A Rigorous Proof on the Radiation Resistance in Generalized PEEC Model

Chou, Chia‐Chun; Lee, Wei-Chiang; Wu, Tzong‐Lin

doi:10.1109/tmtt.2016.2606395

“…To validate the proposed helical model, we plot ⃗ H in Fig. 3 and compare the magnetic field intensity of the helical model M H (29) vs. the aggregated circular-loops model M CL (32). As shown in Figures 3a,3b,3c, M H and M CL are in excellent agreement for H ρ (ρ) and H ρ (z).…”

Section: B Anatomy Of ⃗ Hmentioning

confidence: 99%

Analytical Model of the Canonical 3D Helical Solenoid, for Efficient Computation of the Dynamic Electromagnetic Fields in Near- and Far-Field Regions, Complex Inductance, and Radiation Resistance

Zadehgol¹

2023

Preprint

0

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The recent work in [1] presented a novel analytical model for estimating the 3-dimensional (3D) magneto quasi-static (MQS) fields of the cylindrical solenoid with helical wire winding, using the \textit{static} Green's function and relying on the \textit{Schur} vector product of the electric current source vector and its tangent. In this work, we use the \textit{dynamic} Green's function to extend the model in [1] resulting in a frequency-dependent magnetic vector potential $\vec{A}(\omega)$. We derive expressions for efficient computation of all cylindrical components of the magnetic flux density vector $\vec{B}(\omega)$ as a function of the solenoid's geometric and material parameters. $\vec{A}(\omega)$ may be used to efficiently compute the frequency-dependent flux linkage $\Psi(\omega)$, the complex inductance $L(\omega)$, and the radiation patterns of the solenoid anywhere in 3D space including both near-field and far-field regions, excluding the (source) regions of conducting wire. Additionally, we propose the complex calibration coefficient $\chi(\omega)$ to account for the finite-radius conductor. Several numerical examples are provided to validate the proposed helical model against the superposition of circular loops. The proposed model is demonstrated across a wide spectrum from 60 Hz to 70 GHz, representing a wide range of applications that include low-frequency power systems to high-frequency mm-wave communication systems.

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“…Fig. 4 demonstrates the computation time for the helical model (29) for each field component at a single point in 3D space vs. the number of turns-per-layer N T , while assuming N L = 1. Note that the computation time (in seconds) is of order O(log(N T )), where fit 1 ≊ −1.7869 + 0.3527 log(N T ) for B ρ and B ϕ , and fit 2 ≈ 1.1734−0.4046 log(N T )+0.0876 √ N T for B z ; for 100 ≤ N T ≤ 10k.…”

Section: Computational Complexitymentioning

confidence: 99%

Analytical Model of 3D Helical Solenoids, for Efficient Computation of Dynamic EM Fields, Complex Inductance, and Radiation Resistance

Zadehgol¹

2023

Preprint

0

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The recent work in [1] presented a novel analytical model for estimating the 3-dimensional (3D) magneto quasi-static (MQS) fields of the cylindrical solenoid with helical wire winding, using the \textit{static} Green's function and relying on the \textit{Schur} vector product of the electric current source vector and its tangent. In this work, we use the \textit{dynamic} Green's function to extend the model in [1] resulting in a frequency-dependent magnetic vector potential $\vec{A}(\omega)$. We derive expressions for efficient computation of all cylindrical components of the magnetic flux density vector $\vec{B}(\omega)$ as a function of the solenoid's geometric and material parameters. $\vec{A}(\omega)$ may be used to efficiently compute the frequency-dependent flux linkage $\Psi(\omega)$, the complex inductance $L(\omega)$, and the radiation patterns of the solenoid anywhere in 3D space including both near-field and far-field regions, excluding the (source) regions of conducting wire. Additionally, we propose the complex calibration coefficient $\chi(\omega)$ to account for the finite-radius conductor. Several numerical examples are provided to validate the proposed helical model against the superposition of circular loops. The proposed model is demonstrated across a wide spectrum from 60 Hz to 70 GHz, representing a wide range of applications that include low-frequency power systems to high-frequency mm-wave communication systems.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

Circuit analysis of radiation reaction in metamaterials by retarded electromagnetic coupling

Nakata

¹

,

Hisakado

²

,

Matsushima

³

et al. 2021

IET Circuits, Devices & Syst

0

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Because radiation is essential in high‐frequency circuits, such as those used in metamaterials and plasmonics, the investigation of radiation loss is important. This study describes the characteristics of radiation loss, which is a radiation reaction in circuits with retarded electromagnetic couplings. The structure of wired metallic spheres is used to demonstrate metamaterial equivalent circuits, where charges and current exist on the spheres and wires, respectively. An inductance matrix and a potential coefficient matrix with retarded electromagnetic couplings are defined to address the radiation reaction. Subsequently, based on the topology of the wires and spheres, an equivalent circuit equation with retardation is formulated to discuss the losses in the resonant circuit caused by the inductive and capacitive elements. Thereafter, the relationship between the resonant frequency and radiation loss caused by the retarded couplings is demonstrated and the difference between the retarded couplings and couplings with transmission lines is clarified. Furthermore, we indicate that retarded coupling generates singularity on a dispersion curve for a one‐dimensional array of resonant circuits. Thus, the circuit with retarded couplings generates novel characteristics of radiation reactions that are not represented by the circuit without retardation. This circuit analysis is expected to afford new aspects in studies on topics, such as metamaterials and plasmonics.

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A Rigorous Proof on the Radiation Resistance in Generalized PEEC Model

Cited by 17 publications

References 23 publications

Analytical Model of the Canonical 3D Helical Solenoid, for Efficient Computation of the Dynamic Electromagnetic Fields in Near- and Far-Field Regions, Complex Inductance, and Radiation Resistance

Analytical Model of the Canonical 3D Helical Solenoid, for Efficient Computation of the Dynamic Electromagnetic Fields in Near- and Far-Field Regions, Complex Inductance, and Radiation Resistance

Analytical Model of 3D Helical Solenoids, for Efficient Computation of Dynamic EM Fields, Complex Inductance, and Radiation Resistance

Circuit analysis of radiation reaction in metamaterials by retarded electromagnetic coupling

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