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CHAPTER 2 - Conveying Power at Radio Frequency 46 2.5 Reflection of DC voltage in Transmission lines In this section we will be looking at what happens when we apply DC voltage steps and pulses to open and short-circuited transmission lines. Firstly we will be using a lumped model for the transmission line which uses lumped equivalents to represent the distributed inductance and capacitance along the line (Figure 2.3-4), but for simplicity we will consolidate the inductance in the top and bottom wires into one (Figure 2.5-1). The reader must bear in mind however that the phenomena are still happening along a distributed capacitance and inductance, and that we only use this model because we do not know how to draw the distributed case. Also losses are assumed to be negligible throughout this section. Subsequently we will be looking at what happens at a more physical level, and charge dynamics as well electromagnetic transients will be illustrated. 2.5.1 Line Terminated with an open circuit 2.5.1.1 Circuital Approach 2.5.1.1.1 Voltage Step In this section we will be using the transmission line model shown in Figure 2.5-1. The voltage stimulus is a DC step, created by closing the switch at time t=0s. Figure 2.5-1 Lumped model of open circuited transmission line 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 , that the capacitors in the line are not charged before the switch is closed and, since the line is open-ended, that the terminating impedance is infinitely large. 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. (2.3-3)). This is shown in Figure 2.5-2. Conquer Radio Frequency 46 www.cadence.com/go/awr

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