# Designing an Integrator Circuit with Given Absolute Gain

• Engineering
• PhysicsTruth
In summary, the integrator circuit has a cutoff frequency and an 0dB frequency. The gain is around ##-\frac{1}{sR1C}##.

#### PhysicsTruth

Homework Statement
Keeping in mind the corner frequency at 3dB, design the R,C values for an integrator to maintain a gain of magnitude 10 throughout the band pass.
Relevant Equations
##f_{cutoff} = \frac{1}{2 \pi R_{f}C}##
##f_{0dB} = \frac{1}{2 \pi R_{1}C}##
##DC Gain = -\frac{R_{f}}{R_{1}}##
##AC Gain = -\frac{X_{C}}{R1}##
For the integrator circuit, I can design the cutoff frequency and the 0dB frequency as required. Using Laplace transforms, the gain is around ##-\frac{1}{sR1C}##, where s is the complex impedance parameter. But, how do I maintain the absolute value of this gain at 10 for the whole band pass for this integrator? I need to find out the R1, Rf and C values, given the cutoff frequency and this absolute gain at 10 for the band pass, but I don't know how to utilise this absolute gain in deducing the necessary information in finding out the values. Can someone help me out in this?

What? This question doesn't make sense to me. Integrators don't have passbands (according to me) the gain is essentially infinite at DC and constantly decreases (inversely proportional to frequency) forever. Of course there are some real issues in the real world, like a low frequency pole, but theoretically integrators are simple.

So that makes me think that either:
1) Your instructor is an idiot, or too busy to write a good HW question.
2) You have left out part of the problem description.

So, next step: Draw a schematic of the circuit, take a picture of it with your phone and post it AND tell us the exact wording of the question. For example, you refer to R1 and Rf, but I have no idea what those are (OK, I could guess, but YOU NEED TO TELL US).

BTW, it sounds like you are describing what I would call a low pass filter. A 1st order LPF will have a passband at low frequencies (i.e. constant gain), and will act like an integrator at higher frequencies (gain proportional to 1/f).

The name AC Op-amp Integrator with DC Gain Control is indeed a bit cumbersome, but it can reduce misunderstandings when used.

Tom.G
Tom.G said:
Perhaps both of you could read:
the section

## The AC or Continuous Op-amp Integrator​

At:
https://www.electronics-tutorials.ws/opamp/opamp_6.html

And:
http://www.visionics.a.se/html/curriculum/Experiments/Opamp integrator/Opamp Integrator1.html
Thanks for the referral, but I already know what an integrator is. Better than the person that wrote that second link. That is a 1st order LPF. If you remove R2, it's an integrator. This is assuming we ignore the fact that op-amps aren't actually ideal. Fortunately, the first link has it correctly.

Here's a hint: Integrators have ##H(s)=\frac{1}{(\frac{s}{\omega_o})}##; LPF have ##H(s)=\frac{1}{(1+ \frac{s}{\omega_o})}##. Now I admit that at higher frequencies they behave the same. But, they are topologically different and that is worth recognizing. Fortunately the textbooks get this right; the web links, well that depends...

## 1. What is an integrator circuit?

An integrator circuit is a type of electronic circuit that performs mathematical integration of an input signal over time. It is commonly used in analog signal processing and control systems.

## 2. What is the purpose of designing an integrator circuit with given absolute gain?

The purpose of designing an integrator circuit with given absolute gain is to achieve a specific output voltage for a given input signal. The absolute gain determines the relationship between the input and output voltages, and by designing the circuit with a specific absolute gain, the output can be precisely controlled.

## 3. How do you calculate the absolute gain of an integrator circuit?

The absolute gain of an integrator circuit can be calculated by dividing the output voltage by the input voltage. It is typically expressed in units of volts per second (V/s).

## 4. What factors should be considered when designing an integrator circuit with given absolute gain?

When designing an integrator circuit with given absolute gain, it is important to consider the input signal frequency, the desired output voltage range, the type of op-amp used, and the stability of the circuit. Additionally, the circuit should be designed to minimize noise and distortion.

## 5. What are some common applications of integrator circuits?

Integrator circuits are commonly used in audio and video processing, motor control systems, and electronic filters. They can also be used in scientific instruments, such as oscilloscopes and data acquisition systems, to measure and analyze signals over time.