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!!
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).
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).
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)
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?
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.
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?
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?