Non-integer Exponents in Electronic Circuits: F-Matrix Representation of the Power-Law Conductivity

Michio SUGI  Kazuhiro SAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.6   pp.720-725
Publication Date: 1992/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Analog Circuits and Signal Processing
power-law conductivity,  non-integer exponents,  F-matrix,  transient responses,  long time tail,  

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The F-matrix expressions of inverted-L-type four-terminal networks, each involving an element with the power-law conductivity σ(ω)ωa (0a1) connected to a resistance R, an inductance L or a capacitance C, were derived using the standard procedures of Laplace transformation, indicating that the exponents of the complex angular frequency s, so far limited to the integers for the transmission circuits with finite elements, can be extended to the real numbers. The responses to a step voltage calculated show hysteretic behavior reflecting the resistance-capacitance ambivalent nature of the power-law conductivity.