The propagation of signals along a three-layered region: microstrip

The tangential components of the electric field on the air-substrate surface of a three-layered region such as microstrip are determined for the case when the source is a unit electric dipole on that surface. This is done by integrating the rigorous Hankel transforms subject to the condition k²₀<|k ²₁|≪|k²₂|, where k₀ is the wavenumber of air, k₁ of the substrate, and k₂ of the conductor. It is found that the field consists of lateral-wave terms and direct-wave terms with different wavenumbers and phase velocities with each term consisting of two components. These terms determine the coupling between vertical currents in connections from the air surface to the conducting plane. It is concluded that distortion of signals as they propagate along the surface of microstrip is not due to dispersion in the ordinary sense that the permittivities of the air or the substrate are frequency-dependent; rather it is due to the fact that each signal separates into two parts, the one traveling in the air, the other in the dielectric with different phase velocities. If the permittivity of the substrate is frequency-dependent, the part of the signal traveling in it will suffer dispersion; the lateral-wave part in the air will not