Operational Amplifier - Integrator Simulator

An integrator performs a mathematical integration operation on the input signal.

Circuit Diagram

V_out(t) = -1/(RC) ∫ V_in(τ) dτ + V_initial

Simulation Controls

Input Signal Type:

Signal Frequency (Hz): 1 Hz

Input Amplitude (V): 1 V

Resistance (kΩ): 10 kΩ

Capacitance (μF): 1 μF

Initial Condition (V): 0 V

Combined View

Separate Views

Input and Output Signals

Input Signal

Output Signal

Input Signal

Output Signal

About Integrator Circuits

An op amp integrator is a circuit that performs the mathematical operation of integration. It produces an output voltage that is proportional to the integral of the input voltage over time.

Key Characteristics

Time Constant: τ = RC determines the rate of integration
Phase Shift: 90° phase shift for sinusoidal inputs
Inversion: Output is inverted relative to the integral of the input

Input/Output Relationships

Square Wave Input: Produces a triangular wave output
Sine Wave Input: Produces a cosine wave output (shifted by 90°)
DC Input: Produces a ramp output (integrates to a straight line)
Pulse Input: Produces a step followed by a constant level

Practical Considerations

In real integrators, a high-value resistor is often placed in parallel with the capacitor to prevent output drift due to op amp bias current
The output can saturate at the op amp's supply voltage limits
Integrators are commonly used in analog computers, waveform generators, and active filters