# Integrator circuit

Discussion in 'Homework Help' started by omerysmi, Dec 30, 2014.

1. ### omerysmi Thread Starter Member

Oct 10, 2014
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The frequecy (if it's necessary for the question) is 100Hz.

I need to find the gain (Av) of this circuit, and I have no any idea..

I will be very happy if someone will help me to find the gain of this circuit, thanks!!

Last edited: Dec 30, 2014

Oct 2, 2009
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3. ### WBahn Moderator

Mar 31, 2012
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This development has an error in it. Where does the minus sign magically come from?

The problem is that the voltage across the capacitor is not defined so as to be consistent with the passive sign convention given the defined direction for Ic. Based on that, the voltage across the capacitor is -vo(t).

4. ### WBahn Moderator

Mar 31, 2012
20,225
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How are you expected to express "gain" for this circuit? At a particular frequency? As a function of 's'? As a function of 'jw'?

As a function of time, it doesn't really have a 'gain' per se, but rather a functional relationships (it's called an integrator for a reason).

5. ### omerysmi Thread Starter Member

Oct 10, 2014
48
0
But what is the Av? how can I do Vo/Vi with this integral?
In other words I need to find the transmission function of this circuit (Vo/Vi)

6. ### WBahn Moderator

Mar 31, 2012
20,225
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But in what domain? The complex frequency domain? The frequency domain? At a particular frequency (which seems to be implied by your noting a specific frequency, but I'm not sure)?

What topics are you studying right now that this problem is associated with?

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7. ### omerysmi Thread Starter Member

Oct 10, 2014
48
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I don't understand you very well, anywhy the frequency is 100Hz if that's what you mean

I have some of op amplifires (for example: inverting amplifier) and I need to find the gain of each amplifier.

8. ### WBahn Moderator

Mar 31, 2012
20,225
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What is the context of the question you are asking? Since you are posting in the Homework Help section, I'm assuming that this is part of a homework assignment? But a question like this could be asked in conjunction with several different topics, each looking for a slightly different answer (or at least a different form for the answer).

Have you been studied reactance of inductors and capacitors?

Have you worked with impedance of inductors and capacitors?

Have you worked with phasor representations of voltages and currents?

Is this question asked in the context of the signal being a single frequency AC waveform?

9. ### omerysmi Thread Starter Member

Oct 10, 2014
48
0
Yes of course..I didn't understand the last qusetion..You mean what there is in the Vin?

10. ### WBahn Moderator

Mar 31, 2012
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That's part of it and will move us in the right direction.

11. ### omerysmi Thread Starter Member

Oct 10, 2014
48
0
Vin is square wave of 2V[p-t-p]

12. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
Okay, so if Vin is a square wave, then your signal is not single-frequency and just giving the gain at 10kHz won't suffice because you also have all of the harmonics.

You can either give the transfer function (which is often called the 'gain' but really isn't) as H(s) or H(jw) (either of those look familiar) or you can figure out the form of the output signal. But you really can't take the time domain output signal and divide it by the input signal because of the integral that is involved.

It might help if you provided the exact wording of the entire problem. It could be that what they are asking for is the ratio of the peak-to-peak voltage of the output to the peak-to-peak voltage of the input, which is NOT the same thing as Vout/Vin.

But let's leave that aside for a bit. What do you expect the output waveform to look like, assuming the opamp doesn't saturate?