Striving for small-signal stability

In this article, based on Bodeʹs definition of return ratio with respect to a single controlled source, the loop-based two-port algorithm and device-based gain-nulling are proposed for small-signal stability analysis. These two algorithms are complementary in terms of applicability, and they produce accurate stability information for single-loop networks. After a brief primer on feedback and stability, we review Bodeʹs feedback theory, where the return difference and return ratio concepts are applicable to general feedback configurations and avoid the necessity of identifying μ and β. Middlebrookʹs null double-injection technique, which provides a laboratory-based way to measure return ratio, is then discussed in the modern circuit analysis context; we then extend the unilateral feedback-model used in Middlebrookʹs approach to accommodate both normal-and reverse-loop transmission and characterize the return loop using a general two-port-analysis. This loop-based two-port algorithm determines the stability of a feedback network in which a critical wire can be located to break all return loops. The device-based gain-nulling algorithm is then discussed to evaluate the influence of the local return loops upon network stability. This algorithm determines the stability of a feedback network in which a controlled source can be nulled to render the network to be passive. Conditions under which these two algorithms can be applied are discussed