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CHAPTER 2 - Conveying Power at Radio Frequency 102 2.10 Extra bits As we have seen in previous sections, when a line is mismatched, the voltage at any point along it becomes the sum of incident and reflected voltages and a standing wave is created. We have also seen how the input impedance of the line (Figure 2.9-1) may be represented by equation (2.9-1) for any termination. In this section we will try to give an intuitive explanation as to why in equation (2.9-1), a trigonometric tangent is a suitable function to represent the line impedance. Let us consider the case of a line with characteristic impedance Ω terminated with a Ω load. Let us assume for simplicity that both signals propagate along our line at the speed of light. Incident and reflected voltages will each be moving at speed in opposite directions towards one another as shown in Figure 2.10-1. Figure 2.10-1 Incident, reflected, total voltages and standing wave along a mismatched line at t=0 s Figure 2.10-2 and Figure 2.10-3 show what happens along the line as time progresses. It is apparent that by the time point α goes past point β (Figure 2.10-3), a whole period of the incident voltage will have slid past a whole period of the reflected voltage. After such a time our total voltage waveform and hence its envelope will start repeating again. This means that the period of the standing wave is equal to the time it takes for α and β to reach the point where their paths cross. As shown in Figure 2.10-3, the instant in time at which this occurs is equal to half the period of incident and reflected voltages. A similar argument will hold true for the current. Since our impedance is ratio of voltage and current and since the envelopes of these quantities vary in a periodic manner with a period equal to half that of a sine or cosine, the trigonometric tangent, is ideally suited to represent such an impedance. α β t= 0s Conquer Radio Frequency 102 www.cadence.com/go/awr

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