This paper extends a previous work on synthesis of equivalent circuits using strictly proper canonical R-L and R a-L-R b-C circuit branches, and presents a thorough time-domain and frequency-domain analysis of stability/causality/passivity (SCP) of the R-L circuit branch (based on real pole/residue) and two additional shunt elements R shunt and C shunt parallel to the R-L branch, leading to an improper rational transfer function. We develop a rigorous and comprehensive table of sign-relationships including pole/residue, pole/zero, R/L/C elements, and SCP conditions to describe the interaction of R shunt and C shunt elements with an R-L branch. We also examine the effects on SCP due to negative gain coefficient of the transfer functions. Because such a topology can commonly occur as a result of applying fitting algorithms (e.g., Vector Fitting) on the electrical response of multi-port networks (e.g., impedance, admittance, or scattering parameters), it is important to understand the above SCP conditions for synthesis of practical SPICE models for stable time-domain simulations.
<p>This paper proposes two distinct approaches, namely <em>Piece-by-Piece MNA</em> and <em>General MNA</em>, 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.</p>
<p>This paper presents a comprehensive analysis of stability/causality/passivity (SCP) for improper rational transfer functions with <em>complex-conjugate</em> pair of poles/residues, as an extension of <em>real </em>poles/residues case in our previous work. We derive and validate the frequency-domain constraints of SCP for <em>improper </em>rational transfer functions with <em>complex-conjugate</em> pair of poles/residues, equivalent to an R-L-R-C circuit branch in parallel with R<sub><em>shunt</em></sub> and C<sub><em>shunt</em></sub> 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||R<sub><em>shunt</em></sub>||C<sub><em>shunt</em></sub> 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.</p>
<p>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).</p> <p>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.</p>
<p>This paper proposes two distinct approaches, namely <em>Piece-by-Piece MNA</em> and <em>General MNA</em>, 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.</p>
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