What is the Output voltage of Op-amp for input voltage of Vi1=150 μV,Vi2=140 μV if the amplifier has differential gain of Ad=4000 and value of CMRR is 100. 

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  1. 45.8 mV 
  2. 40.006 mV
  3. 10 μV
  4. 145 μV  

Answer (Detailed Solution Below)

Option 1 : 45.8 mV 
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Detailed Solution

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Explanation:

Output Voltage of an Operational Amplifier (Op-Amp)

The given question involves calculating the output voltage of an operational amplifier (Op-Amp) when differential and common-mode signals are applied. The Op-Amp has a differential gain (Ad) of 4000 and a Common Mode Rejection Ratio (CMRR) of 100. The input voltages are Vi1 = 150 μV and Vi2 = 140 μV.

We will calculate the output voltage step by step:

Step 1: Understanding the Parameters

  • Differential Input Voltage (Vd): The difference between the two input voltages is given by:
    Vd = Vi1 - Vi2
  • Common Mode Input Voltage (Vcm): The average of the two input voltages is calculated as:
    Vcm = (Vi1 + Vi2) / 2
  • Output Voltage (Vout): The output voltage of an Op-Amp is the sum of the differential-mode voltage and the common-mode voltage components, expressed as:
    Vout = Ad × Vd + Acm × Vcm
  • Here, Acm (common-mode gain) is related to the CMRR as:
    Acm = Ad / CMRR

Step 2: Calculating Differential and Common-Mode Input Voltages

  • Differential Input Voltage:
    Vd = Vi1 - Vi2 = 150 μV - 140 μV = 10 μV
  • Common Mode Input Voltage:
    Vcm = (Vi1 + Vi2) / 2 = (150 μV + 140 μV) / 2 = 145 μV

Step 3: Calculating Common-Mode Gain (Acm)

The common-mode gain is given by:
Acm = Ad / CMRR

Substituting the values:
Acm = 4000 / 100 = 40

Step 4: Calculating the Output Voltage (Vout)

The output voltage is the sum of the differential and common-mode components:
Vout = Ad × Vd + Acm × Vcm

Substituting the values:
Vout = (4000 × 10 μV) + (40 × 145 μV)

First, calculate each term:

  • 4000 × 10 μV = 40,000 μV = 40 mV
  • 40 × 145 μV = 5800 μV = 5.8 mV

 

Now, add the two components:
Vout = 40 mV + 5.8 mV = 45.8 mV

Final Answer: The output voltage of the Op-Amp is 45.8 mV.

Correct Option: Option 1 (45.8 mV)

Additional Information

To further understand the analysis, let’s evaluate the other options:

  • Option 2 (40.006 mV): This value could be a miscalculation of the differential gain component only, without correctly adding the common-mode component.
  • Option 3 (10 μV): This value corresponds to the differential input voltage but does not account for the amplification by the Op-Amp.
  • Option 4 (145 μV): This value corresponds to the common-mode input voltage, not the output voltage.

Conclusion:

The output voltage of an Op-Amp is determined by both the differential and common-mode input signals, along with the respective gains. Using the given parameters, the correct output voltage is 45.8 mV, making Option 1 the correct answer.

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