Problem 3: A kossless transmission line exists between an amplifier and antenna

Question

Problem 3: A kossless transmission line exists between an amplifier and antenna in an Apple IPhone 4. The electrical length of the transmission line is 0.3 (310s of a wavelength) and is terminated with a complex load impedance as shown below. Find the reflection coefficient at the load, the SWR on the line, the reflection coefficient at the input of the line, and the input impedance to the line. Use the attached Smith Chart to demonstrate your understanding of this problem. Show all work for full credit. Note you do not need to know the frequency of the wave for this problem. I = 03A Zin Zo = 50

Explanation / Answer

Given, The electrical length of a lossless transmission line = 0.3 * wavelength

Z0 = 50 ohms;  ZL= (30 - 20 * i) ohms

The reflection coefficeint at the load is R= ( ZL - Z0) / (ZL + Z0 )= 0.343

SWR on the line is S = (1+ R ) / (1 - R) = 2.044;

Reflection coefficient at the input of line is ( ZL - Z0) / (ZL + Z0  ) * exp(- 2 * pi * 0.3) = 0.052

The input impedance of the line is Z0 * (( ZL + j * Z0 tan( 2 * pi * 0.3))/(Z0 + j * ZL tan( 2 * pi * 0.3)))

= 29.25 -18.68j ohms

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