GATE EC 2014 Set 3 — Question 35
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Electromagnetics → Transmission Lines → Input Impedance & Reflection
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Question
In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx. The output impedance of Tx, the characteristic impedance of the cable and the input impedance of Rx are all real.
Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?
Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?
Correct answer
(C) Signal distortion implies impedance mismatch at both ends: Z_T ≠ Z₀ and Z_R ≠ Z₀.
Solution
On a line with real impedances, a mismatch produces reflections with coefficients
- If only the receiver is mismatched (, ): part of the wave reflects at Rx, travels back and is fully absorbed by the matched source. The receiver sees only a scaled copy of the incident wave, so the received signal is attenuated but not distorted. Hence (A) is false.
- If only the transmitter is mismatched (, ): no reflection is generated at Rx at all, so nothing returns to Tx; the source mismatch only changes the launched amplitude. Again no distortion, so (B) is false.
- If both ends are mismatched: the wave reflected at Rx is re-reflected at Tx and arrives at Rx again after a round-trip delay , and so on. The received signal is the sum of delayed, scaled copies (echoes). For a wideband signal these echoes produce a frequency-dependent response, i.e. distortion. So distortion implies and : (C) is true.
- (D) is false because, as just shown, mismatch at both ends does cause distortion.
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