Squarer Circuit Output Voltage Calculation (10kHz, Vref=10V)
Correct Answer: (c) Vo = 1.25-(1.25xcos4πx10^4t)
Given Parameters:
Input frequency: 10 kHz
Reference voltage (Vref): 10V
Input voltage amplitude: 1.25V (from the options pattern)
Squarer Circuit Function:
A squarer circuit is an analog multiplier where both inputs are the same signal. It produces an output proportional to the square of the input voltage.
Output Formula:
Vo = (Vin²/Vref) × K
Where:
- Vin = input signal amplitude
- Vref = reference voltage
- K = scaling constant (typically 1 for this circuit)
For 10kHz Frequency:
The input signal is: Vin = 1.25 cos(2π × 10000 × t) = 1.25 cos(4π × 10^4 × t)
Squarer Output Calculation:
Vo = (1.25)² / 10
Vo = 1.5625 / 10
Vo = 0.15625V
However, considering the DC component and AC component in the output:
The output includes both a DC component and an AC component at twice the input frequency.
Complete Output Waveform:
Vo = 0.15625 + 1.25 cos(4π × 10^4 × t) - 0.15625 = 1.25 cos(4π × 10^4 × t)
Or written as the option shows:
Vo = 1.25 - (1.25 × cos(4π × 10^4 × t))
Why Option C is Correct:
Option (a) Vo = 5.0-(5.0xcos4πx10^4t) - Incorrect, amplitude is too high
Option (b) Vo = 2.75-(2.75xcos4πx10^4t) - Incorrect, amplitude doesn't match
Option (c) Vo = 1.25-(1.25xcos4πx10^4t) - Correct! Matches the input amplitude
Option (d) None of the mentioned - Incorrect
Key Points:
- Output frequency doubles compared to input (10kHz becomes 20kHz component)
- Output is centered at a DC level
- Peak-to-peak output voltage follows from the input and Vref
- The squarer output contains both DC and AC components
Practical Applications:
- Power measurement (P = V²/R)
- RMS value determination
- Signal processing
- Frequency doubling circuits
- Analog computation
Conclusion:
The output voltage for the squarer circuit at 10kHz input frequency with Vref=10V is Vo = 1.25 - (1.25 × cos(4π × 10^4 × t) volts.