Direct synthesis techniques for general Chebyshev filters: Lowpass, highpass, and bandstop cases

Abstract

Conventional synthesis techniques for general Chebyshev lowpass, highpass, and bandstop filters are usually based on general Chebyshev filtering function, from which lowpass prototype is set up. By applying the lowpass to lowpass, highpass, or bandstop frequency transformation on realization networks of lowpass prototypes, final realization networks of general Chebyshev lowpass, highpass, and bandstop filters are obtained. In this paper, direct synthesis techniques for general Chebyshev lowpass, highpass, and bandstop filters are discussed. Transmission zeros can be placed wherever they are desired to control the performance of the filters. Unlike conventional synthesis techniques, they derive filtering polynomials constituting network parameters directly in the lowpass, highpass, or bandstop domain, which might find applications in analogue and digital filter design. Several examples are presented for demonstration.