This paper presents SRPOEE which is a novel algorithm and automated Python-based open-source software (OSS) designed to synthesize the reduced-order passivity-enforced equivalent circuits of networks represented by scattering parameters (S-parameters). The proposed algorithm comprises three main modules Full Synthesis, Passive MOR, and Reduced Synthesis, each incorporating a combination of established and novel techniques. The Full synthesis module calculates a full-order passive fitted system in state-space form, via fitting the given S-parameters using the vector fitting (VF) method, and assesses/enforces passivity through the singularity half-size test matrix method. Subsequently, it synthesizes a full-order equivalent circuit, comprised of R/L/C circuit elements, based on the calculated full-order fitted system. The Passive MOR module represents the synthesized full-order equivalent circuits using modified nodal analysis (MNA) matrices, and subsequently reduces the order of these matrices through a model order reduction (MOR) technique known as the Block SAPOR technique. Finally, the Reduced Synthesis module constructs a reduced-order equivalent circuit composed of R/L/C circuit elements based on the reduced-order MNA matrices generated in the previous module. In addition to synthesizing the reduced- and full-order equivalent circuits, SROPEE also generates SPICE-compatible netlists for both the full- and reduced-order equivalent circuits, enabling further circuit analysis in SPICE circuit solvers. We evaluate SROPEE by comparing the network parameters of the synthesized reduced-order equivalent circuit with the original network parameters for a 4-port optical network operating in frequency range of 175 - 215 THz. Furthermore, we compare the computational costs of circuit analysis for synthesized full-and reduced-order equivalent circuits in terms of network order, matrix dimensions, compute-time, accuracy, memory utilization, and passivity considerations. The Python-based OSS may be deployed as a stand-alone tool, or integrated into existing process technology flows and CAD tools to expedite design automation.

We propose a machine learning (ML) modeling methodology to predict the propagation mode number of electromagnetic (EM) fields inside a metallic rectangular waveguide based on the field configuration in the waveguide cross-section, in the presence of noise. We consider the Transverse Electric (TEmn) modes and assume m and n in the range of 0 to 2 inside the waveguides, where the magnitude and phase of the noiseless field configurations are obtained from the analytical solution of the electric vector field E⃗ . We generate training/testing datasets that includes 64,000 plots of the magnitude and phase of E⃗ over the waveguide cross-section, spanning various TE modes in the frequency range of 13-17 GHz. Our methodology for training and evaluation is based on the classification model, and relies primarily on Stochastic Gradient Descent (SGD) and k-Nearest Neighbors. For real-world scenarios which include noise, we introduce two random distributions in the datasets; specifically, the exponential and the Gaussian distributions are added onto the computed E-fields to further challenge the ML model. We discuss the limitations of the proposed ML modeling approach and the challenges in finding the optimal ML model for these types of problems. The proposed methodology may be generalized to predict both the TE and Transverse Magnetic (TMmn) mode numbers with a wide ranges of m and n, as well as for other types of waveguides; e.g., circular, elliptical, etc.

This paper precisely evaluates the existing theoretical expressions for calculating guided power in symmetric dielectric slab waveguides for both transverse-electric (TE) and transverse-magnetic (TM) modes. In this work, we derive the relationships between electric and magnetic fields in both TE and TM modes by assessing potential values for propagation phase constant and subsequently assess the corresponding power expressions for determining total guided power flowing through the cross-section of symmetric dielectric slab waveguide. As a numerical example, we examine a typical dielectric slab waveguide consisting of a silicon core with a refractive index n1 = 3.5, surrounded by silicon dioxide cladding with refractive index n2 = 1.5, operating in optical frequency of 194 THz (i.e., λ ≈ 1.55 µm). Finally, we compare the calculated TE and TM mode field components and guided powers presented in figures and tables, respectively, validated by simulation results.

Our investigation of the Modified Equivalent Current Approximation (MECA) method reveals notable limitations in its ability to accurately model dielectric media in non-half-space (NHS) structures. These limitations are rooted in MECA’s baseline formulation which fundamentally assumes each surface element of the discretized structure is bounded by a half-space composed of a good dielectric-good conductor; thus, not meeting this baseline assumption leads to inaccurate results. Furthermore, our analysis identifies several inaccuracies in MECA’s original formulation, leading us to propose several corrections. To substantiate our results, we conduct numerical simulations to determine the radar cross section for various structures. Our study not only exposes MECA’s limitations in handling dielectric media in NHS structures but also enhances its accuracy for modeling good conductor media.

We develop a deep neural network (DNN) modeling methodology to predict the radiated emissions of a shielding enclosure in terms of its aperture attributes including aperture shape, size, pitch, and quantity. The target structure is the inside of a three-dimensional (3D) enclosure comprised of perfect electric conductor (PEC) boundaries with dimensions of a desktop personal computer (PC) containing thermal dissipation apertures on the surface of its back panel. The DNN model is developed to compute the radar cross section (RCS) as a function of aperture attributes and to enable the efficient assessment of the PC’s electromagnetic compatibility (EMC). To generate training data for machine learning (ML), we implement the modified equivalent current approximation (MECA) method and validate it against analytical methods and a commercial field-solver. We use MECA to compute RCS data for approximately 55,000 experiments across a wide range of aperture attributes. We examine numerous DNN models across parameters such as number of layers and nodes per layer, activation function, optimization algorithm, loss function, batch size, and epoch, to identify the optimal DNN model based on (a) accuracy, (b) computation time, and (c) memory usage. Results show excellent agreement between MECA and DNN predictions for previously unseen cases.

This paper proposes two distinct approaches, namely Piece-by-Piece MNA and General MNA, for construction of Modified Nodal Analysis (MNA) matrices in order to be used in Model Order Reduction (MOR) techniques. In this work, we successfully applied the proposed approaches to construct MNA matrices of a multi-port network with several sub-circuits, then, reduced order of network using obtained MNA matrices in each approach. As a numerical example, the Y-parameters of full-order and reduced-order networks for a 4-port optical network, operating in frequency range 175-215 THz, are obtained through the proposed approaches, validated through simulating in Advanced Design System (ADS) software, and compared in terms of order of system (or matrix dimensions), execution time, Root Mean Square Error (RMSE), reduction controllability, reduction efficiency, and passivity point of view.

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.