Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 160

The medium in which the EM‐wave propagates with equal phase velocity at all frequencies is called the nondispersive medium. For such a medium, the relative permittivity and relative permeability are real quantities, and they are independent of frequency. However, practically every material medium has losses; and thus their relative permittivity and relative permeability are complex quantities, and these are a function of frequency. Thus, normally a material medium supports frequency‐dependent phase velocity. Such a medium is called the dispersive medium. This kind of dispersion is known as material dispersion [B.2, B.3, B.9, B.10]. The material dispersion in the microwave and the mm‐wave ranges is normally negligible for the substrates used in the planar technology. However, a composite substrate, made of the layered dielectric media, is dispersive. Likewise, the artificial metamaterial substrate is also dispersive. The plasma and conducting media are also dispersive in the microwave range. The material dispersion is an important phenomenon near the optical frequency. The constitutive relation for the dispersive medium is

Figure 4.5 Classification of bianisotropic and bi‐isotropic materials.

(4.2.17)

Lorentz oscillator model of a dielectric material, discussed in section (6.5) of chapter 6, helps to understand the frequency‐dependent origin of the ε(ω). When an EM‐pulse, like a Gaussian pulse, passes through a dispersive medium, its pulse‐width widens due to the separation of different frequency components, as each frequency component travels at a different velocity in the dispersive medium. This is known as the pulse‐spreading phenomenon. It limits the speed of digital data transmission through the dispersive medium, as the digital bits can overlap each other. However, a dispersive medium can be nonlinear also, where the pulse spreading can be balanced by the nonlinearity. Under such combined dispersion, and nonlinearity, a pulse can propagate without changing its shape. Such robust EM‐waves are called the solitons. The solitons are useful in optical communication. However, the solitons have also been generated in the microwaves frequency range