Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 129

A complex signal composed of two or more frequency components forms a wave‐packet. However, the frequency components should not be much different from each other like an amplitude modulated signal. Figure (3.23) shows the wave‐packet formed by a group of a narrowband complex signal. The wave‐packet has a central or a carrier frequency of higher value, superimposed with a low‐frequency envelope. The carrier wave travels with the phase velocity v_p, whereas the envelope, i.e. the wave shape travels with the group velocity v_g. In a nondispersive medium, the carrier wave and envelope both travel with the same velocity without a change in the waveshape. However, in the case of a dispersive medium, velocities of the carrier and envelope are different. Depending on the nature of dispersion, the wave could be the forward wave or the backward wave. If the medium has normal (positive) dispersion, the phase velocity, i.e. the velocity of the carrier wave, and the velocity of the envelope, i.e. the group velocity, are in the same direction, as shown in Fig (3.23). The wave is known as the forward wave. However, in the case of a highly anomalous (negative) dispersive medium, under a certain condition, the phase and group velocities are in the opposite directions, forming the backward wave.

Figure 3.23 Description of phase and group velocities of a forward‐moving modulated wave.

The carrier and envelope are combined to form a unified wave structure called the wave‐packet. In the case of normal dispersion, the group velocity is the energy velocity of a signal and the information travels with the group velocity [B.1, B.4, B.5, B.7, B.14, B.16]. However, in the case of anomalous dispersion, the energy velocity and group velocity are different. In this case, group velocity is not velocity of information. Moreover, the concept of group velocity applies only to a narrow‐band wave‐packet, not to the wideband signal. The controversy exists at present on the travel of information with a velocity more than the velocity of light [J.7].