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306 3. Reference Manual
3.8 Pole/Zero Analysis
This chapter describes the Analog Insydes functions for numerical and symbolic pole/zero analysis
by solving generalized eigenvalue problems (GEPs). The GEPs considered here have the form
A ΛBu ⩵
v H A ΛB ⩵
where A and B are real-valued square matrices that arise from decomposing the coefficient matrix
of a system of circuit equations Ts x ⩵ b into the contributions from the static and the dynamic
elements.
Ts ⩵ A sB
In the above GEP, Λ is an eigenvalue, and u and v denote the right and left eigenvectors corresponding
to Λ (v H denotes the Hermitian conjugate of v). In the following, the pairs Λ u and Λ v are referred
to as (left and right) eigenpairs of the matrix pencil A B. Analog Insydes includes two different GEP
solvers: an enhanced version of the QZ algorithm and a variant of the Jacobi orthogonal correction
method (JOCM).
The following table shows the available Analog Insydes functions for solving GEPs:
GeneralizedEigensystem (Section 3.8.1)
computing eigenvalues and eigenvectors by QZ
GeneralizedEigenvalues (Section 3.8.2)
computing eigenvalues by QZ
PolesAndZerosByQZ (Section 3.8.3)
computing poles and zeros by QZ
PolesByQZ (Section 3.8.4)
ZerosByQZ (Section 3.8.5)
RootLocusByQZ (Section 3.8.6)
LREigenpair (Section 3.8.7)
computing poles by QZ
computing zeros by QZ
computing root locus by QZ
computing eigenvalues and eigenvectors by JOCM