Specific Equations for One and Two Section Quarter-Wave Matching Networks for Stub-Resistor Loads

Given a load network consisting of a conductance in parallel with a short-circuited stub, the admittance values of optimum one and two section commensurate transmission line matching networks are derived. These values are expressed in closed form as functions of the bandwidth and ripple level. It is shown that optimum networks have nonzero reflection coefficient minima, as predicted by classical broad-band matching theory.