Discussion
A transmission line having 50 \(\Omega\) impedance is transmitted to a load of (40 + j 30) ohms. The VSWR is
Answer: C
The VSWR is 2. First find the reflection coefficient of the load, with \(Z_0 = 50\ \Omega\) and \(Z_L = 40 + j30\ \Omega\):
\[ \Gamma = \frac{Z_L - Z_0}{Z_L + Z_0} \]
\[ \Gamma = \frac{-10 + j30}{90 + j30} \]
\[ |\Gamma| = \frac{\sqrt{10^2 + 30^2}}{\sqrt{90^2 + 30^2}} \]
\[ |\Gamma| = \frac{\sqrt{1000}}{\sqrt{9000}} = \frac{1}{3} \]
\[ \text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|} \]
\[ \text{VSWR} = \frac{4/3}{2/3} = 2 \]
The options j 0.033 and 0.8 + j 0.6 are complex numbers, but a VSWR is a real ratio, never less than 1, so they cannot be right. A VSWR of 1 would mean a perfectly matched load, which would need \(Z_L = 50\ \Omega\). The answer is 2.
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