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

• Published in: IEEE microwave magazine Vol. 20; no. 7; pp. 36 - 54
• Main Authors: Collantes, Juan-Mari, Mori, Libe, Anakabe, Aitziber, Otegi, Nerea, Lizarraga, Ibone, Ayllon, Natanael, Ramirez, Franco, Armengaud, Vincent, Soubercaze-Pun, Geoffroy
• Format: Magazine Article
• Language: English
• Published: New York IEEE 01-07-2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplifier design; Analytical models; Approximation; Circuit design; Circuit stability; Computer simulation; Dynamic stability; Electromagnetic compatibility; Frequency response; Identification; Linearization; Mathematical analysis; Mathematical models; Maximum likelihood estimation; Mechanical systems; Microwave amplifiers; Microwave circuits; Model reduction; Optimization; Optimization techniques; Polynomials; Probes; Stability analysis; System identification; Transfer functions
• ISSN: 1527-3342; 1557-9581
• DOI: 10.1109/MMM.2019.2909516

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.