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

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The discussion revolves around solving a problem involving a lossless transmission line with a characteristic impedance of 300 ohms, terminated in a load impedance of 35 + j 25 ohms. The input impedance calculated using the Smith chart is 1860 - j1350 ohms, and the standing wave ratio (SWR) is determined to be 9.5. The participant struggles with calculating the input power, initially estimating it at 54.6875W based on load current, but expresses uncertainty about the accuracy of their calculations. They provide detailed voltage and current equations but question whether their results are correct. The overall focus is on using the Smith chart to derive key parameters of the transmission line.
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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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