
The filter can be represented as sequence of N lossless reactive resonant units separated by N1 straight uniform waveguide sections of length close to 1/4wavelength in the waveguide. Each resonator # i shows symmetric scattering matrix Si (b) with reflection function Ri (b) and transmission function Ti (b) , where b is waveguide propagation constant.


The reflection function of each resonator is smooth and monotonic over the filter passband and inverts into zero at the central frequency. Then the loaded Qfactor of the ith resonator is determined from its reflection function as
A procedure of synthesizing the filter structure is written in [1], if we assume
However, because of stability of the filter response for coupling transformer length, it can be kept the same between all resonators to be 1/4lg, little less or more.


Physical realization of such a filter is based on finding such elements providing reflection zero at particular central frequency with variable Qfactor. Resonant iris and cavity of two regular H plane irises [1] are commonly used to compose a 1/4wavecoupled filter. Using modern software a wide variety of such resonant elements can be found and unusual filter structures can be built from them. For example, couple of slots in an evanescentmode ridged waveguide behaves as reflectionzero resonator. Changing ddimension changes central frequency and changing sdimension changes Qfactor.
