How to analyze the opamp circuit

[armandine2]

The examining board (AEB) book recommendation at the time was Martin Hartley Jones A Practical Introduction to Electronic Circuits. The second edition of the book came out in 1985. It has a section on the a.c. amplifier with single power supply on pp.150-151. This section was kept in the third edition, see attached.

[WIMPy]

Because it says impedance, that means AC resistance. And because the frequency isn't specified, step 1 is to assume all capacitors are a short circuit.

Sure, but what  about that output AC coupling cap? If we assume that is a short as well, we have an additional 12K resistor to ground that would mess with our gain, or don't we?

WIMPy (definitely a lot more comfortable in the digital domain)

[SteveThackery]

Sure, but what  about that output AC coupling cap? If we assume that is a short as well, we have an additional 12K resistor to ground that would mess with our gain, or don't we?

My understanding is no - it's just a small load on the output of the opamp. The output impedance of the opamp is relatively low, so the small current drawn by the 12k resistor won't cause any current limiting. More importantly, the feedback around the opamp will ensure that the output voltage remains unaffected by the 12k load (assuming the opamp will, indeed, handle the current drawn by the 12k resistor).

That's my understanding! We'll see what the experts say.

[WIMPy]

My understanding is no - it's just a small load on the output of the opamp. The output impedance of the opamp is relatively low, so the small current drawn by the 12k resistor won't cause any current limiting.

Yes, that is a good explanation.
I was getting cautious as that output resistor of 12k is quite a bit lower than the 32k (30+2) of the voltage divider for the feedback. As they are both in parallel (assuming high frequency and the cap to be a short), clearly the majority of the current must go past the divider.
But you are right. It's not about current, it's about voltage. So as long as that 12k resistor doesn't cause any voltage drop on the output, it can be ignored.

Thanks for the nudge in the right direction.

WIMPy

[EEVblog]

Sure, but what  about that output AC coupling cap? If we assume that is a short as well, we have an additional 12K resistor to ground that would mess with our gain, or don't we?

No, 12k is a nothing-burger compared to the output impedance of even the whimpyist opamp.

[tszaboo]

Sure, but what  about that output AC coupling cap? If we assume that is a short as well, we have an additional 12K resistor to ground that would mess with our gain, or don't we?

My understanding is no - it's just a small load on the output of the opamp. The output impedance of the opamp is relatively low, so the small current drawn by the 12k resistor won't cause any current limiting. More importantly, the feedback around the opamp will ensure that the output voltage remains unaffected by the 12k load (assuming the opamp will, indeed, handle the current drawn by the 12k resistor).

That's my understanding! We'll see what the experts say.

If you connect the output of the circuit to GND (and not 12K), then the opamps output will see a large capacitive loading, and it will be upset about it. If you want a more scientific method, you need to look at the poles and zeros of the opamp, and see that the stability criteria is not fulfilled.
So the output needs resistive loading. Adding yet another capacitor on the the output similarly will cause issues.
The 12K specifies this resistive loading.