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?
Correct answer
(C) Signal distortion implies impedance mismatch at both ends: Z_T ≠ Z₀ and Z_R ≠ Z₀.
Solution
For a wideband signal transmitted over a coaxial cable (transmission line), signal distortion occurs due to reflections caused by impedance mismatches.
1.Reflection at the Load (Receiver): A reflection occurs at the load if the load impedance does not match the characteristic impedance of the cable . The reflection coefficient at the load is given by . If , then , and a portion of the signal is reflected back towards the transmitter.
2.Distortion: This reflected signal travels back and can interfere with the forward-traveling signal. For a wideband signal, which is composed of many frequency components, this reflection causes delayed versions of the signal to superimpose on the original signal at the receiver. This phenomenon is known as inter-symbol interference (ISI) in digital communication and is a form of signal distortion.
3.Role of Source Impedance: The impedance at the source, , affects what happens to the signal that is reflected from the load. If , the backward-traveling reflected signal will be re-reflected at the source and travel again towards the load, causing further distortion. However, the initial and primary cause of distortion is the reflection at the load.
Let's analyze the options:- (A) The signal gets distorted if , irrespective of the value of . This is correct. If there is a mismatch at the load (), reflections will occur, leading to distortion. This happens regardless of whether the source is matched or not. A matched source () would absorb the reflected wave and prevent further re-reflections, but the initial distortion from the first reflection still occurs.
- (B) The signal gets distorted if , irrespective of the value of . This is incorrect. If the load is perfectly matched (), the entire signal is absorbed by the load, and there is no reflection. Without a reflection from the load, there is no backward-traveling wave to cause distortion, even if the source is mismatched.
- (C) Signal distortion implies impedance mismatch at both ends: and . This is incorrect. Distortion occurs as long as there is a mismatch at the load end (). A mismatch at the source end is not a necessary condition for distortion to begin.
- (D) Impedance mismatches do NOT result in signal distortion but reduce power transfer efficiency. This is incorrect. While impedance mismatches do reduce power transfer, they are a primary cause of signal distortion for wideband signals due to reflections and the resulting ISI.
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