Question

An OPAMP has a gain of \( 10^4 \), an input impedance of 10 MΩ and an output impedance of 100Ω. The OPAMP is used in unity-gain feedback configuration in a voltage buffer circuit. The closed-loop output impedance of the OPAMP (in milliohms) in the circuit is _________.

Hint:

In unity-gain feedback configuration, the closed-loop output impedance is reduced by the factor \( (1 + A \times \frac{Z_{out}}{Z_{in}}) \).

Answer 1

Correct Answer: 9.9

We are given the following information:
- Gain (\( A \)) = \( 10^4 \)
- Input impedance (\( Z_{in} \)) = 10 MΩ = \( 10 \times 10^6 \) Ω
- Output impedance (\( Z_{out} \)) = 100 Ω
- The OPAMP is used in a unity-gain feedback configuration in a voltage buffer circuit.
Step 1: Formula for closed-loop output impedance
In a unity-gain feedback configuration, the closed-loop output impedance (\( Z_{out(cl)} \)) is given by the formula: \[ Z_{out(cl)} = \frac{Z_{out}}{1 + A \times \left( \frac{Z_{out}}{Z_{in}} \right)}. \] Step 2: Substituting the given values
Substitute the values of \( Z_{out} \), \( A \), and \( Z_{in} \) into the formula: \[ Z_{out(cl)} = \frac{100}{1 + 10^4 \times \left( \frac{100}{10 \times 10^6} \right)}. \] Step 3: Simplify the expression
First, simplify the term inside the parentheses: \[ \frac{100}{10 \times 10^6} = 10^{-5}. \] Now, substitute this into the equation: \[ Z_{out(cl)} = \frac{100}{1 + 10^4 \times 10^{-5}} = \frac{100}{1 + 1} = \frac{100}{2} = 50 \, \text{Ω}. \] Step 4: Convert to milliohms
The result is in ohms, so to convert it to milliohms (1 Ω = 1000 milliohms), we multiply by 1000: \[ 50 \, \text{Ω} = 50 \times 1000 = 50000 \, \text{milliohms}. \] Thus, the closed-loop output impedance of the OPAMP is \( 50.0 \, \text{milliohms} \).