Two-port two impedances fractional order oscillators

This paper presents a study for general fractional order oscillator based on two port network where two topologies of oscillator structure with two impedances are discussed. The two impedances are chosen to be fractional elements which give four combinations for each topology. The general oscillation frequency, condition and the phase difference between the two oscillatory outputs are deduced in terms of the transmission matrix parameter of a general two port network. As a case study: two different networks are presented which are op-amp based circuit and non-ideal gyrator circuit. The oscillation parameters for each case have been derived, and discussed numerically using Matlab. Spice simulations are presented for some cases to validate the proposed idea. Experimental results for the op-amp network are introduced to validate the reliability of the presented oscillator. The extra degree of freedom provided by the fractional order parameter enables the oscillation frequency band to cover from small Hz to hundreds MHz which is suitable range for most of measuring applications.

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