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

Michio SUGI; Kazuhiro SAITO

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

Michio SUGI, Kazuhiro SAITO

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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)ω^a (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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E75-A No.6 pp.720-725

Publication Date: 1992/06/25

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Type of Manuscript: PAPER

Category: Analog Circuits and Signal Processing

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Michio SUGI, Kazuhiro SAITO, "Non-integer Exponents in Electronic Circuits: F-Matrix Representation of the Power-Law Conductivity" in IEICE TRANSACTIONS on Fundamentals, vol. E75-A, no. 6, pp. 720-725, June 1992, doi: .
Abstract: The F-matrix expressions of inverted-L-type four-terminal networks, each involving an element with the power-law conductivity σ(ω)ω^a (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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e75-a_6_720/_p

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@ARTICLE{e75-a_6_720,
author={Michio SUGI, Kazuhiro SAITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Non-integer Exponents in Electronic Circuits: F-Matrix Representation of the Power-Law Conductivity},
year={1992},
volume={E75-A},
number={6},
pages={720-725},
abstract={The F-matrix expressions of inverted-L-type four-terminal networks, each involving an element with the power-law conductivity σ(ω)ω^a (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.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Non-integer Exponents in Electronic Circuits: F-Matrix Representation of the Power-Law Conductivity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 720
EP - 725
AU - Michio SUGI
AU - Kazuhiro SAITO
PY - 1992
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E75-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1992
AB - The F-matrix expressions of inverted-L-type four-terminal networks, each involving an element with the power-law conductivity σ(ω)ω^a (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.
ER -