Impedance matching for the multilayer medium - toward a design methodology

Trilayered Gires–Tournois Resonator with Ultrasensitive Slow-Light Condition for Colorimetric Detection of Bioparticles

“…In the equivalent transmission line model of the trilayer system, outlined in the following equations, and are the input impedances of the lossy medium and the low RI medium, respectively. The lossy medium is converted to a transmission with impedances of (= ; ) [ 42 ], where n l and k l are the complex RIs of the lossy medium. …”

Prediction of Microwave Absorption Behavior of Grading Honeycomb Composites Based on Effective Permittivity Formulas

“…The ideal design of PIG is to pave a path from R = 1 to 0 by stacking grading impedance layers on the metal plate, then a connection between metal background and air surface is set moderately. For the use of impedance layer with large ε and small ε , μ , and μ , the differentiating R with respect to z can be depicted by [16] …”

“…Then, the reflection and transmission properties can be predicted and manipulated by multilayer impedance matching [16], [17]. The multilayer system studied consists of N homogeneous layers characterized by thickness d n , permittivity ε eff_n , and permeability μ eff_n , as shown in Fig.…”

The Intersection of Computational Design and Wearable‐Optimized Electrospun Structural Nanohybrids for Electromagnetic Absorption

“…and 𝜖 0 ≈8.85 × 10 −12 F m −1 are the intrinsic impedance, permeability, and permittivity of free space, respectively). [30] Therefore, R is proportional to the mismatch between Z out and the input impedance (Z in ) (i.e., the opposition to current flow in the transmission line) as: [29,31,32]…”

“…[ 22,29 ] Since the wave impedance approaches the intrinsic impedance of the homogeneous medium that the wave propagates through, in the case of free space Z out = Z 0 = η 0 = $$\sqrt {{\mu }_0/{\varepsilon }_0} $$ = 377 Ω ( Z 0 , μ 0 = 4 π × 10 −7 H m −1 , and ε 0 ≈8.85 × 10 −12 F m −1 are the intrinsic impedance, permeability, and permittivity of free space, respectively). [ 30 ] Therefore, R is proportional to the mismatch between Z out and the input impedance ( Z in ) (i.e., the opposition to current flow in the transmission line) as: [ 29,31,32 ] $$$$\begin{equation}R\ = {{{\Gamma}}}^2\ = \left( {\frac{{{Z}_{in} - {Z}_{out}}}{{{Z}_{in} + {Z}_{out}}}} \right){\ }^2\end{equation}$$$$where Γ is the reflection coefficient. Z in at the front surface of the assumed transmission line composed of i impedance elements can be calculated as: $$$$\begin{equation}{Z}_i = {\eta }_i\ \frac{{{Z}_{i - 1} + {\eta }_i\tanh \left( {{\gamma }_{i} \ell_{i}} \right)}}{{{\eta }_i + {Z}_{i - 1}\tanh \left( {{\gamma }_{i} \ell_{i}} \right)}}\end{equation}$$$$…”