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I am wondering why the feedback resistor values specified in the datasheet of the AD797 are so small. My understanding is that the low feedback resistances keep the noise small, but isn't it also not ideal to have large currents flowing through the feedback network? My understanding was that feedback resistors should be >1k.

Here is a link to the datasheet: https://www.analog.com/media/en/technical-documentation/data-sheets/ad797.pdf

And a picture of an example application:

26.1 ohms seems like far too small a value for feedback resistors.

This op-amp boasts input noise of 0.9nV/rt.Hz, which is roughly equal to the Johnson noise of a 50 Ω resistor over the human audio bandwidth. If you aren't putting resistors smaller than that around it, you're wasting some of this op-amp's performance, and probably should be buying something cheaper.

If you refer to figure 34, the total noise (assumed to be the white noise region for both en and in) is approximately 8x better at 10 ohms source resistance compared to 1K.

Remember that it’s not only the noise voltage and the Johnson-Nyquist noise from the feedback resistors but the input noise current multiplied by the resistance seen looking out from the inverting input.

The transistors at the input are run at very high currents so the voltage noise is quite low, but there is a cost in current noise.

They all add in quadrature, of course, since they are typically uncorrelated.

The resistors as shown are tolerable for smallish output swings and if you don’t care too much about accuracy of gain.

With honor to Walt Jung (of ADI, et al), low values of resistors can cause detectable THERMAL distortion. Drive the opamp with 20Hz and 2,000Hz; use a spectrum analyzer, and you'll see the 2,000Hz output with some 20Hz sidebands.

Which means what? Use physically larger resistors. Or experiment with resistors having different resistive element structures? The very thin metal-file-spiral-trimmed has a very fast timeconstant for heating/cooling, as heat is dumped into the ceramic/clay core.

And the opamp may need a BUFFER, to avoid generating thermal distortion as the silicon undergoes transient heating, as the UP transistors turn off and the DOWN transistors turn off.

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Separate topic: the opamp has only 70dB PSRR at 10KHz. 70dB is 3,000:1.
So what? Will a thermally-noise VDD-regulator be a problem? Some LDOs have internal equivalent Rnoise of 10,000,000 ohms (Often in poly-silicon servo-feedback resistors, and in diffpairs operating in subthreshold at 100nanoAmp
currents). This produces 1 microvolt per rootHertz random thermal noise on the "clean" VDD rail. Is this a risk?

If you have 60dB PSRR at 10KHz, that 1microVolts becomes 1 nanoVolt Referred to Input, which is a 3dB increase of the opamp's noise floor. And at 100KHz, the opamp has only 50dB PSRR (from a datasheet plot).

Summary: pay attention to the VDD rail random noise. And don't think about using switchRegs in these systems, unless you

---- use magnetic shielding

---- use electric-field shielding

---- pay attention to building "local batteries" for the opamp's two rails

---- design the Ground, with slits, etc to keep trash away from the opamp

A graph in the datasheet of the opamp shows it clipping with an output voltage swing of only plus and minus 2V into the 26.1 ohm resistors which might not be enough.