permittivitycalc

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Scripts to calculate and plot the complex permittivity (and permeability) from S-parameter data acquired from transmission-line measurements

Overview

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.

Usage

For usage examples and a walkthrough on how to use permittivitycalc, see the Docs <https://permittivitycalc.readthedocs.io>_

Installation

Requirements ^^^^^^^^^^^^

permittivitycalc was written for Python 3 and tested on the following versions of Python:

permittivitycalc uses the following packages:

tkinter
numpy
uncertainties
scipy
matplotlib
seaborn
cycler
lmfit
emcee
corner

Installing Anaconda ^^^^^^^^^^^^^^^^^^^

We recommend using Anaconda_ to manage your Python environments.

.. _Anaconda: https://www.anaconda.com/distribution/

Install Anaconda <https://www.anaconda.com/download/>_.
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

.. _conda virtual environment: https://conda.io/docs/using/envs

Quick Install ^^^^^^^^^^^^^

Install permittivitycalc with pip::

pip install permittivitycalc

Manual Install ^^^^^^^^^^^^^^

(Optional) Fork permittivitycalc on Github <https://github.com/boivinalex/permittivitycalc>_
Clone or download the repository.
Navigate to the permittivitycalc root directory and install with::

python setup.py install

Contributors

permittivitycalc was developed with the aid of these contributors <https://github.com/boivinalex/permittivitycalc/graphs/contributors>_.

References

.. [Baker-Jarvis1993] 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 .. [Boughriet1997] 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 .. [Hickson2017] 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 .. [NicolsonRoss1970] 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 .. [Weir1974] 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

Permittivitycalc

Install / Use

README