CHAPTER 2 - Conveying Power at Radio Frequency
62
2.5.2.1.2 Voltage Step
In this section we will be using the transmission line model shown in Figure 2.5-38. The
voltage stimulus is a DC step, created by closing the switch at time t=0s.
Figure 2.5-38 Lumped model of a short-circuited transmission line
As in previous cases, as the switch is closed, our voltage wave starts travelling down the line at the
speed of propagation characteristic of the line as shown in Figure 2.5-39.
Figure 2.5-39 The switch is closed and the voltage wave starts propagating down the transmission 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 2.5-39.
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 2.5-40).
Figure 2.5-40 As the voltage wave advances, it charges up the second capacitor
E
Z
s
E/2
E
I
E/2
Zero
Z
s
E
E/2
I
E/2 E/2
Conquer Radio Frequency
62 www.cadence.com/go/awr
