Notes on bandpass filters whose inter-resonator coupling coefficients are linear functions of frequency

The paper shows that coupled resonator filters in which the inter-resonator coupling coefficients vary linearly with the frequency can be transformed into equivalent networks in which the coupling coefficients do not depend on frequency. The frequency dependence of the coupling coefficients leads to the appearance of transmission zeros at finite frequencies that are not predicted by the shortest path rule. In particular, purely in-line topologies can produce transmission zeros at finite frequencies when the coupling coefficients depend on frequency.