5. Conclusion
This paper introduces a closed-loop local stability analysis without using a rational approximation. Instead, the impedance functions are split into a stable and unstable part by projecting onto an orthogonal basis. Transforming the problem to the unit disc allows to calculate this projection with the FFT which makes the projection-based stability analysis very fast. In a small-signal stability analysis, once the unstable part is obtained, a low-order rational model can be used to find the unstable poles in the circuit.
Due to the model-free nature of the proposed method, it is a very simple method to use: no choice of model order or approximation error needs to be made. The only requirements of the projection-based stability analysis are that the frequency responses are sampled on a sufficiently dense frequency grid and that the maximum frequency of the simulations is large enough. When the circuit impedance is simulated on a too coarse frequency grid, a large interpolation error is introduced in the results. The level of this interpolation error can easily be determined and used to improve the accuracy of the method.
Once the stable and unstable parts of the impedance are obtained with a sufficiently low interpolation error, the obtained unstable part can be compared to the interpolation error to determine whether it is significant or not. From experience, we found that, when the unstable part lies more than above the interpolation error level, the circuit can be considered unstable. Further work is to be done towards automated decision making regarding stability.
The stable/unstable projection has been successfully applied to both the stability analysis of DC and large-signal solutions of RF circuits.