M.

Another phase shifter �n can be used to control the �M value(Fig. 3) without modifying the radius and center phase of thecircle. Therefore, with the switch S set on the reflectioncoefficient is given by (8).

Lnj

Lnmj

njM

eS

eSeS

��

�����

�

���

�

���

211

22112

111

1(8)

To cover all the phase variations in the Smith Chart, isnecessary to vary �m between 0o-180º, what can be providedby a discrete phase shifter.

Fig. 3. Block diagram of the tunable impedance matchingnetwork.

III. PROJECT

Because of practical issues related to the actualimplementation, the phase shifts �m and �n are provided bysections of transmission line and the lossless Q-network isformed by capacitors, inductors or even by a combination ofboth [4], [6].

(a) (b)Fig. 4 Basic matching Q network

Considering an ideal switch S in the on-state, the magnitudeof the S22 (scattering parameter) of the Q-networks illustratedin Fig. 4a and Fig. 4b are given by (9) and (10) respectively.

2220

022

4 xLZ

ZS

��� (9)

2220

022

4 x

x

CZ

CZS

�

�

�� (10)

where � is the angular frequency, Z0 is the referenceimpedance at Q-networks ports, Lx is the matching inductanceand Cx the matching capacitance.

According to [5], the magnitude of S22 can also be expressedas (11).

3

minmax

minmaxmin22

1 ���

�����S (11)

118 2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007)

Analyzing the matchable impedances circles provided by thenetworks illustrated in Fig. 4a and Fig. 4b, a shift betweentheir centers of approximately 90o was observed.

Using this characteristic, a tunable impedance matchingnetwork composed of a �/4-transmission line loaded byinductors and capacitors in series with switches is proposed(Fig. 5).

Fig. 5 Tunable impedance matching network topology

IV. DESIGN EXAMPLE AND RESULTS

A. Ideal Switches

Suppose a system, operating at 2 GHz, with a load reflectioncoefficient magnitude less than 2/3 (��max�) and referenceimpedance at its ports Z0 = 50�. In order to obtain thematched coefficient magnitude less than 1/3 (��min�), it isnecessary a capacitance CX=2.2pF and an inductanceLx = 3nH.

Under these conditions, the matchable impedance regions Si

(i=1, 2, 3, 4, 5, 6) provided by this topology are illustrated inFig. 5a.

(a) (b)

Fig. 6 Impedance matchable region considering a) Lx = 3nHe Cx = 2.2 pF; b) Lx = 3.5nH e Cx = 1.8 pF

As can be seen in Fig. 6a, there are still unmatched regions(shaded). An approach to overcome this problem consists inincreasing the radii of the circles, which demands an increaseof Lx, and a reduction of Cx. As this also implies in a variationof the center of the circles (Fig. 6b) the network matchingcapability is altered. To ensure the impedance matching will

occur in the whole delimited region, it is then adopted themaximum reflection coefficient (�max) equal to 0.5 (greencircle centered at the origin), Lx= 3.5nH and Cx=1.8pF.

The circuit simulations were carried out using AdvancedDesign System (ADS-Agilent). Imposing that at any time onlyone switch is in the on-state, the matching performance of thecircuit for load mismatches ��L�= (0; 0.4; 0.5) with 360°phase variation was then obtained.

Fig. 7 shows the magnitude of the matched reflectioncoefficient �M as well as the associated insertion loss (IL),when all the switches are in the off-state. The objective of thisprocedure is to analyze the system performance when the loadis already matched (�L<�min).

Fig. 7, Fig. 8 and Fig. 9 show the matched reflectioncoefficient (�M) and the insertion loss (IL). It can be seen thatthe matched reflection coefficient (�M) varies between 0.009and 0.327. The insertion loss variation is 0.0003- 0.49dB.

Fig. 7 Simulation results using ideal components and��L�=0

Fig. 8 Simulation results using ideal components and��L�=0.4

2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007) 119

Fig. 9 Simulation results using ideal components and��L�=0.5

B. Non Ideal Switches

To evaluate the network performance with practicalcomponents a new simulation was carried out using MEMS-based switches and inductors.

The MEMS-based passive components present high qualityfactors, low insertion loss, high isolation and low electricconsumption, what will probably make possible the realizationof a low-loss automatic impedance matching system.

The MEMS switch of shunt-capacitive type was chosen. Itcan be modeled by a capacitance in the on-state (CON) and theoff-state (COFF < CON). The typical range found in literature forthese capacitances are COFF=25-75fF and CON = 1.2-4pF [8]-[9]-[10]. In this work, the parameters of the chosen switch areCOFF=70fF and CON=3.1pF [7].

The capacitors and the microstrip transmission lines modelsare from the OMMIC-ED02AH library. The values of theinductance Lx and capacitance Cx are, respectively, 3.5 nH and1.9 pF.

The chosen MEMS based inductor electric model ispresented in [11], C1 and C2 models the parasite capacitancesbetween the lines and the substrate and rS is the resistancerelated to the metal loss (Fig. 10).

Fig. 10. Circuit to extract the inductor parameters

The typical range of MEMS inductors quality factor (QL) is16-100, depending on what material, geometry and techniqueare used. In this work it is adopted an average quality factorQL, associated with Lx, equal to 46 [11].

Through an extraction and optimization procedure, at 2GHz,the following parameters are obtained: rS=0.������L=3.908nH; C1=0.955pF and C2=0.254pF resulting inLx=3.52nH and QL=45.67.

Fig. 11. Simulation results using non-ideal components and��L�=0

Being the network composed by a microstrip transmissionline loaded by MEMS-based switches in series with capacitorsand MEMS-based inductors, the simulation results show thatthe magnitude of the matched reflection coefficient (��M�)varies between 0.038-0.383 and the insertion loss variesbetween 0.74-2.11dB as shown in Fig. 11, Fig. 12 and Fig. 13.

Fig. 12. Simulation results using non-ideal components and��L�=0.4

Fig. 13. Simulation results using non-ideal components and��L�=0.5

V. CONCLUSION

A new tunable impedance matching network based on a �/4-transmission line loaded by 2 inductors and 4 capacitors inseries with switches has been presented. Using MEMS based

120 2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007)

switches and inductors, the system is capable of correctionload reflection coefficients of up 0.5 to better than 0.38 withinsertion loss between 0.74-2.11dB at 2GHz. Despite itsinsertion losses, it should also be mentioned that the insertionlosses of a tunable impedance matching network are not theonly criterion to evaluate its performance. In [5], it is shownthat a power amplifier, with a mismatched load (VSWR 3:1)can produce an attenuation of 10 dB in the output powercompared to the power that could be delivered if the load wasmatched. This example shows that the application can playimportant role in the use of such a matching network.

ACKNOWLEDGEMENT

The authors would like to thank CNPq (Conselho Nacionalde Desenvolvimento Científico e Tecnológico) and FAPESB(Fundação de Amparo à Pesquisa do Estado da Bahia) for thefinancial support.

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[2] Sadeghzadeh, R. A.; Abrishamian, M. S.; McEwan, N. J. Effectof User Head on Mobile Telephone Handset Antenna and Head

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[3] Ishizaki, T. at al. Analysis of Phase Characteristics of a GaAsFet Power Amplifier for Digital Cellular Portable Telephones; p.410-418; 1994.

[4] Lima, R. N. et al. MMIC Impedance Matching System; IEEElectronics Letters, v. 36, n. 16, p. 1393- 1394, august 2000.

[5] R. ����� ����������������������������� ���������� ����� �������� !� ��� ���� " #��$����#� ��� %� ��� &��'��$�( ��MMIC: Applications ��)� *��$�)��#�+, Tese de Doutorado,ENST, Paris, 2001.

[6] Sun, Y.; Lau, W. K. Evolutionary Tuning Method for AutomaticImpedance Matching in Communications Systems; Proc. IEEEInternational Conference on Electronics, Circuits and Systems,USA, p. 73-70, 1998.

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[8] 4� � -#�5��� � !-MEMS Switches for Reconfigurable6���(#���� " #�� ��+�� 6444� &#���� ��� .&&�� 8�$� �9�� �:� ;;��November 1998.

[9] 0�.� �1� 2��,-�.�$�/ ���� !�.4.���5 ��'�������5 ��'�� #�� ��+��6444�. �#�5�/���/�$��� pp. 59-71, Dec. 2001.

[10] Z. J. Yao, S. Chen, S. Eshelman, D. Denniston, C. Goldsmith,�. �#����' ��� ��5-����� . �#�5�/�� �5 ��'��+�� 6444�Journal of Microelectromechanical Systems, Vol. 8, No. 2, pp.129-134, June 1999

[11] Park, J. Y.; Allen, M.G. Packaging-Compatible High QMicroinductors and Microfilters for Wireless Aplications. IEEETransactions on Advanced Packaging, v. 22, n. 2, p.207-212,May 1999.

2007 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC 2007) 121