Transmissionline Transformers for High Transformation Ratios

The problem of matching a resistive load to a resistive generator over a wide range of frequencies by means of a stepped impedance transformer (SIT) has an explicit optimal solution that is well known. This paper presents a reappraisal of this classical problem under the additional constraint that only a limited ohmic range of characteristic impedances in the SIT is available. When the source or load resistance lie far outside the range of characteristic impedances in the SIT, an exact solution becomes difficult to obtain. A comprehensive analysis of this situation is presented and the precise physical limitations are discussed. A simple rational approximation is given in explicit form.