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ECE311_W11_Hwk2_Solutions

ECE311_W11_Hwk2_Solutions - ECE 311 Homework 2 Solutions A...

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ECE 311 Homework 2 Solutions A 50— lossless transmission line is terminated in a load with impedance ZL = (30 j50) . The wavelength is 8 cm. Find: (a) the reflection coefficient at the load, (b) the standing-wave ratio on the line, (c) the position of the voltage maximum nearest the load, (d) the position of the current maximum nearest the load, Soutiou: (a) From r = = (30— j50) 50 = 0 57e’’ 795 Z+Z 5 (30—j50)+50 (b) From l+IF 1+0.57 1—0.57 =j.65. (c) From O? n?. _79.80 x 8 cm t rad n x 8cm lmax = + 2 = 4 igo° + 2 = —0.89 cm+4.0 cm = 3.11 cm. (d) A current maximum occurs at a voltage minimum, and from = —A/4 = 3.11 cm— 8 cm/4 = 1.11 cm.
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-A 5O- lossless line terminated in a purely resistive load has a voltage standing wave ratio of 3. Find all possible values of ZL. Sojution: S-l 3—I Il-,I = = = O.:. S+l 3+1 For a purely resistive load, 8 = 0 or it. For 8, = 0, ZLzo[[] =50{ j = l5O. For9, it, F = —0.5 arid Z 1 = 50 [Lz.j = 16.7
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A lossless transmission line of electrical length I = O.35) is terminated in a load impedance as shown. Find I’, S. and Z,. I I U.35. i ZL = (60 —j30) i Solution: From ZL—ZU = (60+j30)—100 =O307e- 325 ZL+Zs (60+j30)+ 100 From s I + FJ I + 0.307 i 89 1 —fl 1—0.307
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From (ZL+jZan1 = Zo+jZjtanl) ( (60+j30) + jlOO tan = 100 l (6O 3 O)(dO 35 )) = (64.8—j38.3)
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A voltage generator with 5 Q) 5cos(2it x lOot) V and internal impedance Z 5 = 50 is connected to a 50-Q lossless air-spaced transmission line.
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