To find the output voltage $V_o$ of a differential amplifier given the input voltages $V_1$ and $V_2$, the common-mode gain $A_{cm}$, and the common-mode rejection ratio (CMRR), we can use the following steps:

1. Convert dB values to linear scale:

   • Common-mode gain ($A_{cm}$): $A_{cm} = 10^{\frac{40}{20}} = 10^2 = 100$
   • Common-mode rejection ratio (CMRR): $\text{CMRR} = 10^{\frac{80}{20}} = 10^4 = 10000$

2. Calculate the differential gain $A_d$:

   • Differential gain ($A_d$) can be derived from the relationship: $\text{CMRR} = \frac{A_d}{A_{cm}}$ Therefore: $A_d = \text{CMRR} \times A_{cm} = 10000 \times 100 = 1000000$

3. Calculate the common-mode voltage $V_{cm}$: $V_{cm} = \frac{V_1 + V_2}{2} = \frac{0.20\text{ mV} + 0.25\text{ mV}}{2} = 0.225\text{ mV}$

4. Calculate the differential input voltage $V_d$: $V_d = V_2 - V_1 = 0.25\text{ mV} - 0.20\text{ mV} = 0.05\text{ mV}$

5. Calculate the output voltage $V_o$: The output voltage is the sum of the differential output and the common-mode output: $V_o = A_d \times V_d + A_{cm} \times V_{cm}$

   Substituting the values: $V_o = (1000000 \times 0.05 \times 10^{-3}) + (100 \times 0.225 \times 10^{-3})$ $V_o = (1000000 \times 0.00005) + (100 \times 0.000225)$ $V_o = 50 + 0.0225$ $V_o = 50.0225 \text{ mV}$

Thus, the output voltage $V_o$ is approximately $50.0225 \text{ mV}$.

Do you want further details or have any questions?

Here are 8 relative questions that expand on the above information:

1. What is the significance of common-mode rejection ratio (CMRR) in differential amplifiers?
2. How do you derive the differential gain from the given CMRR and common-mode gain?
3. What are typical applications of differential amplifiers?
4. How does the common-mode gain affect the performance of a differential amplifier?
5. Can you explain how input voltages influence the output of a differential amplifier?
6. What factors can affect the accuracy of a differential amplifier's output?
7. How does noise influence the performance of a differential amplifier?
8. What are the differences between a single-ended amplifier and a differential amplifier?

Tip: When dealing with dB (decibel) values, always remember to convert them to linear scale for accurate calculations in practical scenarios.