A TLM Formulation Based on Fractional Derivatives for Dispersive Cole-Cole Media
<p id="p2">An auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of t...
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| Autores principales: | , , |
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2021
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| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/76596 |
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| Sumario: | <p id="p2">An auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of the polarization current when the time discretization is short enough. The polarization current density is approached using Lagrange extrapolation polynomial and the fractional derivation is obtained according to Riemann definition of a fractional <span class="inline-formula"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mi>α</mml:mi></mml:math></span>-order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found to be in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.</p> |
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| ISBN: | 978-1-83968-581-1 |
| DOI: | 10.5772/intechopen.96378 |