Thanks for the reply!
Hm, but in my textbook, they say, you have to assume no current flows to the opamp (assume its a ∞ resistor), wouldn't this make the resistor and capacitor in series?
And, if the the opamp saturates, wouldn't that remove the feedback?
If you power the opamp with 5V, and you give an input of 20v, Vo wouldn't give feedback right?
Hello again,
Yes for the ideal op amp you assume no current flow into the inverting terminal as you noted, but that's not the only assumption you apply. You also have to apply at the same time the assumption that the inverting terminal is at virtual ground (Eric was nice enough to provide a link for this). That means you not only have the same current flowing in the input as the output, but you also have the inverting terminal stuck to ground potential. In a non op amp circuit the resistor and capacitor junction would be allowed to change voltage and that changes everything as the response goes to k*(1-e^-at) instead of k*t. Thus the op amp makes the capacitor integrate perfectly.
In the frequency domain the R and C in series looks like k/(s+a) while the true integrator with op amp is just k/s.
Of course there are some non idealities that have to be considered in the real world such as offset voltage and current.
All of this also assumes that the op amp is operating in the linear mode too. If the op amp goes out of the linear mode for any reason, the circuit changes completely. This means we have to consider the maximum output current and things like that. If we apply an input that at any time forces the op amp out of the linear mode then we have to figure some op amp output resistance and also no more virtual ground, so we would end up with a very different response.
Thus one of the things that you would have to do first in the real world is to calculate some threshold that would allow you to first determine what mode of operation the op amp was working in. Is it linear or not? Then apply the calculations for that mode and always check to see if it moved out of that mode where other equations would have to be applied.
This is a typical operation for various kinds of electronic devices, not just op amps. Normally we assume a linear mode, but that's not always necessarily going to be true for all time.
You already noted that if you apply 1v for 10 years at first the output ramps down, but once it reaches the negative supply rail that's it. It bottoms out and can not go any lower. If you apply -1v for a long time at first the output ramps up, but once that reaches the positive supply rail that's it too...it tops out and stays there. To add to the problem, many op amps can not even reach as far as their plus and minus rails as there is some other limiting factor such as a transistor saturation voltage drop plus the drivers drop so we may end up with something that can only reach as high as the plus voltage minus 1.5 volts. You'd have to check the op amp specs to find this information out.