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 impedance matching circuit. It uses a quarter-wavelength (/4) transmission line loaded by a combination of switches, capacitors and inductors. With MEMS-based switches and inductors, the simulation results show that this circuit is capable of correction load reflection coefficients of up 0.5 to better than 0.38 with insertion loss between 0.74-2.11 dB at 2GHz. Index Terms — Impedance matching; MEMS; Microwave Switches. I. INTRODUCTION The antenna, in a mobile telephone handset, is connected to the power amplifier and to the low noise amplifier (LNA) through a duplexer or a switch. Its input impedance variation was already demonstrated in different works [1] - [2], as well as the effects in the output power and in the phase distortion of the power amplifiers [3]. It was shown that the antenna reflection coefficient can vary from 0 to 0.5 according to the distance between the antenna and the user [2]. An automatic impedance matching system can reduce this variation. An automatic impedance matching system is basically composed of an impedance measurement circuit, a tunable impedance matching network and a digital processor, which through an algorithm operates on the impedance matching network in order to minimize the reflection coefficient. In [4], an MMIC automatic impedance matching system at 5 GHz is presented, 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 is proposed, based on a /4-transmission line loaded by six switches, capacitors and inductors for a future conception of an automatic impedance matching system in integrated circuit technology. II. FUNDAMENTAL THEORY A lossless impedance matching network (Q) transforms the variable reflection coefficient L into a coefficient M . When the match is perfect, M equals zero (Fig. 1), and the power available 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 is arbitrarily variable. Therefore a non-zero reflection coefficient smaller than a predetermined value min is usually accepted. Fig. 1. Transmission line connected to a variable load through a matching network Considering a Q lossless two-port network represented by its scattering matrix [S], being a 1 and a 2 the incident waves and b 1 and b 2 reflected ones at its ports, the reflection coefficient after the matching ( M ) is given by (1). L L M S S S S a a S a S a b 22 21 12 11 1 2 12 1 11 1 1 1 (1) To find the load impedances that are matchable by the Q- network, one firstly consider the following inequation: min 22 21 12 11 min 1 L L M S S S S (2) Assuming a symmetrical and lossless Q-two-port network, one can manipulate (2) to obtain (3) [5]. 2 2 22 min 2 2 22 2 min 2 22 min 2 min * 22 1 1 1 1 S S S S L (3) The solution of (3), in the L plane, is bounded by a circle on the Smith chart, whose center c and radius r are given by: 2 22 min 2 min * 22 1 1 S S c (4) 2 22 min 2 22 min 1 1 S S r (5)