Question
Download Solution PDFWhat 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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.
Last updated on Jun 23, 2025
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