Fractional-step Tow-Thomas biquad filters

Abstract

In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0<α₁+α₂≤2, where α₁ and α₂ are the orders of the fractional capacitors and 0<α_1,2≤1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.