# Op amp integrator

http://pokit.org/get/8119a4b8a37171c67971c3fb13b33063.jpg [Broken]

Consider picture above.

I understand how an integrator behaves when the capacitor is full. It(capacitor) acts as infinite resistance ergo open loop so we get positive saturation at the output.

What I don't understand how come we are starting at 0? Doesn't capacitor act like a short circuit in the very first moments of its charging? Effectively making this a voltage follower? (at very first moments).

I understand what voltage follower does in situation when the Vin is connected to + lead and we have short circuit between output and - lead. Question risen what would happen if I grounded a + lead and connected Vin to - through a resistor like so:

http://pokit.org/get/4b7a8c8dca68aacc548f3a3b2d748715.jpg [Broken]

Have I just short circuited the whole op-amp? As it isn't there?

Getting weird results from simulations.

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T the start, with the switch open, the voltages at the - input and + input of the op amp are zero and there is no charge on the capacitor. The output voltage is also zero.
When the switch is closed there is a voltage across across the input resistor and current flows from the output, into the capacitor and through the input resistor.
This current will be constant and is equal to 1volt/ input resistance. This current charges up the capacitor until Vout is saturated at the +supply voltage. (+15V)

T the start, with the switch open, the voltages at the - input and + input of the op amp are zero and there is no charge on the capacitor. The output voltage is also zero.
When the switch is closed there is a voltage across across the input resistor and current flows from the output, into the capacitor and through the input resistor.
This current will be constant and is equal to 1volt/ input resistance. This current charges up the capacitor until Vout is saturated at the +supply voltage. (+15V)

This doesn't answer my question which is, at the very first moment after the switch is closed, which you say current flows from output through capacitor, is output voltage different from 0?

If the capacitor was uncharged at the start then Vout would be zero.
One way to see what is going on is to imagine the switch is closed for a short time so that the capacitor gains a small amount of charge and Vout has increased but has not reached +15.
If the Switch is now opened the charging will stop and the capacitor will remain charged to thi level which means that Vout will have a steady value.
When the switch is closed again charging will continue from this point.

If the capacitor was uncharged at the start then Vout would be zero.
One way to see what is going on is to imagine the switch is closed for a short time so that the capacitor gains a small amount of charge and Vout has increased but has not reached +15.
If the Switch is now opened the charging will stop and the capacitor will remain charged to thi level which means that Vout will have a steady value.
When the switch is closed again charging will continue from this point.

Oh I understand thank you. I misplaced few parts.

I like Serena
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Isn't the op-amp saturated in its negative voltage supply?
Apparently that is 0 [V].

I would say that Bass's diagram is correct.
the input voltage is -1 therefore current flows from Vout through the capacitor through Rin to the -V which means that Vout is increasing +vely

Yes, since it acts a comparator after the capacitor is charged, and -1 is on the inverting lead, it will go to positive saturation.

I agree with you Bass, if Vin was +1V then Vout would be -15V

I like Serena
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Am I misunderstanding?
After the switch is closed, -1 [V] is on the inverting lead.
Before I believe +15 [V] is on the inverting lead.

Am I misunderstanding?
After the switch is closed, -1 [V] is on the inverting lead.
Before I believe +15 [V] is on the inverting lead.

hmm why would it be +15 on the inverting lead, before closing of the switch?

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=SSE5303

here is the complete animation.

The graph shows V = 0V before the switch is closed. No reference is made to any voltage across the capacitor at t=0 so I take it to be zero (V out = 0 on the graph)

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Homework Helper
Ah, sorry, my mistake.
I interpreted the circuit to have +15V applied on Vout, but in retrospect that actually makes no sense.

Now I see that initially no voltage at all is applied, so Vout will initially be zero (if you wait long enough).

At t = 0 Vout will be whatever voltage there is across the capacitor at t =0.
it makes sense to take this to be zero but it may not be the case....depends what happened for the capacitor before t = 0 !!!!!!!

Bass:
You suggested that the capacitor 'behaves like a short circuit' and you produced your second circuit diagram with 'Key = A' as the capacitor.
You have made a good attempt to produce another model.... but ....a capacitor is not exactly a switch.... it charges up !!!!
And your circuit diagram is incorrect.... the -1V is not connected to earth (ground)
I have produced a diagram which ,I think, shows what you were getting at!!!
Can you see that your model certainly gives the current that would be flowing (1V/100Ω)
but it does not correctly model the capacitor charging up which would give a Vout increasing .
Try this on your software programme.... I imagine it will give you I = 0.01A but not much else.
Change KeyA for a capacitor and see what happens.

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Bass:
You suggested that the capacitor 'behaves like a short circuit' and you produced your second circuit diagram with 'Key = A' as the capacitor.
You have made a good attempt to produce another model.... but ....a capacitor is not exactly a switch.... it charges up !!!!
And your circuit diagram is incorrect.... the -1V is not connected to earth (ground)
I have produced a diagram which ,I think, shows what you were getting at!!!
Can you see that your model certainly gives the current that would be flowing (1V/100Ω)
but it does not correctly model the capacitor charging up which would give a Vout increasing .
Try this on your software programme.... I imagine it will give you I = 0.01A but not much else.
Change KeyA for a capacitor and see what happens.

Yes, I did that. I used -1 in original simulation, don't know why I set it back to 1. I am trying to have a deeper understanding of the op-amp so I am asking questions like this.

I do now understand that the acting of the capacitor as a short circuit, is not something to be taken literally.

I think I have a clear picture how this circuit behaves when the switch (1st picture) is closed.

It acts like a short circuit, but not like the classic short circuit. I think we understand each other.