Question 12.5: Objective: Determine the input resistance of a series input ...
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
The ideal closed-loop voltage transfer function is, from Equation (12.22),
A_{v f} = \frac{V_{o}}{V_{i}} = \frac{A_{v}}{(1 + β_{v} A_{v})} (12.22)
A_{v f} = \frac{A_{v}}{(1 + β_{v} A_{v})}
or
(1 + β_{v} A_{v}) = \frac{A_{v}}{A_{v f}} = \frac{10^{5}}{50} = 2 × 10^{3}
From Equation (12.25), the input resistance is
R_{i f} = \frac{V_{i}}{I_{i}} = R_{i} (1 + β_{v} A_{v}) (12.25)
R_{i f}= R_{i} (1 + β_{v} A_{v}) = (10)(2 × 10^{3}) k \Omega ⇒ 20 M \Omega
and, from Equation (12.28), the output resistance is
R_{o f} = \frac{V_{x}}{I_{x}} = \frac{R_{o}}{(1 + β_{v} A_{v} )} (12.28)
R_{o f} = \frac{R_{o}}{(1 + β_{v} A_{v} )} = \frac{20}{2 × 10^{3}} k \Omega ⇒ 10 \Omega
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.