A Feedback Amplifier Early in the twentieth century engineers struggled to design vacuum-tube amplifiers whose gain remained constant at a predictable value. The gain is the ratio of the output voltage to the input voltage. The vacuum-tube gain G can be made large but is somewhat unpredictable and

Question

A Feedback Amplifier

Early in the twentieth century engineers struggled to design vacuum-tube amplifiers whose gain remained constant at a predictable value. The gain is the ratio of the output voltage to the input voltage. The vacuum-tube gain G can be made large but is somewhat unpredictable and unreliable due to heat effects and manufacturing variations. A solution to the problem is shown in Figure 6.2.8. Derive the input-output relation for [latex]v_{o}[/latex] as a function of [latex]v_{i}[/latex] . Investigate the case where the gain G is very large.

Accepted Answer

Part of the voltage drop across the resistors is used to raise the ground level at the amplifier input, so the input voltage to the amplifier is [latex]v_{i} − R_{2} v_{o}/(R_{1} + R_{2})[/latex]. Thus the amplifier’s output is
[latex]v_{o} = G \left(v_{i} − \frac{R_{2}}{R_{1} + R_{2}} v_{o} \right) [/latex]

Solve for [latex]v_{o}[/latex]:
[latex]v_{o} = \frac{G}{1 + G R_{2}/(R_{1} + R_{2})} v_{i} [/latex]
If [latex]G R_{2}/(R_{1} + R_{2}) >> 1[/latex], then
[latex]v_{o} \approx \frac{R_{1} + R_{2}}{R_{2}} v_{i} [/latex]
Presumably, the resistor values are sufficiently accurate and constant enough to allow the gain [latex](R_{1} + R_{2})/R_{2}[/latex] to be predictable and reliable.

Question 6.2.6: A Feedback Amplifier Early in the twentieth century engineer...

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