On the theory of chained-function filters

For the first time, the new class of filter transfer functions, called chained-function filters, is described in theoretical detail. The chained-function concept can give a variety of transfer functions, having the same order, but different frequency domain, time domain, and implementation characteristics. As a result, a filter can be selected to have the required reduction in sensitivity to manufacturing errors, resonator unloaded-Q, and filter losses. This can be achieved while maintaining a given return-loss level and a predetermined out-of-band rejection performance that is comparable with conventional Chebyshev filters. The transfer-function formulations are given in detail, as well as the analysis of frequency- and time-domain responses, resonator unloaded-Q requirements, and filter loss responses. Theoretical comparison with conventional Chebyshev filter characteristics confirm the already demonstrated advantages of this new family of filter transfer functions.