Determine the output voltage of a differential amplifier for input voltages of 320µV and 260µV. The differential gain of the amplifier is 4000 and the value of CMRR is 200

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.

Learn how to calculate the output voltage of a differential amplifier with given input voltages of 320µV and 260µV. Understand the differential gain and common-mode rejection ratio (CMRR) concepts. Suitable for advanced engineering students and professionals.

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