Generalized Chebyshev Bandpass Filters With Frequency-Dependent Couplings Based on Stubs

This paper presents an accurate synthesis method for inline and cross-coupled generalized Chebyshev bandpass filters with frequency-dependent couplings implemented via open and short stubs. The technique involves the synthesis of a lumped-element prototype in the form of a coupling matrix with a frequency-dependent term and the conversion of this prototype to a distributed-element model composed of sections of TEM lines. This takes into account the impedance (or admittance) of the stubs, thus allowing compensation for the loading effect. The design equations are derived for the stub impedance in terms of a coupling coefficient and for the allowable frequency range in which the model is valid. Additionally, the proposed methodology allows the simultaneous application of frequency-dependent couplings with positive and negative dispersive parts within the same network. The validity of this method is confirmed by numerical tests and through experiments, including filters with dispersive couplings of the opposite signs.