Accurate constant phase elements dedicated for audio signal processing

Abstract

This review paper introduces real-valued two-terminal fully passive RC ladder structures of the so-called constant phase elements (CPE). These lumped electronic circuits can be understood as two-terminal elements described by fractional-order (FO) dynamic, i.e. current-voltage relation described by non-integer-order integration or derivation. Since CPE that behaves close to ideal is still not off-the-shelf component, correct behavior must be approximated in the frequency domain and is valid only in the predefined operational frequency interval. In this study, audio frequency range starting with 20 Hz and ending with 20 kHz has been chosen. CPEs are designed and values tabularized for predefined phase shifts that are commonly used in practice. If constructed carefully, maximum phase error less than 0.5° can be achieved. Several examples of direct utilization of designed CPEs in signal processing applications are provided.

This review paper introduces real-valued two-terminal fully passive RC ladder structures of the so-called constant phase elements (CPE). These lumped electronic circuits can be understood as two-terminal elements described by fractional-order (FO) dynamic, i.e. current-voltage relation described by non-integer-order integration or derivation. Since CPE that behaves close to ideal is still not off-the-shelf component, correct behavior must be approximated in the frequency domain and is valid only in the predefined operational frequency interval. In this study, audio frequency range starting with 20 Hz and ending with 20 kHz has been chosen. CPEs are designed and values tabularized for predefined phase shifts that are commonly used in practice. If constructed carefully, maximum phase error less than 0.5° can be achieved. Several examples of direct utilization of designed CPEs in signal processing applications are provided.