Tuesday, 10 March 2026

Operational Amplifiers – Complete Theory

Page 10 – Op-Amp Differentiator

The Differentiator is an operational amplifier circuit that produces an output proportional to the rate of change of the input signal.

Picture used in analog electronics

Circuit Components

Input capacitor (C)
Feedback resistor (R)
Operational amplifier
Input voltage Vin

Virtual Ground Concept

Since the non-inverting terminal is grounded:

V− ≈ 0

Capacitor Current

Current through capacitor:

I = C ( dVin / dt )

Because op-amp input current ≈ 0, this same current flows through the feedback resistor.

Voltage Across Resistor

Using Ohm’s law:

Vout = − I R

Substituting current:

Vout = − RC ( dVin / dt )

Key Result

Output voltage is proportional to the derivative of input voltage.

Waveform Behavior

Ramp input → Constant output
Triangular input → Square output
Sine input → Cosine output

Applications

Edge detection circuits
Waveform shaping
High-pass filter circuits
Signal processing

GATE Important Points

Differentiator produces output proportional to dVin/dt
Capacitor connected at input
Resistor in feedback path
Acts as a high-pass circuit

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