# Output impedance in a circuit with Operational Amplifier

How I can obtain output impedance of this circuit? I would like to know in the ideal case and the LM741 case.

It is difficult to get good information about output impedance on this ancient (and largely crappy) beast but I'd start here by looking at the equivalent circuit: -

And what I would note are the two resistors inside the red circle I've drawn. If the 741 is operated open-loop these two resistors are the output impedance so then you have to work out what the output impedance is when you have negative feedback.

To do this you need to consider frequency and the open-loop bode plot of the 741: -

At DC, the open-loop gain is really high (106 dB or 200,000) and this will mean that for a unity gain amplifier the output impedance is dragged from the 50 ohm open-loop value to something like 50/200,000 ohms i.e. 0.25 milli ohms.

At 10 kHz, the open-loop gain is about 40 dB or 100 and this means the closed-loop output impedance will be about 0.5 ohms. At 100 kHz, the closed loop output impedance will be about 5 ohms.

Remember this is a rough approximation. It's also worth noting that the Fairchild version of the 741 has a graph showing open loop output impedance as being about 75 ohms up to 100 kHz then it rises to about 300 ohms at 1 MHz.

I would like to know in the ideal case

The ideal case would be zero ohms but it all comes down to what you define as ideal.

• Thanks, so at DC the overall output impedance of the circuit is R||C ?
– Fran
Commented Jul 31, 2017 at 11:10
• I'm not sure what you mean. What R and what C? Commented Jul 31, 2017 at 11:30
• I would like to know the output impedance of the schematic I have attached: i.sstatic.net/gBhkH.png
– Fran
Commented Jul 31, 2017 at 11:55
• For the 741, it is as how I described in my answer: At DC the closed loop output impedance is under 1 milli ohm and this progressively rises in value as frequency rises such that at 100 kHz the impedance is 5 ohms for unity gain closed loop circuit as you show in your picture. Commented Jul 31, 2017 at 12:01
• You should also take note that for the Fairchild version of the 741, the open-loop impedance is shown in this document: egr.msu.edu/eceshop/Parts_Inventory/datasheets/lm741.pdf and at high frequencies, the 50 ohms I assumed rises dramatically above 100 kHz i.e. at 1 MHz it has an output impedance of about 300 ohms. Commented Jul 31, 2017 at 12:04

If it is an ideal Op-amp you can also assume Vdiff=0(Voltage across op-amp inputs) and therefore the voltage across C equals Vo

• In ideal case it would be Zo=0ohm ?
– Fran
Commented Jul 31, 2017 at 10:35
• No, thats only for the ideal Op-amp, but you are interested in the overall impedance. So you have to consider R and C too
– S.G
Commented Jul 31, 2017 at 10:37
• Thanks, so the overall output impedance of the circuit for the ideal Op-amp is R||C ?
– Fran
Commented Jul 31, 2017 at 11:11
• Could you check if that is correct? electronics.stackexchange.com/questions/321624/…
– Fran
Commented Aug 1, 2017 at 11:01

Those resistors are used for short-circuit protection.

The rout is (mostly) set by the reac of the two bipolars.