Question

As shown in the figure, a negative feddback system has an amplifier of gain $100$ with $\pm 10\%$ tolerance in the forward path, and an attenuator of value $9/100$ in the feedback path. The overall system gain is approximately:

• A. $10\pm 1\%$
• B. $10\pm 2\%$
• C. $10\pm 5\%$
• D. $10\pm 10\%$

Answer 1

The correct option is A $10\pm 1\%$

$G=100\pm 10\%$

$\frac{\Delta G}{G}=10\%or0.1$

$H=\frac{9}{100}$

Overall gain,

$T=\frac{G}{1+GH}$

$T=\frac{100}{1+100\times 9/100}=10$

Sensitivity w.r.t 'G' $=\frac{1}{1+GH}\times 10$

$=\frac{1}{1+10\times 1}\times 10\%=\frac{10}{11}\equiv 1\%$

$\therefore$ Overall system gain $=10\pm 1\%$