Pole-Zero Identification: Unveiling the Critical Dynamics of Microwave Circuits Beyond Stability Analysis

The term pole-zero identification refers to obtaining the poles and zeros of a linear (or linearized) system described by its frequency response. This is usually done using optimization techniques (such as least squares, maximum likelihood estimation, or vector fitting) that fit a given frequency response of the linear system to a transfer function defined as the ratio of two polynomials [1], [2]. This kind of linear system identification in the frequency domain has numerous applications in a wide variety of engineering fields, such as mechanical systems, power systems, and electromagnetic compatibility. In the microwave domain, rational approximation is increasingly used to obtain black-box models of complex passive structures for model order reduction and efficient transient simulation. An extensive bibliography on the matter can be found in [3]-[6]. In this article, we focus on a different application of pole-zero identification. We review the different ways in which pole-zero identification can be applied to nonlinear circuit design, for power-amplifier stability analysis, and more. We provide a comprehensive view of recent approaches through illustrative application examples. Other uses for rational-approximation techniques are beyond the scope of this article.