On Limitations of Broad-Band Impedance Matching without Transformers

The basic work of Fano on the limitations for the synthesis of broad-band matching networks is extended to include some relations for determining resistance transformation ratio possible in the band-pass case. Fano's results are used to determine the load (or source) reactance possible and then to synthesize an optimum network. The relationships between the reflection coefficient, order of approximation, and the maximum theoretical resistance ratios are given for a number of cutoff-frequency ratios. These results for the band-pass case include absorption of ideal transformers with maximum turns ratios such that transformerless networks result. Appendixes include a design procedure, necessary polynomials for obtaining the immittance function up to an
n = 6
approximation (i.e., a basic 6-section matching network), and one example using the results of this paper.