Solve Smith Chart Q: Input Imp, SWR, Load Pwr

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SUMMARY

The discussion focuses on solving a transmission line problem using the Smith Chart, specifically for a lossless transmission line with a characteristic impedance of Z0 = 300 ohms and a load impedance of ZL = 35 + j 25 ohms. The input impedance was calculated as Zin = 1860 - j1350 ohms, and the standing wave ratio (SWR) was determined to be 9.5. Additionally, the input power to the line was estimated to be approximately 54.69W based on the load current of 1A and the load power of 35W.

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Homework Statement


A lossless transmission line has a characteristic impedance Z0 = 300 ohms, is 5.3 wavelength long, and is terminated in a load impedance ZL = 35 + j 25 (ohms). Find the following using Smith chart.

a) The input impedance on the line
b) The standing wave ration on the main line.
c)If the load current is 1A, calculate the input power to the line.


Homework Equations





The Attempt at a Solution



a) Zin = 300(6.2 - j4.5) = 1860 - j1350 (ohms)
b) swr = 9.5
c) I am not finding a good equation to calculate part C and not sure how you can extract this information from the chart. P= i^2 R => 35W to the load then the input would need to be 35 /0.8^2= 54.6875W
 
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So i can get VL = 35+j25(V)

Vl = V0+(1+gamma)
35+j25/(1.8)
V0+ = 19.44+j13.89(v)

Vin = V0+(exp(-j0.6pi) + 0.8exp(j0.6pi))
Vin = 18.89+j13.70

Iin = Vo+/Zo(exp(-j0.6pi) - 0.8exp(j0.6pi)
Iin = -1.12-j33.29
Iin* = -1.12+j33.29Pav = 0.5*Re(VI*)
1/2*Re(VinIin*)
then i get -242W (this does not seem correct)

Am i getting close?
 

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