To determine the output voltage $V_o$ of a differential amplifier given the input voltages $V_1$ and $V_2$, the differential gain $A_d$, and the common-mode rejection ratio (CMRR), we can follow these steps:

1. Convert the CMRR from dB to linear scale: $\text{CMRR} = 10^{\frac{200}{20}} = 10^{10}$

2. Calculate the common-mode gain $A_{cm}$: The common-mode gain $A_{cm}$ can be derived from the relationship: $\text{CMRR} = \frac{A_d}{A_{cm}}$ Therefore: $A_{cm} = \frac{A_d}{\text{CMRR}} = \frac{4000}{10^{10}} = 4 \times 10^{-7}$

3. Calculate the common-mode voltage $V_{cm}$: $V_{cm} = \frac{V_1 + V_2}{2} = \frac{320\text{ µV} + 260\text{ µV}}{2} = \frac{580\text{ µV}}{2} = 290\text{ µV}$

4. Calculate the differential input voltage $V_d$: $V_d = V_2 - V_1 = 260\text{ µV} - 320\text{ µV} = -60\text{ µV}$

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: $V_o = (4000 \times -60 \times 10^{-6}) + (4 \times 10^{-7} \times 290 \times 10^{-6})$ $V_o = (4000 \times -0.00006) + (4 \times 10^{-7} \times 0.00029)$ $V_o = -0.24 + 1.16 \times 10^{-10}$ $V_o \approx -0.24 \text{ mV}$

Thus, the output voltage $V_o$ is approximately $-0.24 \text{ mV}$.

Do you want further details or have any questions?

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

1. How does a high CMRR value benefit the performance of a differential amplifier?
2. What are the potential sources of common-mode signals in a differential amplifier circuit?
3. How can you improve the CMRR of a differential amplifier?
4. What role does the differential gain play in the overall performance of a differential amplifier?
5. Can you describe how the output voltage would change if the input voltages were swapped?
6. What are the practical applications of differential amplifiers in real-world circuits?
7. How do temperature variations affect the performance of differential amplifiers?
8. What is the impact of mismatched resistors in the input stage of a differential amplifier?

Tip: When solving amplifier problems, carefully consider the units of all quantities involved. Convert all values to a consistent unit system (e.g., volts, millivolts, microvolts) before performing calculations.