Multi-Variable Richards' Transformations

Hideaki FUJIMOTO; Junya ISHII; Hiroshi OZAKI

Multi-Variable Richards' Transformations

Hideaki FUJIMOTO, Junya ISHII, Hiroshi OZAKI

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The present paper deals with the Richards' transformation which converts a multi-variable positive (real) function to another multi-variable positive (real) function. This transformation is based on the fact that the network function reduces to a constant for all zeros of an irreducible polynomial h (p₁, p₂, ・・・, p_n) (1deg_{p_i} h). And its application to the cascade synthesis or the Bott-Duffin type synthesis of a class of multi-variable driving-point impedances, is discussed. Finally, we present the corresponding transformation for the multi-variable positive (real) matrices.

Publication: IEICE TRANSACTIONS on transactions Vol.E62-E No.8 pp.529-535

Publication Date: 1979/08/25

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Type of Manuscript: PAPER

Category: Circuit Theory

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Hideaki FUJIMOTO
Junya ISHII
Hiroshi OZAKI

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Hideaki FUJIMOTO, Junya ISHII, Hiroshi OZAKI, "Multi-Variable Richards' Transformations" in IEICE TRANSACTIONS on transactions, vol. E62-E, no. 8, pp. 529-535, August 1979, doi: .
Abstract: The present paper deals with the Richards' transformation which converts a multi-variable positive (real) function to another multi-variable positive (real) function. This transformation is based on the fact that the network function reduces to a constant for all zeros of an irreducible polynomial h (p₁, p₂, ・・・, p_n) (1deg_{p_i} h). And its application to the cascade synthesis or the Bott-Duffin type synthesis of a class of multi-variable driving-point impedances, is discussed. Finally, we present the corresponding transformation for the multi-variable positive (real) matrices.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e62-e_8_529/_p

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@ARTICLE{e62-e_8_529,
author={Hideaki FUJIMOTO, Junya ISHII, Hiroshi OZAKI, },
journal={IEICE TRANSACTIONS on transactions},
title={Multi-Variable Richards' Transformations},
year={1979},
volume={E62-E},
number={8},
pages={529-535},
abstract={The present paper deals with the Richards' transformation which converts a multi-variable positive (real) function to another multi-variable positive (real) function. This transformation is based on the fact that the network function reduces to a constant for all zeros of an irreducible polynomial h (p₁, p₂, ・・・, p_n) (1deg_{p_i} h). And its application to the cascade synthesis or the Bott-Duffin type synthesis of a class of multi-variable driving-point impedances, is discussed. Finally, we present the corresponding transformation for the multi-variable positive (real) matrices.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - Multi-Variable Richards' Transformations
T2 - IEICE TRANSACTIONS on transactions
SP - 529
EP - 535
AU - Hideaki FUJIMOTO
AU - Junya ISHII
AU - Hiroshi OZAKI
PY - 1979
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E62-E
IS - 8
JA - IEICE TRANSACTIONS on transactions
Y1 - August 1979
AB - The present paper deals with the Richards' transformation which converts a multi-variable positive (real) function to another multi-variable positive (real) function. This transformation is based on the fact that the network function reduces to a constant for all zeros of an irreducible polynomial h (p₁, p₂, ・・・, p_n) (1deg_{p_i} h). And its application to the cascade synthesis or the Bott-Duffin type synthesis of a class of multi-variable driving-point impedances, is discussed. Finally, we present the corresponding transformation for the multi-variable positive (real) matrices.
ER -