Opamp output impedance & cap selection

[therecordingart]

I've gone blank and can't seem to find the answer on this. On the output of opamp circuits we usually see a series cap that feeds a resistor or volume pot to ground. I know the opamp itself has a very low output impedance. What makes up the total output impedance of the circuit so that cap can be selected purposefully instead of just plopping in a big cap? I know 1/2piRC gives the freq, but I'm trying to solve for R (or Z).

[Digital Larry]

The low frequency roll off of a high pass is going to depend on the source and load impedances.  You can probably safely say that any op-amp is going to have an output impedance less than ten ohms.  If there's a resistor hanging off the other side of the cap to ground, it's more for bleeding off a DC charge than it is for setting the output impedance.  So the answer is going to depend more on what comes after that stage.  Since it could be a variety of unknown things, this may explain the tendency to slap a large cap on there.

Corrections and alternative perspectives always welcome.

[therecordingart]

The low frequency roll off of a high pass is going to depend on the source and load impedances.  You can probably safely say that any op-amp is going to have an output impedance less than ten ohms.  If there's a resistor hanging off the other side of the cap to ground, it's more for bleeding off a DC charge than it is for setting the output impedance.  So the answer is going to depend more on what comes after that stage.  Since it could be a variety of unknown things, this may explain the tendency to slap a large cap on there.

Corrections and alternative perspectives always welcome.

That makes sense. So for the sake of "safety" my equation should be 1/2pi10C. If the next stage is another opamp with the input Z being around 1M would my equation then be 1/2pi1000000C while ignoring that output Z of that opamp? I feel like such a noob, but I got myself confused.

[Digital Larry]

That makes sense. So for the sake of "safety" my equation should be 1/2pi10C. If the next stage is another opamp with the input Z being around 1M would my equation then be 1/2pi1000000C while ignoring that output Z of that opamp? I feel like such a noob, but I got myself confused.

I think you have it right.  Once one factor is 100,000 times bigger than another one in an equation like this, we tend to forget about the smaller one.  The only thing I'd be concerned about it that you might plug it into something with a 10k input impedance someday.  But if you do that, and notice that your low end went away, at least you'll understand why.

[therecordingart]

That makes sense. So for the sake of "safety" my equation should be 1/2pi10C. If the next stage is another opamp with the input Z being around 1M would my equation then be 1/2pi1000000C while ignoring that output Z of that opamp? I feel like such a noob, but I got myself confused.

I think you have it right.  Once one factor is 100,000 times bigger than another one in an equation like this, we tend to forget about the smaller one.  The only thing I'd be concerned about it that you might plug it into something with a 10k input impedance someday.  But if you do that, and notice that your low end went away, at least you'll understand why.

Perfect. That's how I calculated the coupling cap between opamp stages in my last design. I was trying to conserve space and didn't want to plop an electrolytic in there. I didn't notice any loss of bass.