GATE 2023 EC – Question 52
The standing wave ratio on a 50 Ω lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance $R_m$ of the same line. The value of $R_m$ and $l_m$, respectively, are
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Correct answer: (B) $R_m=25\ \Omega,\ l_m=20$ cm; (C) $R_m=100\ \Omega,\ l_m=5$ cm
Explanation
Successive minima are $\lambda/2=30$ cm apart, so $\lambda=60$ cm. The first minimum is 10 cm from the load, i.e. $\lambda/6$. Beyond the load the pattern continues: a voltage maximum (impedance $Z_0S=100\ \Omega$) lies $\lambda/4=15$ cm from a minimum, i.e. $15-10=5$ cm beyond the load: $R_m=100\ \Omega$, $l_m=5$ cm (option C). The next minimum (impedance $Z_0/S=25\ \Omega$) lies $30-10=20$ cm beyond the load: $R_m=25\ \Omega$, $l_m=20$ cm (option B). Both give the same standing-wave pattern on the load side.