Scripts to calculate and plot the complex permittivity from S-parameter data
Scripts to calculate and plot the complex permittivity (and permeability) from S-parameter data acquired from transmission-line measurements
permittivitycalc is a Python package made to take S-parameter data output from METAS VNA Tools II (https://www.metas.ch/vnatools) and process it to determine and plot the complex electric permittivity (and magnetic permeability) of a material measured in a coaxial transmission line.
Two analytical calculation methiods are currently implemented:
The New Non-iterative Method for permittivity calculation from S-parameters from [Boughriet1997] which assumes that the material is non-magnetic (i.e. mu = 1).
The Nicholson-Ross-Weir method to calculate the complex permittivity and permeability of a sample. This method, however, is unstable at multiples of one-half wavelength in the sample [NicolsonRoss1970] [Weir1974].
permittivitycalc can also use MCMC-based Bayesian model fitting/parameter estimation to fit Cole-Cole type models directly to the measured S-parameters to determine the frequency-dependant complex permittivity (and permeability, if desired). Cole-Cole models support multiple relaxation poles as well as a conductivity term.
You can use permittivitycalc to:
Input and plot raw S-parameter data in tabular form with or without uncertainties.
Calculate and plot the complex permittivity with full propagation of uncertainties.
Perform connector de-embedding on the raw S-parameters to extract the sample S-parameters, if necessary. Example: de-embedding washers used to cap the transmission line when measuring powdered samples.
Correct for the boundary effect in the transmission line when measuring powdered samples after [Hickson2017].
Correct for the air gap when measuring solid samples after [Baker-Jarvis1993].
Plot data from multiple measurements together for comparison.
Model measured S-parameters directly with a Cole-Cole model using MCMC-based Bayesian model fitting.
For usage examples and a walkthrough on how to use permittivitycalc, see the Docs
permittivitycalc was written for Python 3 and tested on the following versions of Python:
permittivitycalc uses the following packages:
We recommend using Anaconda to manage your Python environments.
Open a terminal window and create a conda virtual environment (name it anything you like, and set the python version to a compatible version in Requirements):
conda create --name your_env_name anaconda python=3.7
Activate the environment:
conda activate your_env_name
Install permittivitycalc with pip:
pip install permittivitycalc
(Optional) Fork permittivitycalc on Github
Clone or download the repository.
Navigate to the permittivitycalc root directory and install with:
python setup.py install
permittivitycalc was developed with the aid of these contributors.
Baker-Jarvis, J., Janezic, M. D., Grosvenor Jr, J. H., & Geyer, R. G. (1993). Transmission/reflection and short-circuit line methods for measuring permittivity and permeability. NIST Technical Note 1355-R. Boulder, CO. http://doi.org/10.6028/NIST.TN.1355r
Boughriet, A. H., Legrand, C., & Chapoton, A. (1997). Noniterative stable transmission/reflection method for low-loss material complex permittivity determination. IEEE Transactions on Microwave Theory and Techniques, 45(1), 52–57. http://doi.org/10.1109/22.552032
Hickson, D., Sotodeh, S., Daly, M. G., Ghent, R., & Nolan, M. C. (2017). Improvements on effective permittivity measurements of powdered alumina: Implications for bulk permittivity properties of asteroid regoliths. Advances in Space Research, 59(1), 472–482. http://doi.org/10.1016/j.asr.2016.08.011
Nicolson, A. M., & Ross, G. F. (1970). Measurement of the Intrinsic Properties of Materials by Time-Domain Techniques. IEEE Transactions on Instrumentation and Measurement, 19(4), 377–382. http://doi.org/10.1109/TIM.1970.4313932
Weir, W. B. (1974). Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies. Proceedings of the IEEE, 62(1), 33–36. http://doi.org/10.1109/PROC.1974.9382
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