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Q. Define waves and transmission lines?
In basic circuit theory we neglect the effects of the finite time of transit of changes in current and voltage and the finite distances over which these changes occur. We assume that changes occur simultaneously at all points in the circuits. But there are situations in which we must consider the finite time it takes for an electrical or magnetic wave to travel and the distance it will travel. It is in these situations that one must employ traveling-wave theory. Traveling-wave concepts must be used whenever the distance is so great or the frequency so high that it takes an appreciable portion of a cycle for the wave to travel the distance.
For sinusoidal signals, a wavelength λ is defined as the distance that a wave travels in one cycle or period. Since electric waves in free space travel at the velocity of light c(≅ 3×108 m/s), the free-space wavelength is given by c/f. Table shows some free-space wavelengths at selected frequencies. If the traveling-wave technique is to be employed for distances greater than 1/10 wavelength, a distance of 3 mm at 10 GHz would require the use of this technique, whereas the same distance at 100 MHz would not. On the other hand, a distance of 1 km is insignificant at power-line frequencies, but not in the broadcast band.
The connection of the high-power output of a transmitter located on a building to the transmitting antenna on a tower is often made by special conductors called transmission lines, which guide thewaves and usually consist of two ormore parallel conductors,which are separated by insulating (dielectric) materials.While transmission lines are available in many forms, Figure illustrates cross sections of some common types. The two-wire line of Figure (a) isused to connect some television antennas. The coaxial cable of Figure (b) is themost widely used of the many possible cable-type transmission lines. For printed-circuit and integrated-circuit applications, transmission lines sketched in Figures (c) through (f) are commonly employed.
Q. On a per-phase basis, let v = √2 V cos ωt and i = √2 I cos (ωt - θ). (a) Express the instantaneous power s(t) in terms of real power P and reactive power Q. (b) Now consid
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