1 EE172 Homework 3 2.16 A load impedance of ZL = 80 + j20 Ω is to be matched to a Zo=100 Ω line using a length l lossless line of characteristic impedance Z1. Find the required Z1 (real) and l. 2.23 Design a quarter-wave matching transformer to match a 40 Ω load to a 75 Ω line. Plot the SWR for 0.5 ≤ f/fo ≤ 2.0, where fo is the frequency at which the line is λ/4 long. 4.2 Consider the reflection of a TE10 mode, incident from z < 0, at a step change in the height of a rectangular waveguide, as shown below. Show that if the method of Example 4.2 is used, the result Γ = 0 is obtained. Do you think this is the correct solution? Why? (This problem shows that the one-mode impedance viewpoint does not always provide a correct analysis.) 4.7 Derive the [Z] and [Y] matrices for the two-port networks shown below. 4.8 Consider a two-port network, and let Z, Z , Z , Z be the input impedance seen when port 2 is short-circuited, when port 1 is short-circuited, when port 2 is open-circuited and when port 1 is open-circuited, respectively. Show that the impedance matrix elements are given by Z11 = Z , Z22 = Z , Z = Z = (Z − Z )Z b/2 z y x b a z = 0 (a) (b) ZB ZA ZA Port 1 Port 2 YA YA YB Port 1 Port 22 Additional Problem. L = 27.7 nH C1 = 2.716 pF C2 =1.057 pF C3 =2.014 pF C4 =2.094 pF C12 =1.508 pF C23 =0.243 pF C34 =0.2034 pF Plot |S11|, |S12| in dB vs. 800 ≤ f ≤ 1000 MHz. C12 C23 C34 C4 C1 C2 C3 C3 C4 C3 C3 C23 C1 C2 C12 L L L
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