Terminal impedances and transfer functions of ladder networks

Concise mathematical formulas are developed for the input impedances, output impedances and transfer functions of ladder networks containing two kinds of elements only, namely resistance and capacitance or resistance and inductance or capacitance and inductance. A procedure is given for extending these formulas to the most general type of ladder network in which any series or shunt arm may contain all the three types of elements connected in any configuration. As examples of their application, the formulas are used to deduce the design equations of a phase-shift oscillator employing four- and five-section resistance-capacitance ladder networks.