Ladder networks with elements in geometric progression

Simple expressions, in terms of ratios of Chebyshev polynomials, are developed for the network functions of a ladder network of the two-element kind, whose elements follow a geometric progression of the common ratio
\beta
. Explicit solutions for the roots of the denominator polynomial of the transfer impedance and transfer current ratio are presented. Strict constraints are placed on the locations of the roots of the denominator polynomial of the transfer voltage ratio and transfer admittance, with explicit solutions being obtainable when
\beta=1
.