State-Space Model Extraction via Loewner Matrix SVD
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Solution Overview
Problem
Existing state-space model extraction methods from S-parameter data are unreliable and prone to generating unstable models, particularly when dealing with large numbers of ports and actual measurement data, due to their iterative and uncontrollable nature.
Innovation Solution
The use of singular-value decomposition (SVD) of Loewner matrices to directly determine the order and matrices of the state-space model, replacing iterative rational fitting and ensuring stability by generating system poles without discarding data, thus providing a more robust and efficient method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If iterative rational fitting methods are used to extract state-space models from S-parameter data, then the model can be obtained through a multi-step fitting procedure, but the method is uncontrollable, not robust, and prone to generating unstable models particularly when dealing with large numbers of ports and actual measurement data
Solution Approach 1:
The patent replaces the iterative mechanical fitting process with a direct algebraic solution using singular value decomposition (SVD) of Loewner matrices. Instead of iteratively adjusting parameters to match frequency response data, the method constructs Loewner matrices from S-parameter measurements and uses SVD to directly compute the state-space model matrices, eliminating the uncontrollable iterative search process and improving reliability.
Solution Approach 2:
The patent creates a mathematical copy of the system's frequency response characteristics through Loewner matrices constructed from S-parameter data. By decomposing these matrices via SVD, the method directly extracts the state-space representation without needing to iteratively fit the model to the original data, thus avoiding convergence issues while preserving the essential system behavior.
2Productivity
If iterative rational fitting procedures are used to determine model order and matrices, then the approach can handle complex systems, but the iterative nature causes convergence issues and increased computational time
Solution Approach 1:
The patent substitutes the iterative optimization process with a direct algebraic computation using singular value decomposition. The method constructs Loewner matrices from frequency response data and applies SVD to directly obtain the state-space model matrices in a single computational step, eliminating repeated iterations and ensuring consistent convergence regardless of the system's complexity or the quality of measurement data.
3Manufacturing precision
If frequency-domain S-parameter data is converted to time-domain state-space models using conventional methods, then time-domain simulation can be performed, but the iterative fitting process generates unstable models that compromise simulation accuracy
Solution Approach 1:
The patent replaces the iterative frequency-response matching procedure with a direct algebraic approach using SVD of Loewner matrices. By constructing these matrices from S-parameter data and decomposing them, the method directly computes the state-space model matrices (A, B, C, D) without iterative fitting, ensuring both accuracy and stability in the time-domain representation.
Solution Approach 2:
The method creates an accurate time-domain copy of the frequency-domain system behavior through direct algebraic transformation. The Loewner matrix SVD process preserves the essential input-output characteristics of the original system while producing a stable state-space model suitable for time-domain simulation, avoiding the instability introduced by iterative fitting methods.
Data Source
AI summary
A simulator includes an analysis module for extracting a state-space model of response of a physical system to an input from a frequency-domain representation thereof, using a SVD, and singular vectors thereof, of a Loewner matrix derived from the frequency-domain representation, and a simulator module for simulating the response of the physical system in the time domain based on the extracted state-space model.