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

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. 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 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.