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OP AMP Spec - noise gain configuration??
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innkeeper:
I ran into something on a spec sheet for an opamp that I do not understand what it is or what it means. "noise gain configuration"

What are they referring to when they talk about "noise gain configuration"?  Can someone explain this to me?

from the spec sheet:
The LTC®6090/LTC6090-5 are high voltage, precision
monolithic operational amplifiers. The LTC6090 is unity
gain stable. The LTC6090-5 is stable in noise gain
configurations of 5 or greater. Both amplifiers feature high
open loop gain, low input referred offset voltage and noise,
and pA input bias current and are ideal for high voltage,
high impedance buffering and/or high gain configurations.
Zero999:
https://www.analog.com/en/analog-dialogue/raqs/raq-issue-91.html
https://www.analog.com/media/en/training-seminars/tutorials/MT-033.pdf
https://www.edn.com/electronics-news/4054393/Noise-gain-influences-op-amp-choice
Zero999:
Here are two op-amp circuits. Both have a unity inverting signal gain.

A basic inverting amplifier


An inverting amplifier with 30k resistor connected between the op-amp's inverting input and 0V.

At first it may seem like the one with R3 aught to have a lower gain and it does by a small margin, especially at high frequencies, but the inverting input is a virtual ground node, so it's not that straightforward. There are two effects which cancel one another out.

R2 and R3 form a potential divider, which should divide the input signal by 5. VOUT = VIN*R3/(R2+R3) and when VIN = 1V:
VOUT = 1*30k/(120k+30k) = 0.2V.

But the output impedance of the potential divider is equal to the value of the two resistors in parallel.
ROUT = (120k*30k)/(120k+30k) = 24k

This can be simplified to an equivalent circuit, showing 0.2V in series with 24k.

When connected to the op-amp circuit,  the gain is now 5.


So we have an attenuator dividing the signal by a factor of 5, connected to an op-amp with an inverting gain of 5, giving a total gain of 1.

Now, imagine the input is connected to zero and a noise voltage is injected into the inputs. To simplify matters assume it's the non-inverting input. Say the noise voltage is 10nV. The circuit is now a non-inverting amplifier. Remove R3 and it has a gain of Av = 1+ 120k/120k = 2, keep it and you have a gain of 6. So assuming there are no other noise sources, the output noise will be 20nV, without R3 and 60nV with it in place.


So why might an op-amp only be stable when the noise gain is over a certain figure?

The op-amp has phase shift and if there's still gain, when the phase shift is 180º it will oscillate, since negative feedback, will become positive. The resistors in the feedback network, attenuate the op-amp's output, before it's fed back into the negative input. If the op-amp has a gain of 5, when the phase shift is 180º, then it will oscillate if the resistive divider attenuates the signal by less than a factor of 5. In the circuit with the noise gain of 6, but signal gain of unity, the resistive divider is attenuating the output by a factor of 6, so it won't oscillate, if the op-amp has a gain of 5, with a 180º phase shift.

In practice, the circuit can still ring, even if the gain us under unity, when the phase shift is 180º, as it will be under-damped, so op-amps are designed to have a phase margin or less than that, so they're over-damped.

To reduce the noise at lower frequencies, yet still avoid oscillation, R3 can be connected to 0V, via a capacitor. Here's a demonstration of a noise analysis. I've made the input noise of the op-amp stupidly high, at 10mV, (en = 10mV) so it dominates. At low frequencies the noise gain is 2, at higher frequencies it's 6, followed by a roll-off at much higher frequencies, due to the op-amp running out of gain.
David Hess:
The simple answer is that the noise gain is equal to the non-inverting gain of the circuit.  So an inverting configuration with a gain of -1 has a noise gain of 2 if it was treated as a non-inverting amplifier.  A unity gain follower is an non-inverting amplifier with an infinite shunt resistance so its noise gain is 1 and therefore the least stable configuration.
Zero999:
A simulation showing an op-amp, which isn't fully unity gain stable. It rings when the noise gain is 2, but is made stable, with a noise gain of 12, at high frequencies. To minimise noise, R3 is AC coupled, so the noise gain only increases at high frequencies.


The above circuit's step response. It's fully stable, no ringing, with a noise gain of 12.


The above circuit with C1 and/or R3 deleted. It's no longer stable and rings on the edges of the square wave.
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