Design method for impedance matching networks

Abstract

The design of basic passive LC networks, with particular attention to the ubiquitous Π network, is studied for conjugate matching any two impedances and meeting a specified loaded quality factor Q0. Algebraic design formulae are analytically demonstrated, which prove extremely simple. Explicit expressions of network frequency responses and harmonic rejection in terms of the loaded Q0 and the given impedances are established and a method for determining the loaded Q0 for any required harmonic attenuation is developed. The authors formulate and discuss all tolerance and parasitic sensitivities and their relation to the loaded Q0. The design method is also presented from the power transmission viewpoint. In particular, actual power transmission relations, taking the finite unloaded Qu into account, are derived in terms of the loaded and unloaded Q. The authors also address the design problem with regard to the standing wave ratio and reflection coefficient. Using the relations derived we can achieve both the maximum power transfer and the required harmonic rejection at any frequencies precisely, and we can also readily evaluate and incorporate other performances.