An Analytical Algorithm for Pi-Network Impedance Tuners

In this paper, an analytical tuning algorithm for a pi-network impedance tuner is presented. The pi-network consists of tunable capacitors with finite tuning range, and a fixed value inductor. The algorithm is able to determine all tunable network component values for matching any given load impedance. The resulting matching performance measured either in terms of the input VSWR or transducer gain, is equivalent to that obtained from a commercial iterative optimization methods, but the algorithm runs significantly faster than the optimizer simulation. The proposed algorithm can be extended to a network tuner topology comprised of four or less tunable components as long as it can be transformed into an equivalent pi-network topology. It is suitable for the design of fixed as well as tunable matching networks.