# Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium

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## Abstract

**:**

## 1. Introduction

## 2. Group Velocity Measurement Based on Electromagnetic Wave Theory

## 3. Compensation of Group Velocity in Dispersive Medium

## 4. Experimental Results

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Cho, J.; Kim, H.; Jung, K.-Y. Simple transmission line model suitable for the electromagnetic pulse coupling analysis of twisted-wire pairs above ground. IEICE Electron. Express
**2016**, 13, 20160149. [Google Scholar] [CrossRef] - Chowdary, K.M.; Majetich, S.A. Frequency-dependent magnetic permeability of Fe10Co90 nanocomposites. J. Phys. D Appl. Phys.
**2014**, 47, 175001. [Google Scholar] [CrossRef] - Chang, S.J.; Lee, C.K.; Lee, C.-K.; Han, Y.J.; Jung, M.K.; Park, J.B.; Shin, Y.-J. Condition monitoring of instrumentation cable splices using Kalman filtering. IEEE Trans. Instrum. Meas.
**2015**, 64, 3490–3499. [Google Scholar] [CrossRef] - Lee, C.K.; Park, J.B.; Shin, Y.J.; Yoon, T.S. High resolution LFMCW radar system using model-based beat frequency estimation in cable fault localization. IEICE Electron. Express
**2014**, 11, 20130768. [Google Scholar] [CrossRef] - Lee, S.H.; Lee, C.K.; Park, J.B.; Choi, T.H. Diagnostic method for insulated power cables based on wavelet energy. IEICE Electron. Express
**2013**, 10, 20130335. [Google Scholar] [CrossRef] - Kwak, K.S.; Doo, S.; Lee, C.K.; Yoon, T.S. Reduction of the blind spot in the time-frequency domain reflectometry. IEICE Trans. Electron.
**2008**, 5, 265–270. [Google Scholar] [CrossRef] - Lee, C.K.; Kwak, K.S.; Yoon, T.S.; Park, J.B. Cable Fault Localization Using Instantaneous Frequency Estimation in Gaussian-Enveloped Linear Chirp Reflectometry. IEEE Trans. Instrum. Meas.
**2013**, 62, 129–139. [Google Scholar] [CrossRef] - Shin, Y.J.; Song, E.S.; Kim, J.W.; Park, J.B.; Yook, J.G.; Powers, E.J. Time-frequency domain reflectometry for smart wiring systems. Proc. SPIE
**2002**, 4791. [Google Scholar] [CrossRef] - Chang, S.J.; Lee, C.K.; Shin, Y.-J.; Park, J.B. Multiple Resolution Chirp Reflectometry for Fault Localization and Diagnosis High Voltage Cable in Automotive Electronics. Meas. Sci. Technol.
**2016**, 27, 125006. [Google Scholar] [CrossRef] - Selesnick, I.W.; Figueiredo, M.A.T. Signal restoration with overcomplete wavelet transforms: comparison of analysis and systhesis priors. Proc. SPIE
**2009**, 7446. [Google Scholar] [CrossRef]

**Figure 3.**The results of acquired signals: 40 m lossy cable, 80 m lossy cable, lossless cable (

**a**) total signal; (

**b**) reflected signal.

Group Velocity | |||
---|---|---|---|

Cable Length: 40 m | Cable Length: 80 m | Cable Length: 120 m | |

TFCC accuracy | $1.82\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $100\phantom{\rule{1.em}{0ex}}[\%]$ | $1.81\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $99\phantom{\rule{1.em}{0ex}}[\%]$ | $1.81\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $97\phantom{\rule{1.em}{0ex}}[\%]$ |

proposed method accuracy | $1.83\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $99\phantom{\rule{1.em}{0ex}}[\%]$ | $1.81\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $99\phantom{\rule{1.em}{0ex}}[\%]$ | $1.76\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ $99\phantom{\rule{1.em}{0ex}}[\%]$ |

measurement value | $1.82\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ | $1.80\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ | $1.77\xb7{10}^{8}\phantom{\rule{1.em}{0ex}}[\mathrm{m}/\mathrm{s}]$ |

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**MDPI and ACS Style**

Chang, S.J.; Moon, S.-I. Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium. *Appl. Sci.* **2017**, *7*, 1306.
https://doi.org/10.3390/app7121306

**AMA Style**

Chang SJ, Moon S-I. Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium. *Applied Sciences*. 2017; 7(12):1306.
https://doi.org/10.3390/app7121306

**Chicago/Turabian Style**

Chang, Seung Jin, and Seung-Il Moon. 2017. "Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium" *Applied Sciences* 7, no. 12: 1306.
https://doi.org/10.3390/app7121306