This paper presents a comprehensive analysis of stability/causality/passivity (SCP) for improper rational transfer functions with complex-conjugate pair of poles/residues, as an extension of real poles/residues case in our previous work. We derive and validate the frequency-domain constraints of SCP for improper rational transfer functions with complex-conjugate pair of poles/residues, equivalent to an R-L-R-C circuit branch in parallel with Rshunt and Cshunt elements. We also develop detailed tables to establish a relationship between the transfer function parameters (pole, residue, zero), the equivalent circuit parameters (R, L, C), and the SCP conditions, for an improper system of R-L-R-C||Rshunt||Cshunt circuit branches. The aforementioned circuit-block structure serves as an important canonical topology for macromodeling of multi-port electrical systems across numerous applications. The presented methodology may be used for synthesis of guaranteed-stable SPICE equivalent circuits of electrical systems represented by network parameters (e.g., S/Y/Z-parameters), including power systems operating at tens of Hertz (Hz), high-speed micro-wave/mm-wave electronics operating at hundreds of MHz/GHz, and ultra high-bandwidth opto-electronic and optical systems operating at hundreds of THz.

Two-dimensional (2D) analytical models are only approximations for 3D structures where one cross-sectional dimension is much larger than the other. This paper uses the finite-difference time-domain method (FDTD) to perform numerical experiments on fully 3D dielectric waveguide structures to compute the wave-impedance and the propagation-constant for finite-width dielectric waveguides. These data are used to determine the width required to achieve good correlation against 2D analytical models. Results show that width ≥ 10x height is the limit for good approximation.

We apply machine learning (ML) techniques to identify the modes in rectangular waveguides from images of 2D modal field patterns injected with uniform, exponential, correlated exponential, and Gaussian noise distributions. A binary classifier is used to identify either transverse electric (TE) or transverse magnetic (TM) modes, and a Multi-class classifier is used to identify the mode numbers. Signal to noise ratios of 1, 0.1, and 0.01 are used to show the effectiveness of each model. Results show accuracy scores up to 99.95%. Several examples demonstrate that noisy modal patterns (unidentifiable to human eyes) may be successfully classified by the ML model.

The dielectric slab waveguide (DSW) has been the subject of much analysis in the past decades, with many important applications in high-speed high-bandwidth electromagnetic propagation; however, nearly all analysis of the DSW’s stochastic propagation loss $\alpha$ (dB/cm), associated with random surface roughness of its sidewalls, has revolved around the transverse-electric (TE) mode of operation. This work derives analytical expressions for $\alpha$ in the transverse-magnetic (TM) mode, and correlates it against numerical experiments in the method of finite-difference time-domain (FDTD) in both two-dimensional (2D) and three-dimensional (3D) space. In this work, we introduce the novel \textit{singular effective impedance} (SEI) formulation for normalization of the TM mode $\alpha$ and verify its accuracy through FDTD which shows near 0\% mean-error in both TM and TE modes. We perform several stochastic numerical experiments in 3D FDTD, where the DSW’s width is set to be much larger than its height, and show that $\alpha$ correlates quite well against the proposed 2D analytical model and 2D FDTD. Finally, analysis of FDTD-computed data reveals that existing analytical models of $\alpha$ may be missing higher-order interaction terms involving correlation length $L_c$ (m) of the surface roughness.

The solenoid has been used extensively in a wide range of electrical applications. In the present work, an analytical model is presented for estimating the 3-dimensional (3D) magneto quasi-static fields of the cylindrical solenoid with helix-shaped (helical) wire winding. The proposed integral formulation is based on the Schur (Hadamard) vector product of the current vector I and the helical tangent vector T, to express the magnetic vector potential A. The model is used to estimate the magnetic flux density vector B and the flux linkage Psi anywhere in 3D space, excluding the (source) regions of conducting wire. A constant scaling coefficient, based on measured terminal inductance, is proposed for calibration of the model’s magnetic field. Error analysis is presented on the numerical integration, based on truncated series expansion of complete elliptic integrals in terms of Chebychev polynomials. The model may be used to estimate all three cylindrical components of the magneto quasi-static fields of solenoids as a function of core diameter, wire radius, the number of wire turns per winding layer, the number of winding layers, and the complex permeability of frequency-dependent linear material. Several numerical examples are provided to validate the helical model against the superposition of circular loops, and an idealized circuit model.