Ultra-broadband material spectroscopy from scattering parameters obtained from time domain measurements

Ajay Bandla, Nathaniel Hager, Mohammad-reza Tofighi

Research output: Contribution to journalArticle

Abstract

The relaxation phenomena (e.g. free and bond water relaxations) and the frequencies at which they occur (from kHz to GHz) can convey valuable information in dielectric spectroscopy for material process monitoring and biology research. Finding the ultra-broadband frequency domain reflection and transmission coefficients (scattering parameters) from time domain measurements can be challenging. The current approach, often employed by material scientists, involves numerical integration of Laplace transform of the time domain data. On the other hand, the more computationally efficient fast Fourier transform (FFT) techniques have been well-developed and widely used in the engineering community. In this study, we propose a novel method, based on FFT of non-uniformly sampled time domain reflectometry (TDR) data, to obtain the frequency domain information from kHz to GHz. We perform FFT operations on multiple time windows of fixed number of points. The time duration of each window is increased, and the sample rate is decreased progressively. We correct for the truncation errors using Nicolson ramp prior to applying the FFT. We combine the FFT׳s of these multiple windows to obtain a single spectrum for each sample. We test this method to known lossy materials and hydrating cement samples. The results are in close agreement with those obtained using direct numerical integration.

Original languageEnglish (US)
Pages (from-to)8747-8757
Number of pages11
JournalJournal of the Franklin Institute
Volume354
Issue number18
DOIs
StatePublished - Dec 1 2017

Fingerprint

Scattering parameters
Fast Fourier transform
Fast Fourier transforms
Broadband
Spectroscopy
Time Domain
Scattering
Numerical integration
Frequency Domain
Reflectometry
Transmission Coefficient
Process Monitoring
Reflection Coefficient
Truncation Error
Time Windows
Dielectric spectroscopy
Laplace transform
Biology
Process monitoring
Laplace transforms

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

Cite this

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title = "Ultra-broadband material spectroscopy from scattering parameters obtained from time domain measurements",
abstract = "The relaxation phenomena (e.g. free and bond water relaxations) and the frequencies at which they occur (from kHz to GHz) can convey valuable information in dielectric spectroscopy for material process monitoring and biology research. Finding the ultra-broadband frequency domain reflection and transmission coefficients (scattering parameters) from time domain measurements can be challenging. The current approach, often employed by material scientists, involves numerical integration of Laplace transform of the time domain data. On the other hand, the more computationally efficient fast Fourier transform (FFT) techniques have been well-developed and widely used in the engineering community. In this study, we propose a novel method, based on FFT of non-uniformly sampled time domain reflectometry (TDR) data, to obtain the frequency domain information from kHz to GHz. We perform FFT operations on multiple time windows of fixed number of points. The time duration of each window is increased, and the sample rate is decreased progressively. We correct for the truncation errors using Nicolson ramp prior to applying the FFT. We combine the FFT׳s of these multiple windows to obtain a single spectrum for each sample. We test this method to known lossy materials and hydrating cement samples. The results are in close agreement with those obtained using direct numerical integration.",
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Ultra-broadband material spectroscopy from scattering parameters obtained from time domain measurements. / Bandla, Ajay; Hager, Nathaniel; Tofighi, Mohammad-reza.

In: Journal of the Franklin Institute, Vol. 354, No. 18, 01.12.2017, p. 8747-8757.

Research output: Contribution to journalArticle

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