Model-Free Closed-Loop Stability Analysis:
A Linear Functional Approach
Adam Cooman, Fabien Seyfert, Martine Olivi,Sylvain Chevillard and Laurent Baratchart
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex right half-plane, the circuit is unstable. The classic way to detect unstable poles is to fit a rational model on the impedance.
In this paper, a projection-based method is proposed which splits the impedance into a stable and an unstable part by projecting on an orthogonal basis of stable and unstable functions. When the unstable part lies significantly above the interpolation error of the method, the circuit is considered unstable. Working with a projection provides one, at small cost, with a first appraisal of the unstable part of the system.
Both small-signal and large-signal stability analysis can be performed with this projection-based method. In the small-signal case, a low-order rational approximation can be fitted on the unstable part to find the location of the unstable poles.
- 1. Introduction
- 2. Determining the frequency responses
- 3. Stable/unstable projection
- Example 1: Random state space system
- Example 2: Balanced amplifier
- Example 3: Two-stage Power Amplifier
- Example 4: R-L-diode circuit
- 5. Conclusion
- Appendices
- Bibliography
This page contains the full text of the accepted version of the paper published in IEEE Transactions on Microwave Theory and Techniques. The content was modified slightly to better fit the format of this website
This research was partly supported by the French space agency CNES, partly by the Flemish Agency for Innovation by Science and Technology (IWT-Vlaanderen) and partly by the Strategic Research Program of the VUB (SRP-19). We are also thankful to Juan-Marie Collantes (UPV) for fruitful discussions on the topic of closed loop stability analysis. We would like to thank Kurt Homan, Johan Nguyen and Dries Peumans for the design and measurement of the balanced amplifier. Finally, we would like to thank Marc van Heijningen for providing the data of the MMIC PA.