Abstract

In this paper a third-order band-pass (BP) filter with geometrically-symmetrical characteristic is presented, for the first time to the authors knowledge. This filter characteristic is only possible to be obtained by fractional-order (FO) filter design. The desired characteristic was Chebyshev 0.1dB pass-band ripple and with normalized bandwidth $\mathrm{B}=0.1$ . Starting from common fourth-order BP transfer function the design was performed numerically using the nonlinear trust-region-reflective, least square algorithm in Matlab. The resulting third-order BP filter approximates very well in the pass-band frequency region, while possessing fractional step in the stop band. The wanted BP transfer function is realized as cascade in two ways: biquads with integer order (IO) and biquads with FO. The obtained design parameters in the IO and FO realizations are compared. Approximation of the constant phase element by Foster I passive RC network is used in a Pspice analysis. That Pspice analysis in a frequency and a time domain are confirming the realizability and stability of the proposed filter, respectively.

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