Rigorous derivation of lossy equivalent circuit for narrowband waveguide direct-coupled-cavity filters

This study presents a technique to rigorously derive a complete lossy equivalent circuit of narrowband direct-coupled-cavity filters with arbitrary cross-section and arbitrary coupling geometries. Traditionally, only dissipation loss and stored energy because of closed unperturbed cavities have been taken into account in the design of complete filters and the contribution because of coupling structures has been neglected. An additional challenge is the non-trivial discrimination of cavities and couplings in a direct-coupled-cavity filter. With the proposed circuit, the contribution of the coupling structures to the total dissipated power and total stored energy of the filter can be derived and a clear separation between resonators and couplings is established. The technique developed uses the even and odd mode theory to successfully derive lossy equivalent circuits for inter-cavity couplings. The lossy circuit of external (input/output) couplings is also derived. A fifth degree direct-coupled-cavity filter has been designed, simulated and manufactured. Its lossy equivalent circuit has been extracted and comparisons with simulations and measurements show excellent agreement. Applications of the novel equivalent circuit in the prediction of losses in waveguide filters and in yield analyses are also illustrated.