A differential amplifier has a typical common mode gain of 40dB and CMRR of 80dB. Find the output voltage Vo when the input voltages are 0.20mV and 0.25mV.

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.

Learn how to calculate the output voltage \( V_o \) of a differential amplifier using the given input voltages, common-mode gain, and CMRR. Follow a detailed step-by-step solution and understand the significance of CMRR and differential gain in differential amplifier circuits.

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