What is the maximum gain for 1 op amp stage?

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The higher the gain, the higher the slew rate and the lower the frequency response. Off the top of my head when uA741C was all the rage, it had an overall gain of 10,000 but at that rate the frequency cut off was 3kHZ. Read the data sheet on your selected chip for an accurate response time.
Another thing to bear in mind is voltage output. It takes a longer time to move + - 10volts that it does for + - 1volt. Why do you think processors are so fast now ... because they move within 1 1/4volts instead of the old DX2 chip that used 5volts (plus newer technology of course).
 
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Unfortunately that Texas Instruments datasheet does not contain a plot of open loop gain versus frequency.

However, the NE5534A datasheet from On Semiconductor, does contain this plot. I copied it below.

In my opinion, one way to estimate the maximum gain is to take out the plot of open loop gain vs frequency, and draw a vertical red line at 50,000 Hertz (5.0e4 Hz). Wherever the red line intersects the open loop gain curve, that gain is the maximum you can possibly expect to get.

In the case of the NE5534, that's 53dB (blue line). Which is a voltage gain of 446x.

Remember that datasheets show a "typical" unit. If you imagine this means that half of the produced chips are "better" and half are "worse", then half of the NE5534A's made, will be able to give you 446x gain at 50kHz. And half of the NE5534A's made WON'T be able to give you 446x gain at 50kHz.

Harry Callahan asks, "Do you feel lucky?"
 

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Would there be lower noise or less THD if instead of pushing 1 gain stage close to it's max, you used 2 stages of half of the gain to sum to the same level?

you really need geometric mean gain in 2 series amps to get the same final gain

noise doesn't change enough to worry about if the total closed loop gain is >10 but is in principle a little worse in the series lower gain amps scenario

audio THD, closed loop bandwidth improve with the series lower individual gain feedback amps

you can do even better by using as much of both amp's gain as possible inside a common global feedback loop
but stability concerns with the 2 op amps inside a common global feedback loop make more complicated multiloop feedback necessary
 
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While it is theoretically to have all the gain in one OP-amp I never go over 100x with a single device and usually try to keep it 10x to 30x.

Is there an application in analog audio where you would ever need that much gain? I just did the passive RIAA project and it had 56dB of gain with 2 gain stages. Noise was a pain in the a$$. I can't even imagine doubling that.
 
Here is an example datasheet for the NE5532:
http://www.ti.com/lit/ds/symlink/sa5532a.pdf

What should I look at to determine the maximum gain without losing anything in the audio bandwidth for1 stage of gain?

Would there be lower noise or less THD if instead of pushing 1 gain stage close to it's max, you used 2 stages of half of the gain to sum to the same level?
You may wish to look for an opamp with a high open loop bandwidth. It's easy enough to assume most opamps used at unity gain have at least 100dB of feedback at a couple hundred Hertz, but at 20kHz there may be less than 10dB of distortion correction available. This is why most THD specifications on audio products are taken at 500Hz or 1kHz. Companies with greater integrity will provide a 20-20kHz specification.

The actual harmonics above 10kHz are maybe of limited importance, but since the feedback is ineffective at high frequencies in low open loop designs, the opamp becomes prone to transient distortions too. This may account for the hardness or harshness that people hear in some designs. Harmonic distortion in sinewave test is a lesser evil compared to how a design reproduces rapidly changing signals to the start and finish. I read an engineer's paper on this about 7 months ago and it was an eye opener. Alot of other engineers out there miss those points.

The problem with getting wide open loop bandwidth is that these designs are typically unstable at unity, so you can't apply alot of feedback either (must be used above unity) but it may be on the order of 10, 20, or 30dB lower THD at 20kHz compared to a unity stable opamp. More feedback at high frequencies means better signal integrity. You can reference the bode plots for weighing this all in. It would be nice to compile a spreadsheet of opamp comparing this information for making informed opamp choices.
 
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