Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 253

Figure (5.17a) shows the obliquely incident wave on a conductor backed lossy DNG slab. The angle of refraction is negative. The incident wave could be either TE or TM‐polarized discussed in section (5.2). Following the results of equations (5.2.8c) and (5.2.16c) the reflection coefficients of both polarizations could be written as follows:

(5.5.46)

where θ_i = θ is the angle of incidence, is the refractive index of a DNG slab and (μ_r, ε_r) are material parameters of the DNG medium. The reflectivity for the incident TE and TM‐polarized waves is defined as and . In the case of normal incidence θ = 0^∘, the above results provide the following expression for reflectivity:

(5.5.47)

To get no reflection, i.e. for R^nor = 0, the material parameters are n = ε_r, i. e. μ_r = ε_r. Thus, the DNG slab is impedance matched i.e. . The transmission coefficient τ^nor and transmissivity T^nor of a normally incident wave on the impedance matched DNG slab is obtained from equation (5.4.15):

(5.5.48)

The condition 2n^″k₀d_min = 1 provides the minimum propagation depth to attenuate the absorbed RF power to 1/e:

(5.5.49)

The conductor backing reflects the attenuated EM‐wave that gets further attenuated by 1/e before appearing as the reflected wave from the air‐DNG interface. It degrades the absorption of the absorbing slab. An expression for the reflection coefficient is available, using the theory of multiple reflections [J.29]. However, for a thicker slab, multiple reflections can be ignored and simpler expression can be used to get the absorptivity of an absorber:

(5.5.50)