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

• Published in: IEEE transactions on electromagnetic compatibility 2023-12, Vol.65 (6), p.1-11
• Main Author: Zadehgol, Ata
• Format: Article
• Language: English
• Subjects: Analytical models; Communications systems; Complex inductance; Computational efficiency; Computational modeling; Conduction; cylindrical solenoids; Far fields; Flux density; Green's functions; Inductance; inductors; Magnetic flux; Magnetic vector potentials; Mathematical models; Millimeter waves; multiscale electromagnetics (EMs); Numerical models; Radiation; Radiation tolerance; Solenoids; Solid modeling; spiral antennas; Three dimensional models; Windings; Wires
• ISSN: 0018-9375; 1558-187X
• DOI: 10.1109/TEMC.2023.3298886

In this article, we use the dynamic Green's function to produce a frequency-dependent magnetic vector potential \vec{A}(\omega) and derive expressions for the efficient (accurate and fast) computation of 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 \Phi (\omega), the complex inductance L(\omega), and the radiation patterns of the solenoid anywhere in space including both near-field and far-field regions, excluding the (source) regions of conducting wire. In addition, 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 for a wide range of applications across the spectrum from 60 Hz to 170 GHz, representing low-frequency power systems to high-frequency mm-wave communication systems. A plan is being developed for experimental validation of the model.