Numerical Method

Overview

The numerical method behind EmCAD is based on a direct full-wave formulation that transforms an arbitrary 3D electromagnetic structure into a passive equivalent circuit. Unlike conventional simulation techniques that produce S-parameters or field distributions, this approach yields a reduced-order circuit model suitable for both frequency and time-domain analysis.

Beyond Fitting Techniques

Traditional macromodeling tools rely on zero-pole fitting of frequency response curves. While useful for small or low-port-count systems, these techniques scale poorly and often require complex preprocessing.

EmCAD avoids these limitations by constructing the equivalent circuit directly from the inspection of the discretized structure — specifically, a tetrahedral mesh — without the need for curve fitting or rational approximation.

The method handles arbitrary port configurations, including multiple excitation modes, and supports internal multiport definitions required for hierarchical decomposition.

Construction of the Circuit Model

A set of lumped circuit elements is inserted into the netlist for each tetrahedron, resulting in an initial circuit that may be very large. However, a powerful Model Order Reduction technique is applied independently to each subdomain circuit before inclusion in the upper-level hierarchical model. This typically reduces the circuit size by several orders of magnitude, enabling fast simulation while preserving accuracy.

A custom Model Order Reduction process compresses the initially large network into a compact equivalent, often reducing tens of thousands of elements to just a few hundred, with negligible loss in accuracy.

Guaranteed Physical Properties

The generated circuit obeys critical physical constraints:

  • Passivity: No artificial gain or energy creation
  • Causality: Accurate time-domain response without pre-echoes
  • Reciprocity: Consistent with electromagnetic theory

These properties make the resulting model stable, reliable, and portable across different simulation platforms.

Link with Hierarchical Decomposition

Although independent of decomposition, the method is designed to be decomposition-friendly. Each subdomain is modeled using the same principles, and interface conditions are handled via multimodal ports that preserve interactions among higher-order modes. This makes the global system assembly consistent, modular, and well-suited for parallel execution.

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