16-11-2012, 05:45 PM
Transmission Lines
TransmissionLines.ppt (Size: 1.88 MB / Downloads: 379)
Points to Remember
In this chapter we have surveyed several different types of waves on transmission lines. It is important that these different cases not be confused. When approaching a transmission-line problem, the student should begin by asking, “Are the waves in this problem sinusoidal, or rectangular pulses? Is the line ideal, or does it have losses?” Then the proper approach to the problem can be taken.
The ideal lossless line supports waves of any shape (sinusoidal or non-sinusoidal), and transmits them without distortion. The velocity of these waves is . The ratio of the voltage to current is , provided that only one wave is present. Sinusoidal waves are treated using phasor analysis. (A common error is that of attempting to analyze non-sinusoidal waves with phasors. Beware! This makes no sense at all.)
When the line contains series resistance and or shunt conductance it is said to be lossy. Lossy lines no longer exhibit undistorted propagation; hence a rectangular pulse launched on such a line will not remain rectangular, instead evolving into irregular, messy shapes. However, sinusoidal waves, because of their unique mathematical properties, do continue to be sinusoidal on lossy lines. The presence of losses changes the velocity of propagation and causes the wave to be attenuated (become smaller) as it travels.
For lines other than the simple ideal lossless lines, the velocity of propagation usually is a function of frequency. This velocity, the speed of voltage maxima on the line, is properly called the phase velocity Up. The change of Up with frequency is called dispersion. The velocity with which information travels on the line is not Up, but a different velocity, known as the group velocity . The phase velocity is given by . However
Examples of non-sinusoidal waves are short rectangular pulses, and also infinitely long rectangular pulses, which are the same as step functions. Problems involving sudden voltage steps differ from sinusoidal problems, just as in ordinary circuits, problems involving transients differ from the sinusoidal steady state. Pulse problems are usually approached by superposition; that is, one tracks the pulses that propagate back and forth, adding up the waves to obtain the total voltage at any place and time.