P2.20 Assume in example 2.8 that the transmission line on the right is 1.5 times as long as the transmission line on the left. Draw a lattice diagram of the circuit and sketch the voltage at the open-circuit loads of both lines. Is the voltage better behaved in this case than it was in problem 2.19? Example 2.8 As was done in the previous example, we perform a detailed analysis of the series terminated connection driving the two lines shown in figure 2.25. At time zero the step source sends out a voltage V/2 on both lines, as shown in the lattice diagram of figure 2.26. To get a better understanding of the sequence of events, we will concentrate our attention on the left line. The incident voltage gets reflected at the left open circuit and arrives at the interface AA ′ . Looking to the right this wave sees an impedance of [30+10∥(30+50)]=38.9Ω. This impedance produces a reflection coefficient of −1/8 and a transmission coefficient of 7/8 at AA ′ . The voltage that gets reflected is therefore −V/16 and the voltage that is transmitted to the network to the right of AA ′ is V AA ′ ​ =7 V/16. In going from AA ′ to BB ′ , the transmitted signal is attenuated by the factor V AA ′V BB ′ = 30+10∥(30+50) 10∥(30+50) ⋅ 30+5050​ = 71​
Figure 2.25 Two lines terminated in series according to the second option. igure 2.26 Lattice diagram for the circuit of figure 2.25.