Question

Calculate the common-mode voltage gain for the circuit

(a) 30*10^-3

(b) 17*10^-3

(c) 51*10^-3

(d) 2.4*10^-3

The question was posed to me by my school teacher while I was bunking the class.

My query is from Common Mode Configuration and  Rejection Ratio topic in section Practical Limitations of Op Amp Circuits of Linear Integrated Circuits

Answer 1

To calculate the common-mode voltage gain for the circuit, you would need to know the specific circuit values, such as the resistor values in the feedback loop, the op-amp's parameters (like the open-loop gain), and the common-mode rejection characteristics.

However, without the exact details of the circuit, I can't provide a direct calculation for the common-mode voltage gain. Here's a general approach to calculating it:

Steps for Calculation:

1. Common-Mode Gain Formula: The common-mode voltage gain (AcmA_{cm}Acm​) can be calculated by considering the feedback network of the op-amp. For a simple op-amp with resistors R1R_1R1​ and R2R_2R2​ in the input and feedback loop, the common-mode gain is influenced by the resistor values and the open-loop gain of the op-amp.

2. CMRR and Differential Gain: If the Common-Mode Rejection Ratio (CMRR) is given, the relationship between differential gain AdA_dAd​ and common-mode gain AcmA_{cm}Acm​ is:

   CMRR=AdAcm\text{CMRR} = \frac{A_d}{A_{cm}}CMRR=Acm​Ad​​

   Rearranging the formula:

   Acm=AdCMRRA_{cm} = \frac{A_d}{\text{CMRR}}Acm​=CMRRAd​​

   From this equation, if you know the differential gain AdA_dAd​ and the CMRR, you can calculate the common-mode gain.

3. Op-Amp Characteristics: Typical op-amps, like the 741, have a high CMRR, which results in a very low common-mode gain. However, with specific resistor configurations, even op-amps with high CMRR can still show some small common-mode gain.

Given this general approach, the final value would depend on the circuit specifics, but it should be one of the choices listed in your options.

If you have access to the actual circuit diagram and values, you can apply this approach directly to calculate AcmA_{cm}Acm​.

For example, assuming the open-loop gain and CMRR are specified for the op-amp in question, you'd apply the relationship and use the resistor values in the circuit to find the common-mode voltage gain.