Name: Page 3 Problem 2. (28 points) A lossless TL of length 1.1 and characterist

Question

Name: Page 3 Problem 2. (28 points) A lossless TL of length 1.1 and characteristic impedance 50 (S) is connected to a load with impedance of 30-j10 (). Use attached Smith chart to find (1) SWR, (2) the voltage reflection coefficient, (3) the input impedance, (4) the location of the first voltage minimum, (5) the location of the first voltage maximum, (6) the total number of voltage minima, and (7) the total number of voltage maxima. Write vour steps on this page to get those answers.] Write your steps. on this page to sct those answers. Write your steps on this nage to get th

Explanation / Answer

Refer to Fig. P2.53. The normalized impedance zL = (50+ j25) 50 = 1+ j0.5 is at point Z-LOAD. (a) = 0.24e j76.0 The angle of the reflection coefficient is read of that scale at the point r

. (b) At the point SWR: S = 1.64.

(c) Zin is 0.350 from the load, which is at 0.144 on the wavelengths to generator scale. So point Z-IN is at 0.144 + 0.350 = 0.494 on the WTG scale.

At point Z-IN: Zin = zinZ0 = (0.61 j0.022)×50 = (30.5 j1.09) .

(d) At the point on the SWR circle opposite Z-IN, Yin = yin Z0 = (1.64+ j0.06) 50 = (32.7+ j1.17) mS.

(e) Traveling from the point Z-LOAD in the direction of the generator (clockwise), the SWR circle crosses the xL = 0 line first at the point SWR. To travel from Z-LOAD to SWR one must travel 0.250 0.144 = 0.106. (Readings are on the wavelengths to generator scale.) So the shortest line length would be 0.106.

(f) The voltage max occurs at point SWR. From the previous part, this occurs at z = 0.106

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