Fractional-Order Phase Shifters with Constant Magnitude Frequency Responses

Abstract

This contribution presents and experimentally analyzes the idea how to reach the constant magnitude as well as the phase response in the fractional-order (FO) phase when shifting two-ports. The straightforward method employing the automatic gain control circuit (AGC) in a cascade after so-called constant phase block approximating FO integrator or differentiator is studied. The variable gain amplifier utilized in AGC and simple RC-based FO constant phase elements (approximating capacitors with order alpha = 1/4 and alpha = 1/2 as an example) connected in the feedback of operational amplifier-based integrator are established in the experimental setup. The operation indicated in three decades (between 100 Hz and 100 kHz) is evaluated. The known solutions of the standard FO phase shifting circuits are discussed and generally compared with the features obtained in this paper, together with the supposed effects of AGC on their performances.This contribution presents and experimentally analyzes the idea how to reach the constant magnitude as well as the phase response in the fractional-order (FO) phase when shifting two-ports. The straightforward method employing the automatic gain control circuit (AGC) in a cascade after so-called constant phase block approximating FO integrator or differentiator is studied. The variable gain amplifier utilized in AGC and simple RC-based FO constant phase elements (approximating capacitors with order alpha = 1/4 and alpha = 1/2 as an example) connected in the feedback of operational amplifier-based integrator are established in the experimental setup. The operation indicated in three decades (between 100 Hz and 100 kHz) is evaluated. The known solutions of the standard FO phase shifting circuits are discussed and generally compared with the features obtained in this paper, together with the supposed effects of AGC on their performances.