Consider series-shunt amplifier in which the open loop gain is Av= 105...
The ideal closed-loop voltage transfer function

The input resistance

The output resistance is

View all questions of this testConsider series-shunt amplifier in which the open loop gain is Av= 105...
Ω and Ro= 100 Ω respectively. Determine the values of the feedback resistor Rf and the shunt resistor Rs.
We can use the formula for closed loop gain in a series-shunt amplifier:
AVf = Av / (1 + Av*(Rs/Ri) + (Rs/Ro) + (Rs/Rf))
Substituting the given values:
50 = 105 / (1 + 105*(Rs/10kΩ) + (Rs/100Ω) + (Rs/Rf))
Simplifying:
50 = 105 / (1 + 10.5*(Rs/10kΩ) + (Rs/1000Ω) + (Rs/Rf))
Multiplying both sides by the denominator:
1 + 10.5*(Rs/10kΩ) + (Rs/1000Ω) + (Rs/Rf) = 2.1
Subtracting 1 from both sides:
10.5*(Rs/10kΩ) + (Rs/1000Ω) + (Rs/Rf) = 1.1
We have one equation with two variables, so we need another equation. We know that the feedback network should provide a feedback factor of β = AVf / Av = 50 / 105 = 0.476. We can use the formula for the feedback factor in a series-shunt amplifier:
β = (Rs / (Rs + Ri)) * (Rf / (Rf + Ro))
Substituting the given values:
0.476 = (Rs / (Rs + 10kΩ)) * (Rf / (Rf + 100Ω))
Simplifying:
0.476 = (Rs / (Rs + 10kΩ)) * (Rf / (Rf + 100Ω))
Multiplying both sides by the denominators:
0.476 * (Rs + 10kΩ) * (Rf + 100Ω) = Rs * Rf
Expanding:
0.476 * Rs * Rf + 0.0476 * Rs * 100Ω + 0.476 * 10kΩ * Rf + 0.0476 * 10kΩ * 100Ω = Rs * Rf
Simplifying:
0.4292 * Rs * Rf + 476Ω * Rs + 4.76MΩ * Rf + 476kΩ = Rs * Rf
Subtracting 476kΩ from both sides:
0.4292 * Rs * Rf + 476Ω * Rs + 4.76MΩ * Rf = Rs * Rf - 476kΩ
We now have two equations with two variables, which we can solve simultaneously. We can rearrange the first equation to get Rs/Rf in terms of the other variables:
Rs/Rf = (105/50 - 1) / (1 + 10.5*(Rs/10kΩ) + (Rs/1000Ω))
Rs/Rf = 0.1 - 0.00952*(Rs/10kΩ) - 0.000952*(Rs/1000Ω)
Substituting this into the second equation:
0.4292 * Rs * (