Learn what a differential amplifier is, how it works, common topologies (op-amp, instrumentation, fully-differential), key specifications like CMRR, applications, and design tips.
Sep 23 ,26
The Integrator Amplifier: Definition, Circuit, Transfer Function, and Uses
An integrator amplifier is an op-amp based active circuit whose output voltage is proportional to the time integral of the input signal. Built around an op-amp with a feedback capacitor and an input resistor, it produces an analog integration operation used in waveform generation, analog computing, signal conditioning, and control systems.
1. What Is an Integrator Amplifier?
An integrator amplifier (often called an op-amp integrator) is a circuit that performs the mathematical operation of integration on an input voltage signal. It is the time-domain counterpart of the differentiator amplifier and is one of the most fundamental building blocks in analog signal processing.
Unlike a passive RC integrator, an active op-amp integrator offers:
- A very low output impedance, so the integrated signal is not loaded by the next stage.
- High input impedance, which prevents the input source from being affected.
- Gain control independent of the integration time constant.
- An almost ideal integration behavior over a wide frequency range.
2. Integrator Amplifier Circuit Diagram
The classic op-amp integrator uses one operational amplifier, one input resistor R, and one feedback capacitor C. The input signal is applied to the inverting input through R; the non-inverting input is grounded. The capacitor connects the output back to the inverting input.
Fig. 1 — Ideal op-amp integrator: input resistor R and feedback capacitor C
3. Integrator Transfer Function
Because the inverting input is held at a virtual ground, the current flowing through R equals Vin / R, and the same current charges the feedback capacitor C. The output voltage is therefore the negative integral of the input:
Ideal op-amp integrator output
In the frequency domain this corresponds to an inverting gain that decreases at 20 dB/decade:
Frequency-domain transfer function
Magnitude falls as 1/f; phase = −90°
The corner frequency of the integrator is fa = 1 / (2πRC). Frequencies well above this value are integrated faithfully; below it the op-amp's open-loop gain limits accuracy.
4. How to Design an Op-Amp Integrator
Follow these practical steps when designing an integrator amplifier for a real application:
-
Choose a time constant
RCbased on the lowest input frequency you need to integrate. - Keep the expected peak output swing below the op-amp supply rails to avoid saturation.
- Add an input resistor at the non-inverting terminal to balance the input bias currents.
- Add a feedback resistor in parallel with the capacitor to set a low-frequency gain limit (see Section 5).
- Verify stability and bandwidth with the op-amp's gain-bandwidth product (GBW).
Practical issue — DC drift and saturation
An ideal integrator has infinite DC gain, so even tiny input offset voltages and bias currents cause the output to drift toward one of the supply rails. Real designs must include a feedback resistor Rf in parallel with C to limit the low-frequency gain and prevent drift.
5. Practical (Lossy) Integrator
Adding a large feedback resistor Rf in parallel with the feedback capacitor produces the so-called lossy integrator. Its transfer function becomes:
Practical integrator transfer function
DC gain = −Rf /R; integration occurs for f ≫ 1/(2πRf C)
Below 1 / (2πRfC) the circuit behaves as an inverting amplifier with gain −Rf/R; well above that corner it integrates the input.
6. Common Applications
Analog Computers
Solving differential equations by integrating signals in real time.
Function Generators
Converting a square wave into a triangle wave.
Active Filters
Low-pass filters with 20 dB/dec roll-off in Sallen-Key and state-variable topologies.
Signal Conditioning
Charge amplifiers for accelerometers, photodiodes and piezoelectric sensors.
PID Controllers
Implementing the integral term (I-action) in industrial control loops.
A/D Converters
Dual-slope integrating ADCs for high-accuracy digital voltmeters.
7. Integrator vs Differentiator Amplifier
Integrator Amplifier
R at input, C in feedback. Output is proportional to the integral of the input. Used to recover triangle waves, smooth signals, and implement the I-term of PID.
Differentiator Amplifier
C at input, R in feedback. Output is proportional to the derivative of the input. Used for edge-trigger circuits and high-frequency emphasis, but is noisier and less stable.
8. FAQ
Why does an op-amp integrator need a feedback resistor in practice?
The ideal integrator has infinite DC gain, so the output saturates from any input offset or bias current. A feedback resistor limits the low-frequency gain to a finite value and prevents drift.
What op-amp is best for an integrator circuit?
Choose an op-amp with low input bias current, low offset voltage, and high gain-bandwidth product. FET-input op-amps such as the TL072, LF353, or OPA2134 are common choices.
Can I integrate a DC signal?
Mathematically yes, but a constant DC input drives the output of an ideal integrator to saturation. A practical integrator with a feedback resistor will instead settle to a finite DC gain value.
Is an integrator the same as a low-pass filter?
Both attenuate high frequencies, but an ideal integrator has a 20 dB/dec slope extending indefinitely, while practical filters have a defined stopband and order. Integrators focus on accurate integration over a band; low-pass filters focus on rejecting high frequencies.
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About the Author — MeiXun Team
Wang
Chief Engineer Wang
High-tech Enterprise, Feifeng Talent
Chief Engineer Wang graduated with a master's degree in high-power microwave from the Institute of Electronics, University of Chinese Academy of Sciences.
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