Operational Amplifiers – Complete Theory
Page 9 – Op-Amp Integrator
The Integrator is an operational amplifier circuit that produces an output proportional to the integral of the input signal.
Circuit Components
- Input resistor (R)
- Feedback capacitor (C)
- Operational amplifier
- Input voltage Vin
Virtual Ground Concept
Since the non-inverting terminal is grounded:
V− ≈ 0
Input Current
The current through the input resistor is:
I = Vin / R
Because op-amp input current ≈ 0, this current flows through the capacitor.Capacitor Current Equation
Current through capacitor:
I = C ( dVout / dt )
Derivation
Equating currents:Vin / R = C ( dVout / dt )
Rearranging:dVout / dt = Vin / RC
Integrating:Vout = − (1 / RC) ∫ Vin dt
Key Result
Output voltage is proportional to the integral of input voltage.
Waveform Behavior
- Square input → Triangular output
- Constant input → Ramp output
- Sine input → Cosine output
Applications
- Analog computers
- Signal processing
- Waveform generation
- Control systems
GATE Important Points
- Integrator produces output proportional to ∫Vin dt
- Uses capacitor in feedback path
- Important for waveform conversion
- Common question: square → triangular waveform
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