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2.2 The true sense of Wavelength 33 From this calculation it is apparent is that, at 50Hz, we need to travel a very long way in order for the finite propagation speed of the signal to cause appreciable delays. However if the period of our signal was much shorter, i.e. if our signal varied much faster with time, then the distance over which such delays become appreciable would be considerably reduced, as we will see shortly. Now one may ask, "If we have a generator with a load at the end of it, what does it matter if the signal gets to it with a bit of delay? After all, that is inevitable because of the finite speed of propagation so what's the big deal?". Well, that is a very fair point and indeed if you have a pure sinusoid travelling down a power line, into some sort of load which is going to rectify your AC signal and turn it into DC then there is no problem. However, suppose that you have additional elements connected along your line and that the distance between such elements is of the order of 100's of kilometres as shown in Figure 2.2-4. Figure 2.2-4 Long Power Line with several elements connected In this case, at any instant in time, the phase offsets with respect to the signal generator are 45⁰ across the inductor, 90⁰ across the capacitor and 135⁰ across the resistor due to the finite speed of propagation of the signal alone. The inductor and the capacitor will also introduce phase changes themselves which in turn will take time to propagate to other components. This complicates circuit analysis considerably since the voltages across the various circuit elements are not cophasal. In a small electrical circuit instead, you would have distances of the order of meters between the elements and one may therefore assume that the signal propagates at infinite speed. This means that voltages appear 'instantly' across shunt elements and are cophasal which simplifies matters considerably. Let us stop for a moment and reflect on how we could avoid these problems. There are three things we could do: 1. Increase the speed of propagation 2. Decrease the frequency of the signal 3. Reduce the dimensions of our circuit Option 1 is clearly impossible, but the other two are possible to some extent. However, in a power line, you are unlikely to get this sort of scenario with components at such large distances between one another so there's no reason to worry. R L V S Power Line Power Line Power Line 750 km 750 km 750 km L C (2.2-1) Conquer Radio Frequency 33 www.cadence.com/go/awr