Effect of Feedback on Noise MCQ Quiz - Objective Question with Answer for Effect of Feedback on Noise - Download Free PDF
Last updated on Apr 7, 2025
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Effect of Feedback on Noise Question 1:
For an LTI system in figure \(\rm x(s)\) is input and \(\rm y(s)\) is output. In order to nullify the effect of noise \(\rm N(s)\), the gain of the feed forward path \(\rm {G_e}\left( s \right)\) is
Answer (Detailed Solution Below)
\(\rm \frac{{s\left( {s + d} \right)\left( {s + b} \right)}}{{c\left( {s + a} \right)}}\)
Effect of Feedback on Noise Question 1 Detailed Solution
\(\rm \begin{array}{l} {\left. {\frac{{y\left( s \right)}}{{N\left( s \right)}}} \right|_{x\left( s \right) = 0}} = \frac{{1 - {G_e}\left( s \right).\frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}}}}{{1 + \frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}}}}\\ \rm {\left. {\frac{{y\left( s \right)}}{{x\left( s \right)}}} \right|_{N\left( s \right) = 0}} = \frac{{\frac{{c\left( {s + a} \right)}}{{s\left( {s + b} \right)\left( {s + d} \right)}}}}{{1 + \frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}}}}\\ \rm \therefore y\left( s \right) = \frac{{x\left( s \right).\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right) + \left( {s + a} \right)c}} + \frac{{1 - {G_e}\left( s \right)\frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}}.N\left( S \right)}}{{1 + \frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}}}} \end{array}\)
\(\rm N(s)\) term can be zero if \(\rm 1 - {G_e}\left( s \right)\frac{{\left( {s + a} \right)c}}{{s\left( {s + b} \right)\left( {s + d} \right)}} = 0\)
\(\rm {G_e}\left( s \right) = \frac{{s\left( {s + b} \right)\left( {s + d} \right)}}{{c\left( {s + a} \right)}}\)