Objective: Determine the input resistance of a series input connection and the output resistance of a shunt output connection for an ideal feedback voltage amplifier.

Consider a series–shunt feedback amplifier in which the open-loop gain is $A_v = 10^{5}$ and the closed-loop gain is $A_{vf} = 50$ . Assume the input and output resistances of the basic amplifier are $R_{i} = 10 k \Omega$ and $R_{o} = 20 k \Omega$ , respectively

Question

Objective: Determine the input resistance of a series input connection and the output resistance of a shunt output connection for an ideal feedback voltage amplifier.

Consider a series–shunt feedback amplifier in which the open-loop gain is [latex]A_v = 10^{5}[/latex] and the closed-loop gain is [latex]A_{vf} = 50[/latex]. Assume the input and output resistances of the basic amplifier are [latex]R_{i} = 10 k \Omega[/latex] and [latex]R_{o} = 20 k \Omega[/latex], respectively

Accepted Answer

The ideal closed-loop voltage transfer function is, from Equation (12.22),

[latex]A_{v f} = \frac{V_{o}}{V_{i}} = \frac{A_{v}}{(1 + β_{v} A_{v})} [/latex] (12.22)
[latex]A_{v f} = \frac{A_{v}}{(1 + β_{v} A_{v})} [/latex]
or
[latex](1 + β_{v} A_{v}) = \frac{A_{v}}{A_{v f}} = \frac{10^{5}}{50} = 2 × 10^{3}[/latex]
From Equation (12.25), the input resistance is

[latex]R_{i f} = \frac{V_{i}}{I_{i}} = R_{i} (1 + β_{v} A_{v}) [/latex] (12.25)

[latex]R_{i f}= R_{i} (1 + β_{v} A_{v}) = (10)(2 × 10^{3}) k \Omega ⇒ 20 M \Omega[/latex]
and, from Equation (12.28), the output resistance is

[latex]R_{o f} = \frac{V_{x}}{I_{x}} = \frac{R_{o}}{(1 + β_{v} A_{v} )} [/latex] (12.28)
[latex]R_{o f} = \frac{R_{o}}{(1 + β_{v} A_{v} )} = \frac{20}{2 × 10^{3}} k \Omega ⇒ 10 \Omega[/latex]
Comment: With a series input connection, the input resistance increases drastically, and with a shunt output connection, the output resistance decreases substantially, with negative feedback. These are the desired characteristics of a voltage amplifier.

Question 12.5: Objective: Determine the input resistance of a series input ...

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