# Intergrator/Differential Op-Amp Frequency

• big_tobacco
In summary, the differentiator will give an output that is closer in time to the input frequency, and the integrator will give an output that is farther in time from the input frequency.
big_tobacco
Hello,

I'm baffled as to why different frequencies affects the output (amplitude) of a integrator and differentiator op-amp circuit.

I'm using a variety of frequencies (100 Hz - 10Khz), with a fixed 1V square wave input? Why does the frequency cause a change in the amplitude?

This isn't a homework question, I work with simple op-amps all the time and it's about time that I should know the principles.

Any help would be greatly appreciated.

Regards

Last edited by a moderator:
Also another factor could be the op-amp's frequency range.

For example, a 741 works up to 20 KHz,

but a square wave is composed of odd order harmonics. So if you apply a 10 KHz square wave, then there is a frequency component at 30 KHz, which would likely be killed by the op-amp like the 741 - and hence signal amplitude is reduced.

Another way to look at this is that with a square-wave input, an integrator should give a triangular-wave output. Thus the output amplitude is inversely proportional to frequency. Provided that the fundamental frequency of the square wave lies well within the bandwidth of your op-amp, the practical result should be a fair approximation to this.

The situation for a differentiator is more complicated. In fact, a perfect square-wave input applied to a perfect differentiator would give an output consisting of infinitely narrow and high pulses. In the real world, a square-wave will have limited edge speeds, and an integrator will have limited maximum output amplitude and limited slew rate.

If the frequency of a square-wave input to a practical differentiator is increased from a low value, the output will most likely be a series of alternating narrow pulses of roughly constant amplitude, which get closer in time as the frequency increases. If the frequency is increased sufficiently, there will not be enough time for each pulse to reach full height, and the output amplitude will begin to drop off if the frequency is increased further.

## 1. What is an integrator/differential op-amp frequency?

An integrator/differential op-amp frequency is a measure of the frequency response of an operational amplifier circuit when used as an integrator or differentiator. This frequency response refers to the change in output voltage as a function of input frequency and is important in understanding the performance of these circuits.

## 2. How does an op-amp integrator work?

An op-amp integrator circuit is constructed by connecting a capacitor in the feedback loop of an operational amplifier. This capacitor acts as a storage element, allowing the circuit to integrate the input signal over time. The output voltage of the circuit is proportional to the integral of the input voltage, hence the name "integrator."

## 3. What is the ideal frequency response for an op-amp integrator?

The ideal frequency response for an op-amp integrator is a straight line with a slope of -6 dB per octave. This means that for every doubling of the input frequency, the output voltage decreases by 6 dB. In reality, due to limitations in the op-amp and other components, the frequency response may deviate from this ideal response.

## 4. What is the purpose of an op-amp differentiator?

An op-amp differentiator circuit is used to amplify high-frequency components of an input signal while attenuating low-frequency components. This can be useful in applications such as noise filtering or signal differentiation. The circuit is constructed by placing a capacitor in series with the input signal and using the output of the op-amp as the differentiated signal.

## 5. How does the frequency response of an op-amp differentiator compare to an integrator?

The frequency response of an op-amp differentiator is the inverse of an integrator. This means that the output voltage decreases by -6 dB per octave for every doubling of the input frequency, resulting in a straight line with a positive slope. Additionally, the differentiator has a high-pass filter response, while the integrator has a low-pass filter response.

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