Constant resistance networks with applications to filter groups

The problem investigated is the determination of two finite networks such that, when connected in parallel, they will have a constant resistance at all frequencies. The admittance of any network may be written as the ratio of two polynomials in frequency. A network to be one of a constant resistance pair must have certain restrictions imposed on its admittance. In case the two networks are both filters of negligible dissipation, the expression for the input conductance of each may be written from a knowledge of the required loss characteristic. The poles of the expression for the conductance are then found. They will be identical for the two networks. The networks are then built up by synthesis from those poles of the conductance which have negative real parts, these corresponding to real network elements. The methods which have been developed for this last process are described in detail.