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CHAPTER 2 - Conveying Power at Radio Frequency 58 2.5.2 Line terminated with a short circuit 2.5.2.1 Circuital Approach 2.5.2.1.1 Voltage Pulse In this section we will be looking at what happens along a short-circuited line when a pulse stimulus is applied (Figure 2.5-28). In order for this behaviour to be observed in sufficient details, the pulse width must be lower than the time it takes a signal to travel to the end of the line at the speed allowed by the transmission line. Figure 2.5-28 Short-circuited line with pulse stimulus As in the case of the open-circuit, let us assume that the battery in this circuit has an internal impedance Z s equal to the characteristic impedance of the transmission line Z 0 and that the capacitors in the line are not charged before the switch is closed. When the switch is closed, a voltage wave starts making its way down the transmission line at the speed of propagation characteristic of the line (eq. (2.3-2)). This is shown in Figure 2.5-29 and Figure 2.5-30. Figure 2.5-29 Pulse travelling down the line Since Z s = Z 0 , one-half of the applied voltage (E/2) will appear across the internal battery impedance, Z s , and one-half across the impedance of the line, Z 0 . This voltage wave applies a potential of E/2 across the first inductor-capacitor section and hence a current I flows through the inductor to charge the respective capacitor up to a voltage equal to E/2 volts. This is again shown in Figure 2.5-29. Once the first capacitor is charged, no further current will flow through it and, as the voltage wave advances, the current I will flow through the second inductor to charge the second capacitor up to a E/2 volts (Figure 2.5-30). E Z s E/2 E I E/2 Zero Z s + Conquer Radio Frequency 58 www.cadence.com/go/awr

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