The synthesis of ladder networks with resistances at both ends by the recurrent-continuant method

Abstract

The recurrent-continuant method of synthesizing a ladder network due to Holbrook is limited to the lossless quadrupoles terminated in resistance at only one end. The technique has been modified to cover the general class of lossless quadrupoles terminated in resistances at both the ends. The proposed synthesis procedure starts with a given realizable polynomial which is separated into two realizable component polynomials, one of the same order and the other of one order less under the condition that the continuants corresponding to the component polynomials are such that one becomes the first minor of the other. By applying simple mathematical manipulations, the final continuant is formed out of these continuants. The element values of the final continuant are evaluated by solving certain sets of equations. The sensitivity of the transfer function of the network with respect to the terminal resistance, the non-realizability of the characteristic polynomial for a given terminal resistance ratio, and the multiple sets of values of the circuit elements for a given characteristic have also been investigated.In the case of active RC low-pass ladder networks Nesbitt has presented a technique for transforming the recurrent determinant into the continuant determinant provided the elements of the main diagonal of the latter are specified. His method however does not provide a solution for active RC ladder networks which are terminated in a resistance at the output end. In this paper a modified transformation technique, applicable to resistively-terminated active RC ladder networks, is proposed.