Theoretical study of surface wave characteristics of a circular cyclindrical conductor coated with 2 graded dielectric layers embeoded in isotropic & anisotropic media

Abstract

The study investigates a cylindrical conductor coated with two dielectric layers, both having radially varying dielectric constants, and the external medium being lossless, either:

(a) Isotropic, or (b) Anisotropic

The dielectric constant ?(S)\varepsilon(S)?(S) is assumed to vary according to the following radial profiles:

?(S)=?0[1?(dS)2]\varepsilon(S) = \varepsilon_0 [1 - (dS)^2]?(S)=?0?[1?(dS)2] ?(S)=?0[1?(dS)]\varepsilon(S) = \varepsilon_0 [1 - (dS)]?(S)=?0?[1?(dS)] ?(S)=?0?sech2(dS)\varepsilon(S) = \varepsilon_0 \, \text{sech}^2(dS)?(S)=?0?sech2(dS) ?(S)=?0exp?(?dS)\varepsilon(S) = \varepsilon_0 \exp(-dS)?(S)=?0?exp(?dS)

where:

ddd = inhomogeneity factor SSS = radial distance from the center of the structure

All cases have been considered for both isotropic and anisotropic external media.

Summary of Analysis 2.1 Wave Equations in Different Media For the three regions shown in Fig. 1, the wave equations are: ?2E+k2?(S)E=0\nabla^2 E + k^2 \varepsilon(S) E = 0?2E+k2?(S)E=0 When both dielectric layers are graded, the equation becomes: d2EdS2+1SdEdS+k2?(S)E=0\frac{d^2 E}{dS^2} + \frac{1}{S} \frac{dE}{dS} + k^2 \varepsilon(S) E = 0dS2d2E?+S1?dSdE?+k2?(S)E=0 For homogeneous dielectrics, this reduces to: d2EdS2+1SdEdS+k2?E=0\frac{d^2 E}{dS^2} + \frac{1}{S} \frac{dE}{dS} + k^2 \varepsilon E = 0dS2d2E?+S1?dSdE?+k2?E=0 Assuming slow variation of dielectric constant over one wavelength, approximate forms are derived for graded profiles.

Characteristic Equations Characteristic equations for different cases (single graded layer, both graded layers, and homogeneous layers) are derived using appropriate field components and boundary conditions. These involve Bessel functions and their derivatives for cylindrical geometry.

Attenuation Constant The attenuation constant (?\alpha?) is calculated for all cases using the power-loss method. Numerical computations provide:

Radial propagation constant Axial phase constant Phase velocity Guide wavelength Surface reactance Power division among media Attenuation in dB/m

(Figures comparing power division and attenuation constants for different cases are included in the thesis.)

Excitation of Surface Wave: Launching Efficiency The launching efficiency of the structure when excited by a circular symmetrical slot is calculated for all cases.

Conclusions

A conductor coated with two different dielectrics having radially varying dielectric constants generally gives improved transmission characteristics. Of all profiles studied, the fourth power profile yields the best characteristics (low attenuation and greater power concentration within dielectric layers). Anisotropy of the external medium significantly affects propagation characteristics. There exists an optimum ratio of slot radius to overall radius for maximum launching efficiency.

The results contribute to understanding the practical utility of cylindrical surface wave lines for transmitting microwave power.