On the passivity of the quasi‐static partial element equivalent circuit method

Abstract

Summary The partial element equivalent circuit (PEEC) electromagnetic method has attracted a lot of attention for its capability to give a circuit interpretation to Maxwell's equations. The PEEC equivalent circuits are usually connected with terminations such as drivers and receivers in a time‐domain circuit simulator. Passivity is a fundamental property for the time‐domain simulations of circuit models connected to terminations at their electrical ports. Stable, but nonpassive, models can produce unstable systems when connected to other stable, even passive, loads. The so‐called quasi‐static PEEC formulations leads to a descriptor state‐space circuital representation of the electromagnetic phenomena. Multiple state‐space representations are possible. In this paper, we study the passivity property of different quasi‐static PEEC representations in detail. A novel analytical additive decomposition is proposed concerning the admittance formulation, which allows extracting the polynomial part of the transfer function that represents the behavior at infinity in the Laplace domain. This decomposition is discussed from a mathematical and a physical point of view. Such a detailed study for the passivity of quasi‐static PEEC models and the novel analytical decomposition is not available in the literature. Numerical results support the theoretical analysis.

On checking dissipativity of parameterized linear and time‐invariant circuits and systems

“…Here, we test the proposed method with increasingly complex polynomial representations of the curve f in (25). Starting with a simple constant, we increase complexity up to a polynomial order D ¼ 4.…”

“…Based on the above considerations, the dissipativity verification of reduced-order models is recognized as a crucial step to enable MOR-based CAD flows, thus justifying the huge amount of literature on the subject. As an example, we mention the seminal theoretical works 3,[15][16][17] as well as the more application-oriented frameworks, including passivity enforcement algorithms of LTI behavioral representations of circuit blocks, [18][19][20][21][22] fractional-order systems, 23,24 circuit approximations of electromagnetic systems via integral formulations, 25 and others. 26,27 When the dynamics of the system under investigation depend on one or more parameters, the problem of enforcing dissipativity (or passivity, both terms are used here as synonyms) in the reduced model is quite challenging.…”

A highly accurate and robust source reconstruction method of printed circuit boards based on complex‐valued neural network

“…According to the basic electromagnetic theory, the near-field of a PCB is quasi-static, and it contains a wealth of information on the radiation properties of the PCB. 18 Therefore, the near-field information obtained from near-field scanning can be used to build an equivalent model of the PCB. Essentially, the source of radiation from a PCB is the time-varying current on it.…”

Circuit analysis of radiation reaction in metamaterials by retarded electromagnetic coupling

“…The partial element equivalent circuit (PEEC) is a full‐wave circuit model with meshes of metallic structures [14–16], representing the radiation loss as the retardations between the meshes [17, 18]. Recently, the topic of the passivity of PEEC [19] and the discussion on its validity as a model of radiation has been reported in [20, 21]. Another method has been proposed to derive a simple circuit by specified structures, consisting of capacitive spheres and inductive wires [22].…”