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.Comment: Longer version of the paper published in IEEE Transactions on Microwave Theory and Technique

The impedance of a microwave circuit has an infinite number of poles due to the distributed elements. This complicates locating those poles with a rational approximation. In this paper, we propose an algorithm to locate the unstable poles of a circuit with distributed elements. The proposed method exploits the fact that a realistic circuit can only have a finite number of unstable poles. We first determine the unstable part whose poles coincide with the unstable poles of the circuit. A rational approximation of the unstable part is used to estimate the unstable poles.

A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the actual source of the distortion. Classically, the DCA uses the Volterra theory to model the circuit and its sub-circuits. This DCA has been proven useful for small circuits or heavily simplified examples. In more complex circuits however, the amount of contributions increases quickly, making the interpretation of the results difficult. In this paper, the Best Linear Approximation (BLA) is used to perform the DCA instead. The BLA represents the behaviour of a sub-circuit as a linear circuit with the unmodelled distortion represented by a noise source. Combining the BLA with a classical noise analysis yields a DCA which is simple to understand, yet capable to handle complex excitation signals and complex strongly non-linear circuits.

The non-linear performance of analogue electronic circuits is crucial during the design phase, while circuit simulators only give measures about the distortion generated by the total circuit, leaving designers clueless about the source of the problem. Distortion Contribution Analysis (DCA) is a simulation-based analysis technique that determines the distortion generated in the sub-circuits and shows their contribution to the total distortion of the circuit. DCA can be used to efficiently decrease the distortion generated by a circuit, because it points the designer to the origin of the problem. Recently, a DCA based on the Best Linear Approximation (BLA) has been introduced as alternative to the Volterra-based techniques. However, a major drawback of the current implementation of the BLA-based DCA is its limitation to singleinput single-output frequency response functions to model the behaviour of the sub-circuits. This approach ignores the input and output impedance of the stages, and hence introduces errors. In this paper, an extension of the BLA-based DCA is proposed which uses a MIMO port representation of the sub-circuits. Combining the port representation with a multi-port noise analysis allows the analysis of non-linear circuits without adapting the modelling of the sub-circuits.