A Study of Recurrent Ladders Using the Polynomials Defined by Morgan-Voyce

Recurrent ladders have received considerable attention in the literature. In the present paper, the matrix parameters of a recurrent ladder network with general series and shunt arms are derived in terms of a set of polynomials, which were first defined by Morgan-Voyce in his studies on the special case of a resistive ladder. [11] Since the polynomials are factorizable, the matrix parameters can be conveniently utilized to yield network response to any given excitation. Also, the zeros and poles of any network function may be found in terms of the zeros of these polynomials. For purposes of illustration, response to a square-wave input has been worked out in detail in the case of an RC ladder. The chief merit of the analysis lies in its simplicity and compactness.