2D Transmission Line Field Solver

A browser-based quasi-static and full-wave 2D field solver for transmission line analysis. Computes characteristic impedance, effective permittivity, RLGC parameters, losses, and S-parameters.

Try it online: https://hforsten.com/field_solver.html

Features

• Transmission Line Types: Microstrip, stripline, GCPW (single-ended and differential)
• Electric Field Solving: Calculates characteristic impedance
• Full RLGC Extraction: Resistance, inductance, capacitance, conductance per unit length
• Loss Modeling: Conductor losses (skin effect, surface roughness) and dielectric losses
• S-Parameter Export: Touchstone .s2p and .s4p file generation
• Visualization: 2D potential plots, E-field streamlines, frequency-dependent plots
• Adaptive Meshing: Automatic mesh refinement for accurate field solutions

Quick Start

1. Build (or obtain) the WASM solver binaries (see below). They are not checked into git.
2. Host src folder on a web server (for example python -m http.server 8000). Open src/field_solver.html in a browser.

Validity

• Designed for microstrip, stripline, and coplanar waveguide structures commonly used in PCB RF and high-speed digital designs.
• Provides good results when the transmission line supports TEM or quasi-TEM propagation, which covers most practical PCB geometries below the onset of higher-order modes.
• Results have been checked against EM solver and actual measurement data with different geometries and transmission line types, showing close agreement with small error in typical use cases (tests folder).
• Accurate from RF through microwave and high-speed digital frequencies where return currents are confined and skin effect is significant.
• Sufficient for Most Practical Designs. Suitable for impedance control, loss estimation, and S-parameter generation in the vast majority of PCB transmission line applications.
• Dispersion and higher-order modes are support with full-wave solver.

Common Tasks

Run Tests

Tests are organized into tiers and run through tests/run.mjs:

npm run test:fast   # ~1 min, run before every commit
npm run test:slow   # full solver validation, ~5 min
npm test            # fast + slow
npm run test:e2e    # browser tests (see below)
npm run test:fuzz   # QS-vs-fullwave fuzzer (~10 min, deterministic seed)

Fast tier: Tests small parts of the solver. Slow tier: Test against reference structures. Browser (e2e) tier, needs playwright-core (npm install).

Build WASM Solvers

The solver numerics run as WebAssembly (WASM) modules built with Emscripten. All of them live in src/wasm_solver/:

Output	Source	Used by
solver.{js,wasm}	solver.cpp	quasi-static FDM backend
eigen_solver.{js,wasm}	eigen_solver.cpp	full-wave backend
gmsh.{js,wasm}	gmsh/ submodule	full-wave mesh generation

Prerequisites

Emscripten Compiler (emcc)

Install the Emscripten SDK:

# Clone the emsdk repository
git clone https://github.com/emscripten-core/emsdk.git
cd emsdk

# Install and activate the latest SDK
./emsdk install latest
./emsdk activate latest

# Add to PATH (add this to your .bashrc or .zshrc for permanent use)
source ./emsdk_env.sh

Verify installation:

emcc --version

Submodules (Eigen, Spectra, gmsh)

Third-party sources are git submodules under src/wasm_solver/. Initialize them:

git submodule update --init --recursive

Build Steps

cd src/wasm_solver
make all          # builds solver.{js,wasm} and eigen_solver.{js,wasm}

Building gmsh is heavier: it additionally needs OpenCASCADE cross-compiled to WASM. See src/wasm_solver/README.md for the OCCT prerequisite, then:

OCCT_WASM=/path/to/occt-wasm-install make gmsh   # builds gmsh.{js,wasm}