Apparatus and method for analyzing passive circuits using reduced-order modeling of large linear subcircuits
First Claim
1. An apparatus comprising:
- a processing unit having;
a first program for generating a symmetric matrix transfer function relating to a matrix transfer function associated with circuit characteristic data representing a circuit;
a second program for generating a frequency response signal as a function of the matrix transfer function data; and
a processor for executing the programs; and
an output device for displaying said circuit frequency response signal.
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Accused Products
Abstract
A method and apparatus for generating and analyzing a reduced-order model of a linear circuit. The method and apparatus generates the symmetric multi-port transfer function of an RLC circuit. The invention employs a novel symmetric block-Lanczos-type procedure, termed SyMPVL for Symmetric Matrix Pade via Lanczos, to reduce original circuit matrices to a pair of banded symmetric matrices. When the circuit comprises only two of the three RLC components, the matrices are also positive definite. These matrices are typically much smaller than the original circuit matrices and determine a reduced-order model of the original multi-port transfer function of the circuit. The reduced transfer function represents a matrix-Pade approximation of the original multi-port matrix transfer function.
43 Citations
34 Claims
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1. An apparatus comprising:
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a processing unit having; a first program for generating a symmetric matrix transfer function relating to a matrix transfer function associated with circuit characteristic data representing a circuit; a second program for generating a frequency response signal as a function of the matrix transfer function data; and a processor for executing the programs; and an output device for displaying said circuit frequency response signal. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
- 9. An apparatus as set forth in claim 7 wherein
- space="preserve" listing-type="equation">Re(y.sup.H (I.sub.n +sT.sub.n)y)=∥
y∥
.sub.2.sup.2 +(Re s)y.sup.H T.sub.n y≧
0
for all yε
n,when said circuit is an RC, RL or LC circuit, where y represents any complex vector, In is an n by n identity matrix, and N is a set of complex vectors of length n. - space="preserve" listing-type="equation">Re(y.sup.H (I.sub.n +sT.sub.n)y)=∥
-
- 10. An apparatus as set forth in claim 7 wherein the frequency response transfer function is
- space="preserve" listing-type="equation">Z.sub.n (s)=ρ
.sub.n.sup.T (I.sub.n +sT.sub.n).sup.-1 ρ
.sub.n
for RC, RL and LC circuits, where In is an n by n identity matrix. - space="preserve" listing-type="equation">Z.sub.n (s)=ρ
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11. An apparatus for generating a frequency response signal indicative of a frequency response of a circuit, the apparatus comprising:
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a data source providing circuit characteristic data representing the circuit; and a processing unit having; a memory for receiving and storing the circuit characteristic data from the data source; a set of at least one program including a symmetric Matrix Pade via Lanczos type (SyMPVL) program for generating a symmetric matrix Pade approximant of a transfer function relating to the circuit characteristic data; a processor for executing the SyMPVL program; and means for generating the frequency response signal in response to the symmetric matrix Pade approximant. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18)
- 17. An apparatus as set forth in claim 15 wherein
- space="preserve" listing-type="equation">Re(y.sup.H (I.sub.n +sT.sub.n)y)=∥
y∥
.sub.2.sup.2 +(Re s)y.sup.H T.sub.n y≧
0
for all yε
n,when said circuit is an RL, RC or LC circuit, where Tn is a banded n by n matrix; s is complex frequency; y represents any complex vector, In is an n by n identity matrix, and N is a set of complex vectors of length n. - space="preserve" listing-type="equation">Re(y.sup.H (I.sub.n +sT.sub.n)y)=∥
-
- 18. An apparatus as set forth in claim 15 wherein the frequency response transfer function is
- space="preserve" listing-type="equation">Z.sub.n (s)=ρ
.sub.n.sup.T (I.sub.n +sT.sub.n).sup.-1 ρ
.sub.n
for RL, RC and LC circuits, where Tn is a banded n by n matrix; s is complex frequency; ρ
n is an n by p matrix; andIn is an n by n identity matrix. - space="preserve" listing-type="equation">Z.sub.n (s)=ρ
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19. A circuit analyzer for generating a graphic representation of a predicted performance of a circuit, the circuit analyzer comprising:
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an input device for inputting a plurality of circuit parameters representing the circuit; memory for receiving and storing the circuit parameters; a processor for executing stored programs and including; means for generating matrix characteristic data representing a transfer function of the circuit; means for performing a block-Lanczos type procedure on the matrix characteristic data; means for calculating a symmetric matrix Pade approximant of the transfer function of the circuit; means for generating the graphic representation from the symmetric matrix Pade approximant to predict the performance of the circuit; and a display for displaying the graphic representation. - View Dependent Claims (20, 21, 22, 23)
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24. A method for generating a frequency response signal of a circuit, the method comprising the steps of:
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providing circuit characteristic data associated with the circuit; generating characteristic matrix data associated with the circuit characteristic data representing parameters associated with characteristic matrices of the circuit characteristic data; generating a symmetric matrix transfer function data relating to a matrix transfer function associated with the characteristic matrix data; and generating the frequency response signal in response to the matrix transfer function data. - View Dependent Claims (25)
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26. A method for analyzing a circuit to predict performance of a circuit, comprising the steps of:
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receiving from an input device a plurality of circuit parameters representing the circuit; processing the circuit parameters to generate characteristic matrix data representing parameters associated with characteristic matrices; performing a block-Lanczos type procedure on the processed parameters to generate a plurality of Lanczos vectors; calculating a symmetric matrix Pade approximant of a transfer function of the circuit from the plurality of Lanczos vectors; generating a graphic representation from the symmetric matrix Pade approximant to predict the performance of the circuit; and displaying the graphic representation on a display. - View Dependent Claims (27, 28, 29, 30, 31, 32)
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33. An apparatus comprising:
a processing unit having; a memory for storing circuit characteristic data representing a circuit; a first program for generating a symmetric matrix transfer function relating to a matrix transfer function associated with circuit characteristic data representing a circuit; a second program for generating a frequency response signal as a function of the matrix transfer function data; and a processor for executing the programs.
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34. An apparatus comprising:
a processing unit having; a memory for storing circuit characteristic data representing a circuit; a program for generating a symmetric matrix transfer function relating to a matrix transfer function associated with circuit characteristic data representing a circuit; a processor for executing the programs; and means for generating a frequency response signal in response to the matrix transfer function data.
Specification