Question

An amplifier has an open loop voltage gain of -500. This gain is reduced to -100 when negative feedback is applied. The reverse transmission factor, \( \beta \), of the system is

• A. \( 0.008 \)
• B. \( -0.025 \)
• C. \( 0.1 \)
• D. \( -0.2 \)

Hint:

In feedback amplifier problems, use the formula: \[ A_f = \frac{A}{1 + A\beta} \] Always keep signs of gain values in mind while simplifying equations, but for identifying feedback strength, the magnitude of \( \beta \) is usually sufficient.

Answer 1

The Correct Option is A

The gain with negative feedback is given by:\[ A_f = \frac{A}{1 + A\beta} \]Where:\( A = -500 \)is the open-loop gain,\( A_f = -100 \)is the gain with feedback,\( \beta \)is the feedback factor.Substituting the known values:\[ -100 = \frac{-500}{1 + (-500)\beta} \]Multiply both sides by the denominator:\[ -100(1 - 500\beta) = -500 \]\[ -100 + 50000\beta = -500 \]\[ 50000\beta = -500 + 100 = -400 \]\[ \beta = \frac{-400}{50000} = -0.008 \]Since\( \beta \)is a feedback factor (magnitude is what matters here),\[ \boxed{|\beta| = 0.008} \]Thus, the correct option is\( \boxed{0.008} \).