Transitional Frequencies of Fractional-Order Transitional Transfer Functions Using Butterworth and Sync-Tuned Approximations

In this work, the transitional frequencies of fractional-order transitional transfer functions designed using Butterworth and Sync-Tuned approximations are quantified to advance understanding of which response dominates the magnitude response. Numerical searches identify these frequencies for cases where i) Butterworth order is fixed at 2.54 and Sync-Tuned order is varied from 1 to 4, and ii) Sync-Tuned order is fixed at 2.54 and Butterworth is varied from 1 to 4. LTSpice simulations and measured results of an inverse-follow-the-leader topology designed to realize a transitional response (with Butterworth order of 2.54 and Sync-Tuned of 1.8) using an approximated fractional-order capacitor confirm the characteristics of this transitional design.