State-space model-based simulators and methods
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.
1. A simulator comprising:
a processing module; and
a memory,
the processing module being configured as or controlling an analysis module for extracting a state-space model of response of a physical system to an input from a frequency-domain representation of the response, using a singular-value decomposition (SVD) and singular vectors of a Loewner matrix derived by the analysis module from the frequency-domain representation; and
the processing module being configured as or controlling a simulator module for simulating the response of the physical system in a time domain based on the extracted state-space model.
2. The simulator of claim 1 , further comprising an input module for receiving input signals for at least a portion of the modeled physical system.
3. The simulator of claim 2 , wherein the modeled physical system comprises an electronic circuit.
4. The simulator of claim 3 , wherein the input signals are in the form of digital values representative of signal levels at terminals of the electronic circuit.
5. The simulator of claim 3 , wherein the simulator module produces simulated output values from the modeled electronic circuit based on the input signals, and further comprising an output module for supplying the simulated output values to at least one of a display, a device, or another simulator module.
6. The simulator of claim 1 , wherein the Loewner matrix is scaled.
7. The simulator of claim 6 , wherein the scaled Loewner matrix is frequency-scaled.
8. A method of simulation, the method comprising:
representing operation of a physical system in frequency domain;
obtaining a frequency domain representation of a response of the physical system to an input;
extracting a state-space model of the response using a singular-value decomposition (SVD) and singular vectors of a Loewner matrix derived from the frequency-domain representation; and
simulating the response of the physical system based on the state-space model.
9. The method of claim 8 , wherein the state-space model is a time-domain model.
10. The method of claim 8 , wherein the frequency-domain representation comprises a set of scattering parameters.
11. The method of claim 10 , wherein extracting the state-space model comprises using the SVD to generate system poles of the state-space model.
12. The method of claim 11 , wherein the SVD is used to extract models for a plurality of single input-output relations of the scattering parameters.
13. The method of claim 11 , wherein the SVD is used to extract models for each of p single-input p-output columns of relations among the scattering parameters.
14. The method of claim 8 , wherein the Loewner matrix is scaled.
15. The method of claim 14 , wherein the scaled Loewner matrix is frequency-scaled.
16. The method of claim 8 , wherein the SVD indicates an optimal order of the state-space model.
17. The method of claim 8 , wherein the physical system comprises an electronic circuit.
18. The method of claim 17 , further comprising receiving, from a user, input signals for at least a portion of the electronic circuit.
19. The method of claim 18 , wherein the input signals are in the form of digital values representative of signal levels at terminals of the electronic circuit.
20. The method of claim 18 , wherein the simulating step produces simulated output values from the modeled electronic circuit.
21. The method of claim 20 , further comprising using the output values to drive a device.
22. The method of claim 20 , further comprising using the output values to drive a second simulation.