Nicolson-Ross-Weir Material Parameter Extraction

Measuring a material's permittivity and permeability from waveguide S-parameters, in a short MATLAB script.

Details

Type	Personal / research tool
When	2026
Language	MATLAB
Test case	6.3 mm PTFE (Teflon) sample in WR-90 waveguide, 8–12 GHz (HFSS simulation)
License	MIT
Code	git.natetheokay.com/nathan/Nicolson-Ross-Weir-…

What it is

A simple MATLAB script to extract the effective permittivity and permeability of a material from its S-parameters measured in a rectangular waveguide. The method used is the Nicolson-Ross-Weir method.

Waveguide measurement setup: two coax-to-waveguide adapters on the VNA cables, joined by two waveguide sections with the sample holder clamped between them — Fig. 1. (a) Measurement setup: coax-to-waveguide adapters on the VNA cables, with the sample holder clamped between the two waveguide sections. (b) The sample fitted into the holder. Click either photo for the full-size image.

Material sample fitted into the opening of a flange-sized sample holder plate — Fig. 1. (a) Measurement setup: coax-to-waveguide adapters on the VNA cables, with the sample holder clamped between the two waveguide sections. (b) The sample fitted into the holder. Click either photo for the full-size image.

How it works

A sample of known thickness fills the cross-section of a rectangular waveguide. From the measured (or simulated) two-port S-parameters, the Nicolson-Ross-Weir equations recover the reflection coefficient at the sample face and the transmission through it, and from those the complex relative permittivity (ε_r) and permeability (μ_r) across the band. The implementation follows NIST Technical Note 1536 (p. 112).

HFSS model of the Teflon block filling a section of WR-90 waveguide, with the wave ports at both ends highlighted in red — Fig. 2. Simulation model for the Teflon block in WR-90. Excitations and de-embedding are highlighted.

Results

The repository includes a reference case: a 6.3 mm block of PTFE simulated in WR-90 waveguide. The extraction should return values close to Teflon's known properties (ε′ ≈ 2.1).

Extracted relative permittivity of the PTFE reference sample from 8 to 12 GHz: the real part is flat at about 2.1, the imaginary part is near zero, and the loss tangent stays between about 0.9 and 1.3 times 10 to the minus 3 — Fig. 3. Extracted relative permittivity (top) and dielectric loss tangent (bottom) for the 6.3 mm PTFE reference simulation, 8–12 GHz.

Extracted relative permeability of the PTFE reference sample from 8 to 12 GHz: the real part is flat at about 1, the imaginary part is near zero, and the magnetic loss tangent stays below about 5 times 10 to the minus 4 — Fig. 4. Extracted relative permeability (top) and magnetic loss tangent (bottom) for the same simulation. As expected for a non-magnetic material, μ_r ≈ 1.

Example output for the Teflon test case:

Averages:
er = 2.1000
tanD = 0.0010584
ur = 0.99962
magtanD = 8.2202e-05
At 10 GHz
er = 2.1000
tanD = 0.0010094
ur = 0.99962
magtanD = 8.9186e-06

Practical notes

Measure the sample thickness carefully. An error in the thickness goes straight into both ε and μ across the whole band. Use a micrometer or calibrated caliper and average several readings.
Pick the sample length. Aim for about a quarter of the guided wavelength in the material. High-permittivity materials need thinner samples to avoid phase-ambiguity errors.
Don't renormalize simulated S-parameters. When exporting from HFSS, keep the S-parameters normalized to the waveguide impedance, not 50 Ω.
I initially wrote this code to extract the effective permittivity of 3D printed samples with different infill values. With a period small enough compared to wavelength, the gyroid infill pattern makes a nice effectively isotropic material that can emulate an arbitrary permittivity less than that of the bulk material.

References

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Transactions on Instrumentation and Measurement, 1970.
W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proceedings of the IEEE, 1974.
M. D. Janezic and J. A. Jargon, Complex Permittivity Determination from Propagation Constant Measurements, NIST Technical Note 1536, 2004.