Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 203

Both the unbounded medium and transmission line supports the 1D wave propagation. So an unbounded medium could be easily modeled, shown in Fig (5.1b), as a transmission line. The propagation constant of wave on the equivalent transmission line could be treated as identical to that of in the medium. This approach is simple and effective in obtaining the impedance transformation and also impedance matching by using the multilayer dielectric medium. On comparing the wave equations for the E_y (x) and H_z (x), given in equation (4.5.13) of chapter 4, against the voltage and current wave equation (2.1.37) of chapter 2, the following equivalences are observed:

(5.1.14)

The solution of the voltage and current waves, given in equations (2.1.63) and (2.1.64), can be converted to the solution of E_y and H_z. Finally, the expression of the input impedance of a lossless line of length d, given in equation (2.2.65) of chapter 2, terminated in a load Z_L, helps to write the following expression of the input impedance of a dielectric slab of thickness d; and also the expressions for the reflection coefficient, and transmission coefficient at the interface PQ:

Figure 5.1 Normal incidence of TM‐polarized plane wave at the interface of two media.

(5.1.15)

In expression (5.1.15), medium #2 has an infinite extent. In medium #1, the incident wave is located at a distance d from the interface. The transmission line model is used for the multilayer dielectric medium also [B.1–B.4].