8. Conclusions

In this paper, we discussed properties of linear circuits containing lumped and distributed elements and their implications for closed-loop stability analysis. When the active devices in the circuit do not have finite bandwidth, it is possible to generate unstable circuits that have no poles in the right half-plane. We have therefore introduced a working definition for realistic components, based on the notion that realistic passive devices are not lossless and that active devices should become passive at very high frequencies. The main contribution of this paper is to show that a circuit made out of realistic components is unstable only when it has poles in the right half-plane. Moreover, a realistic circuit can have at most finitely many unstable poles, which makes its unstable part a rational function, even if distributed elements are present in the circuit.

To show that our definition of realistic components is feasible, we showed several examples of component models that are realistic, including passive devices, active devices and transmission lines.