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Problem 6: As discussed in class, a T-junction 2-way splitter is always mismatched, and this is bad at 50-500 MHz since it creates a reflected wave and ghost images in TV receptions. To solve this problem, a low-cost splitter is used which results in a wideband matched T-junction at the expense of some loss in the network.
Zin = Zo matched-T
R
Z
Zo 1
R WW
R
3
TV Splitter
Z = 75 for TV applications. All t-line lengths are zero.)
a) Calculate R so as to result in Zin = Zo - a matched-T network - at all ports. You can do this using circuit/nodal analysis. This means that you need to find the value of R such that the input impedance seen by Port 1 or Port 2 or Port 3 is Zo. Do this using standard nodal analysis. What is the reflection coefficient at Port 1 or Port 2 or Port 3?
b) Calculate the power loss in the splitter with the value of R obtained in part a. Do this using a combination of circuit and wave analysis. First, calculate the input power to the splitter V(rms = 1 V), and then calculate the power delivered to Zo at Port 2 and Port 3 (once you know the voltage at node 2 using circuit analysis, you know the power. In fact, this shows you that with lumped element networks, it is best to use circuit analysis).
c) What happens if an open circuit occurs at Port 2 instead of Zo? Calculate the new input reflection coefficient and the reflected power at Port 1 (you can also get the impedances using circuit/nodal analysis). What is the power delivered to Ports 2 and 3? Calculate all the voltage waves shown in the figure.
d) What happens if the load at Port 2 is now Zo/2? Repeat part c.