Direct synthesis technique (DST) for complex general Chebyshev filters

摘要

Recently, we discussed the concept of direct synthesis technique (DST), in which real-coefficient filtering polynomials containing all information of the filters to be synthesized are derived directly for realization, and they could find applications in the design of lumped-element LC filters, active RC filters, and infinite impulse response digital filters. In this paper, another DST for complex general Chebyshev bandpass filters is discussed, which is based on a complex mapping relation and featured by complex-coefficient filtering polynomials. It is called as complex DST in this paper. Compared with real-coefficient filtering polynomials whose polarities are determined by the number of their zeros at zero frequency, the polarities of complex-coefficient filtering polynomials can be easily changed by multiplying imaginary unit j. Such advantage might make their realization more flexible. The analysis shows that conventional coupling matrix could be considered as narrow-band approximation of network matrix derived by complex DST in the normalized frequency domain. In order to demonstrate the validity of complex DST in this paper, it is applied in the design of classic parallel-coupled microstrip bandpass filters. Compared with conventional synthesis techniques, complex DST could find out better dimensions and provide more choices for realization and synthesize both even-order and odd-order parallel-coupled microstrip bandpass filters. Copyright (c) 2017 John Wiley & Sons, Ltd.