Simple circuit equivalents for the constant phase element.

Area of Science:

• Electrical Engineering
• Condensed Matter Physics
• Physical Chemistry

Background:

• The constant phase element (CPE) is a fractional circuit element used to model complex physical phenomena in fields like bioimpedance and electrochemistry.
• The physical interpretation of CPEs, both capacitive and inductive, remains partially understood, often viewed as idealized components.
• CPEs exhibit frequency-independent phase shifts, interpolating between capacitive and resistive behaviors.

Purpose of the Study:

• To provide alternative equivalent circuits for constant phase elements (CPEs) to improve physical interpretations.
• To explore time-domain responses of CPEs and their relation to fractional circuit elements (fractance).
• To offer a better understanding of the link between CPEs and their real-world applications.

Main Methods:

• Deriving time-domain impulse and step responses for capacitive and inductive CPEs.
• Proposing novel equivalent circuits involving time-varying components.
• Verifying proposed equivalents using circuit simulation software (Micro-Cap) capable of handling time-varying elements.

Main Results:

• The current impulse response of a capacitive CPE was shown to be equivalent to a time-varying series RL-circuit with a linearly increasing inductance.
• The voltage response of an inductive CPE was found to correspond to a parallel RC circuit with a linearly increasing capacitance.
• Circuit simulations confirmed the accuracy of the proposed time-varying equivalents, with errors within 0.1%.

Conclusions:

• The proposed time-varying equivalent circuits offer a more interpretable physical basis for CPEs.
• These findings correlate with known time-varying properties in practical applications.
• The study facilitates a deeper understanding of the connection between fractional circuit elements and their applications.