System Characterization of Equivalent Circuits of Improper Rational Transfer Functions with Complex-Conjugate Poles and Residues

Abstract

<p>This paper presents a comprehensive analysis of stability/causality/passivity (SCP) for improper rational transfer functions with <em>complex-conjugate</em> pair of poles/residues, as an extension of <em>real </em>poles/residues case in our previous work. We derive and validate the frequency-domain constraints of SCP for <em>improper </em>rational transfer functions with <em>complex-conjugate</em> pair of poles/residues, equivalent to an R-L-R-C circuit branch in parallel with R<sub><em>shunt</em></sub> and C<sub><em>shunt</em></sub> elements. We also develop detailed tables to establish a relationship between the transfer function parameters (pole, residue, zero), the equivalent circuit parameters (R, L, C), and the SCP conditions, for an improper system of R-L-R-C||R<sub><em>shunt</em></sub>||C<sub><em>shunt</em></sub> circuit branches. The aforementioned circuit-block structure serves as an important canonical topology for macromodeling of multi-port electrical systems across numerous applications. The presented methodology may be used for synthesis of guaranteed-stable SPICE equivalent circuits of electrical systems represented by network parameters (e.g., S/Y/Z-parameters), including power systems operating at tens of Hertz (Hz), high-speed micro-wave/mm-wave electronics operating at hundreds of MHz/GHz, and ultra high-bandwidth opto-electronic and optical systems operating at hundreds of THz.</p>

Comparative Analysis of Piece-by-Piece MNA and General MNA Approaches for Model Order Reduction

“…several sub-circuits X ij , where i, j = 1, 2, ..., p, containing branches made up of R/L/C elements. These branches may be any R/L/C circuit branch, but the most popular cases are canonical R-L and R a -L-R b -C circuit branches corresponding rational transfer functions with Real and complex-conjugate pole/residues, respectively [11]- [13]. Since R a -L-R b -C branch is a general form of R-L branch, we consider it as internal circuit branches of sub-circuits in Fig.…”