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Weeks Microstrip Calculator with Dielectric Support

CI License: MIT

About This Project

I created this project in the mid-90s and have uploaded it to GitHub in case someone finds it useful.

This code implements the partial inductance formulas developed by W.T. Weeks et al. at IBM Research in 1979. The original work was groundbreaking for calculating resistance and inductance in rectangular conductors, accounting for skin effect and proximity effect. This Weeks implementation is built upon this foundation, and the recent 2025 enhancements add support for real-world PCB materials like FR4 and Rogers substrates.

While modern field solvers have become more sophisticated, this calculator remains valuable for quick impedance estimates and understanding the fundamental physics of microstrip transmission lines. It's particularly useful for educational purposes and preliminary PCB design work.

I used Claude Code and Google Gemini to port this project to Linux and to create tests.

Overview

This is an enhanced version of the Weeks microstrip resistance calculator with support for reading FR4 and general dielectric substrate parameters.

Scope: This tool computes the series resistance (R) and inductance (L) matrices of rectangular conductors using the PEEC method. These matrices are dielectric-independent (μr≈1), so changing only the substrate material (e.g. air vs FR4) does not change them. In addition, a per-line quasi-TEM transmission-line section reports effective permittivity, characteristic impedance (Z0), capacitance, attenuation and complex propagation γ — this is where the dielectric (er, tan_delta) takes effect. The substrate height is the trace-to-ground gap derived from the conductor geometry, not a separate input. See Understanding the Physics.

Features

✅ YAML input format - Modern, human-readable configuration files
✅ Per-unit-length R and L matrices for multi-conductor systems (PEEC)
✅ Per-line transmission-line parameters — effective permittivity (Hammerstad-Jensen), Z0, capacitance, attenuation (incl. dielectric loss) and complex propagation γ
✅ Pre-defined material constants (FR4, Rogers, Alumina, PTFE)
✅ Frequency defined in input file - No need to recompile!
✅ Example YAML files for multiple materials
✅ Independent validation against the FastHenry field solver (make check-fasthenry) and the Hammerstad-Jensen Z0 closed form (make check-z0)

Quick Start

# Check dependencies
make check-deps

# Build
make

# Run with FR4 (default)
./weeks

# Or test with different materials
make test-fr4     # FR4 substrate
make test-air     # Air (baseline comparison)
make test-rogers  # Rogers RO4003C

# Validate R/L against the FastHenry field solver (needs fasthenry on PATH)
make check-fasthenry

# Run the cross-check harness unit tests
python3 -m pytest tools/fh_crosscheck/

Requirements

  • GCC or compatible C compiler
  • Meschach library (matrix operations)
  • libyaml (YAML parsing)
  • Linux/Unix operating system

Installing Dependencies

Ubuntu/Debian:

sudo apt-get install libmeschach-dev libyaml-dev

Fedora/RHEL:

sudo dnf install meschach-devel libyaml-devel

From Source (Meschach):

The original Meschach homepage is no longer available. On Debian/Ubuntu the easiest way to get the source is the distribution source package:

# Enable deb-src for the 'universe' component first, then:
apt-get source meschach          # unpacks meschach-1.2b/ with Debian patches
cd meschach-1.2b
./configure && make
sudo make install

On GCC 10+ you may need -fcommon (e.g. make CFLAGS='-O2 -fcommon') because Meschach relies on legacy common-symbol linkage. See docs/fasthenry-crosscheck.md for the same note applied to FastHenry.

From Source (libyaml):

git clone https://github.com/yaml/libyaml
cd libyaml
./bootstrap
./configure
make
sudo make install

Input File Format (YAML)

The calculator uses YAML format for input files, making configuration human-readable and easy to edit.

Basic Structure

# Frequency of operation
frequency: 30e6  # 30 MHz (use scientific notation)

# List of conductors
conductors:
  - name: line0      # Ground plane
    w: 2800e-6       # Width in meters
    h: 2.0e-6        # Thickness in meters
    x: 0.0           # X position
    y: 0.0           # Y position
    nw: 201          # Width mesh divisions
    nh: 3            # Height mesh divisions
    b: 0.2           # Mesh density parameter
    er: 4.4          # Dielectric constant
    tan_delta: 0.02        # Loss tangent
    
  - name: line1      # Signal trace; its y sets the substrate height (gap to ground)
    w: 150e-6
    h: 35e-6         # 35 μm = 1 oz copper
    x: 600e-6
    y: 1.602e-3      # 1.6 mm above the ground-plane top => the substrate height
    nw: 21
    nh: 7
    b: 0.9
    er: 4.4
    tan_delta: 0.02

Parameter Descriptions

Frequency:

  • frequency: Operating frequency in Hz (use scientific notation: 30e6 = 30 MHz)

Geometric Parameters:

  • w: Conductor width (meters)
  • h: Conductor thickness/height (meters)
  • x: X-position of the left edge (min-x corner) (meters)
  • y: Y-position of conductor bottom (meters). For a signal trace, its height above the ground-plane top is the substrate height used for εeff/Z0.

Mesh Parameters:

  • nw: Number of divisions along width
  • nh: Number of divisions along height
  • b: Mesh density parameter (0.2-0.9)

Dielectric Parameters:

  • er: Relative permittivity (dielectric constant)
  • tan_delta: Loss tangent at operating frequency

The substrate height is not a parameter — it is derived from geometry as the gap between the signal trace bottom and the ground-plane top. A legacy substrate_h: key is ignored (with a note on stderr).

IMPORTANT: All dimensions must be in METERS!

  • 1.6 mm = 1.6e-3 meters (not 1.6!)
  • 150 μm = 150e-6 meters

Example Materials (YAML Format)

FR4 Standard PCB

frequency: 30e6

conductors:
  - name: line0
    # ... geometry parameters ...
    er: 4.4
    tan_delta: 0.02

Rogers RO4003C (RF/Microwave)

frequency: 1e9  # 1 GHz for RF

conductors:
  - name: line0
    # ... geometry parameters ...
    er: 3.38
    tan_delta: 0.0027

Rogers RO4350B (High-Speed Digital)

frequency: 2e9

conductors:
  - name: line0
    # ... geometry parameters ...
    er: 3.48
    tan_delta: 0.0037

Air (Baseline/Original Behavior)

frequency: 30e6

conductors:
  - name: line0
    # ... geometry parameters ...
    er: 1.0
    tan_delta: 0.0

Tip: Copy one of the ready-made files from the examples/ directory (test_air.yaml, test_fr4.yaml, test_rogers4003.yaml, test_single.yaml) and modify it for your needs. The material blocks above show only the dielectric values to plug in — RO4350B does not have its own example file, so copy test_rogers4003.yaml and change the three dielectric fields. (Recall that the dielectric values do not change the R/L/|Z| output; see Scope.)

Compilation

Simple (Recommended)

make

This will:

  • Check for required libraries (libyaml, meschach)
  • Create the build/ directory
  • Compile all source files from src/ (lowercase .c files)
  • Link with Meschach and libyaml libraries
  • Create the weeks executable in the root directory

Check Dependencies First

make check-deps

This will verify that both Meschach and libyaml are installed.

Custom Library Paths

make INCLUDES='-Iinclude -I/custom/path/include' LDFLAGS='-L/custom/path/lib'

Manual Compilation

mkdir -p build
gcc -o weeks \
    src/weeks.c src/build.c src/calcl.c src/input.c src/lpp.c \
    -Iinclude -I/usr/local/include \
    -L/usr/local/lib \
    -lmeschach -lyaml -lm -O2

Troubleshooting

"Cannot find yaml.h":

sudo apt-get install libyaml-dev

"Undefined reference to yaml_parser_initialize":

# Make sure libyaml is installed and linked
sudo ldconfig

Output

The program calculates and displays:

  1. Resistance Matrix (R) in Ω/m
  2. Inductance Matrix (L) in H/m
  3. Impedance Magnitude |Z| at operating frequency

Example Output:

========================================
RESULTS
========================================

FREQUENCY: 3.000000e+07 Hz (30.00 MHz)

*** RESISTANCE MATRIX (Ohm/m) ***

           1           2           3

  1 +1.2345e-02 +2.3456e-03 +1.2345e-03
  2 +2.3456e-03 +1.2345e-02 +2.3456e-03
  3 +1.2345e-03 +2.3456e-03 +1.2345e-02

*** INDUCTANCE MATRIX (H/m) ***

           1           2           3

  1 +4.5678e-07 +1.2345e-07 +5.6789e-08
  2 +1.2345e-07 +4.5678e-07 +1.2345e-07
  3 +5.6789e-08 +1.2345e-07 +4.5678e-07

*** IMPEDANCE MAGNITUDE (Ohm) at 30.00 MHz ***
...

Understanding the Physics

Note: The series R and L matrices are dielectric-independent (μr≈1). The dielectric instead enters the per-line TRANSMISSION-LINE PARAMETERS section, via a quasi-TEM model built on the geometry-derived substrate height. See Scope.

Effective Dielectric Constant

For microstrip, the EM field exists partly in the dielectric and partly in air. The effective dielectric constant εeff is calculated using:

εeff = (εr + 1)/2 + ((εr - 1)/2) × F(w/h)

where F(w/h) is the Hammerstad-Jensen approximation and h is the substrate height (the geometry-derived trace-to-ground gap).

Dielectric Loss

The dielectric loss is reported as an attenuation constant α_d (units 1/m):

α_d = (ω√εeff/c) × ((εr-1)/(εeff-1)) × (εeff/εr) × tan(δ)

It is not folded into the series R matrix (a 1/m attenuation cannot be added to an Ω/m resistance). Instead it enters the shunt side of the transmission-line model and shows up in the reported total attenuation and complex propagation γ.

Per-line transmission-line parameters

From each line's diagonal series R/L and the effective permittivity, the tool reports (quasi-TEM, single-line): capacitance C = εeff/(c²L), characteristic impedance Z0 = √(L/C), conductor + dielectric attenuation, phase constant β and complex propagation γ. So unlike the R/L matrices, this section does differ between air and FR4:

Parameter Air (εr=1.0) FR4 (εr=4.4) Effect
Capacitance 1× ↑ Increases by εeff
Inductance 1× ~1× Approximately same
Z0 1× ↓ Decreases by √εeff
Loss Conductor only Conductor + Dielectric Increases
Velocity c c/√εeff Slows down

This is a single-line characterization (it does not model inter-line capacitive coupling); cross-check it with make check-z0.

Directory Structure

weeks/
├── README.md              # This file
├── INSTALL.md             # Quick start guide
├── YAML_USER_GUIDE.md     # Detailed YAML input reference
├── LICENSE                # MIT license
├── Makefile               # Build script
├── CLAUDE.md              # Guidance for AI coding assistants
├── test.yaml              # Active input file read by ./weeks
│
├── src/                   # Source files (5 files, lowercase .c)
│   ├── weeks.c            # Main program (with YAML support)
│   ├── calcl.c            # Impedance matrix; effective εr / dielectric loss
│   ├── input.c            # YAML parser using libyaml
│   ├── build.c            # Element/mesh builder
│   └── lpp.c              # Partial inductance formulas
│                          # (complex solvers provided by libmeschach)
│
├── include/               # Header files (3 files, lowercase .h)
│   ├── weeks.h            # Main header with dielectric support
│   ├── calcl.h            # Calculator header
│   └── lpp.h              # Partial inductance header
│
├── examples/              # YAML input examples (6 files)
│   ├── test.yaml          # Default (FR4)
│   ├── test_air.yaml      # Air baseline
│   ├── test_fr4.yaml      # FR4 standard PCB
│   ├── test_microstrip.yaml  # Single trace for Z0 cross-check
│   ├── test_rogers4003.yaml  # Rogers RO4003C
│   └── test_single.yaml   # Single trace (used by check-fasthenry)
│
├── tools/                 # FastHenry cross-check harness (Python, stdlib-only)
│   └── fh_crosscheck/     # Compares weeks R/L against FastHenry; has unit tests
│
├── docs/                  # Additional documentation
│   ├── fasthenry-crosscheck.md    # FastHenry cross-check setup
│   └── meschach-static-analysis.md # cppcheck report on linked Meschach
│
├── .github/workflows/     # CI (build + test on push/PR)
│
└── build/                 # Build artifacts (auto-created by make)
    └── *.o                # Object files

Validation

To validate results:

  1. Compare against FastHenry: Run make check-fasthenry for independent numerical validation of R/L values.
  2. Mesh Alignment & Accuracy: When both solvers use uniform meshes (by setting b: 1.0 in weeks to match FastHenry's uniform sub-segmentation in the harness), they match to within 2.3% across all self and mutual resistance/inductance terms. See docs/fasthenry-crosscheck.md for details.
  3. Online calculators: Cross-check with analytical formulas.

Troubleshooting

"Cannot find meschach.h"

# Find where it's installed
find /usr -name "meschach.h" 2>/dev/null

# Then compile with:
make INCLUDES='-I/path/to/meschach/include'

"Undefined reference to zm_get"

# Meschach library not linked properly
make LDFLAGS='-L/path/to/meschach/lib'

Wrong Results

  • Check units: all dimensions must be in METERS!
  • Check trace height: the substrate height is the signal trace's gap above the ground plane — place the trace at the intended height (e.g. y: 1.602e-3 for a 1.6 mm substrate over a 2 µm ground plane)
  • Check dielectric values: Typical FR4 is εr=4.4, not 44!
  • Compare with air: Run with er=1.0 to verify baseline

Technical Details

Algorithm

  • Method: Partial Element Equivalent Circuit (PEEC)
  • Formulation: Weeks method (IBM, 1979)
  • Frequency: Quasi-static (valid in the low-GHz range; the Rogers examples run at 1–2 GHz)
  • Matrix: Complex impedance Z = R + jωL

Modifications from Original Weeks

  1. Added dielectric structure members to conductor
  2. Modified src/input.c to parse dielectric parameters
  3. Modified src/calcl.c to calculate effective εr and dielectric loss
  4. Modified src/weeks.c to pass conductor info to calcl
  5. Removed Windows-specific _CRT debug code (Linux compatibility)
  6. Added material constant definitions in header

Backward Compatibility

  • Omitting dielectric parameters defaults to air (εr=1.0)
  • Original input files work without modification
  • Because the dielectric parameters do not affect the R/L/|Z| matrices, results match the original code whether or not dielectric params are supplied

References

  1. Original Weeks Paper:
    W.T. Weeks et al., "Resistive and Inductive Skin Effect in Rectangular Conductors"
    IBM J. RES. DEVELOP., Vol 23, No. 6, Nov. 1979

  2. Hammerstad-Jensen:
    E. Hammerstad & O. Jensen, "Accurate Models for Microstrip Computer-Aided Design"
    IEEE MTT-S, 1980

  3. Material Properties:

    • IPC-4101 Specification for Base Materials
    • Rogers Corporation Datasheets
    • Standard PCB manufacturer references

License

MIT License — see LICENSE. (The project was relicensed to MIT when it was published on GitHub.)

Credits

  • Original WEEKS code: Ole Saether (1995)
  • Weeks formulas: W.T. Weeks et al., IBM (1979)
  • Dielectric modifications: 2025 enhancement

Support

Questions, bug reports, and contributions are welcome via GitHub Issues and pull requests.

Before opening an issue, it may help to:

  1. Check this README and the YAML User Guide
  2. Verify the Meschach and libyaml installation (make check-deps)
  3. Compare against the provided examples/
  4. Validate with external tools (make check-fasthenry, online calculators)

About

This code implements the partial inductance formulas developed by W.T. Weeks et al. at IBM Research in 1979.

Topics

electromagnetics transmission-line microstrip inductance fasthenry peec partial-inductance microstrip-calculator

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MIT license
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