Formulas for the elements of lossy low-pass ladder networks

Realizability conditions for low-pass ladder networks containing inductances and capacitances with losses not necessarily uniform are presented. Explicit formulas for the element values are derived in terms of the Taylor coefficients and also in terms of the coefficients of the numerator and denominator polynomials of the driving-point function. Using these formulas, necessary and sufficient conditions for the driving-point function are obtained. In addition the relation between poles and zeros ofS_{11}and the Taylor coefficients of the driving-point function are derived. From these relations the element values can be calculated from a knowledge of the poles and zeros ofS_{11}. The results presented constitute a generalization from the lossless to the more practical lossy low-pass ladder network.