Eur. Phys. J. Spec. Top. (2022) 231: 4213-4220
https://doi.org/10.1140/epjs/s11734-022-00570-1

Regular Article

Approximate solution of impedance matching for nonmagnetic homogeneous absorbing materials

¹ School of Physics and Electronics, Central South University, 410083, Changsha, Hunan, People’s Republic of China
² Powder Metallurgy Research Institute, Hunan Key Laboratory of Advanced Fibers and Composites, Central South University, 410083, Changsha, Hunan, People’s Republic of China

^b duzuojuan@csu.edu.cn

Received: 15 November 2021
Accepted: 8 April 2022
Published online: 20 April 2022

Abstract

Impedance matching is an essential concept in the design of absorbing materials. Its basic form $Z_{\mathrm{in}}$–$Z_0=$ 0 derived from the expression of reflectivity transmission line is often used to explain the reason for the reflectivity peak. Still, the relationship between impedance matching and material parameters has not been accurately described so far. In this paper, for nonmagnetic homogeneous materials, a solution of impedance matching equation is proposed to illustrate the relationship between impedance matching and the complex permittivity of absorbing materials. The thickness required for impedance matching is also obtained in the proposed solution. An eigenvalue P containing the relationship between the real and imaginary parts of the permittivity is presented. When P is equal to a positive odd number squared, with a corresponding definite thickness, the material can achieve impedance matching. With the parameters data in the available references, the solution is verified to be effective.