Stability, Causality, and Passivity Analysis of Canonical Equivalent Circuits of Improper Rational Transfer Functions With Real Poles and Residues
Stability, Causality, and Passivity Analysis of Canonical Equivalent Circuits of Improper Rational Transfer Functions With Real Poles and Residues
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DOI：
10.1109/access.2020.3007854
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发表时间：
2020
期刊：
影响因子：
3.9
通讯作者：
Rasul Choupanzadeh;A. Zadehgol
中科院分区：
文献类型：
--
作者：
Rasul Choupanzadeh;A. Zadehgol
This paper extends a previous work on synthesis of equivalent circuits using strictly proper canonical R-L and ${\text{R}}_{a}$ -L- ${\text{R}}_{b}$ -C circuit branches, and presents a thorough time-domain and frequency-domain analysis of stability/causality/passivity (SCP) of the R-L circuit branch (based on real pole/residue) and two additional shunt elements ${\text{R}}_{shunt}$ and $\text{C}_{shunt}$ parallel to the R-L branch, leading to an improper rational transfer function. We develop a rigorous and comprehensive table of sign-relationships including pole/residue, pole/zero, R/L/C elements, and SCP conditions to describe the interaction of ${\text{R}}_{shunt}$ and $\text{C}_{shunt}$ elements with an R-L branch. We also examine the effects on SCP due to negative gain coefficient of the transfer functions. Because such a topology can commonly occur as a result of applying fitting algorithms (e.g., Vector Fitting) on the electrical response of multi-port networks (e.g., impedance, admittance, or scattering parameters), it is important to understand the above SCP conditions for synthesis of practical SPICE models for stable time-domain simulations.
This paper extends a previous work on synthesis of equivalent circuits using strictly proper canonical R-L and ${\text{R}}_{a}$ -L- ${\text{R}}_{b}$ -C circuit branches, and presents a thorough time-domain and frequency-domain analysis of stability/causality/passivity (SCP) of the R-L circuit branch (based on real pole/residue) and two additional shunt elements ${\text{R}}_{shunt}$ and $\text{C}_{shunt}$ parallel to the R-L branch, leading to an improper rational transfer function. We develop a rigorous and comprehensive table of sign-relationships including pole/residue, pole/zero, R/L/C elements, and SCP conditions to describe the interaction of ${\text{R}}_{shunt}$ and $\text{C}_{shunt}$ elements with an R-L branch. We also examine the effects on SCP due to negative gain coefficient of the transfer functions. Because such a topology can commonly occur as a result of applying fitting algorithms (e.g., Vector Fitting) on the electrical response of multi-port networks (e.g., impedance, admittance, or scattering parameters), it is important to understand the above SCP conditions for synthesis of practical SPICE models for stable time-domain simulations.