OpAmp input noise and noise gain

[raff5184]

Hi all,
few questions about op amp input noise and noise gain.

1) Given the input noise voltage n (typically in [nV/sqrt(Hz)] )  if I want to know the noise voltage in output, I calculate:
n*sqrt(Bw)*A
where Bw is my bandwidth and A the closed loop gain.
But what if I work only at one specific frequency f*? Is it simply n*A?

2) If n is not constant but changes with the frequency (for example see Figure 11: https://www.apexanalog.com/resources/products/pa90u.pdf), and I work in the range, say from 10 Hz to 1kHz then I need to integrate the input Noise Voltage curve given in the datasheet over the operating frequency range, correct?

3) The noise gain.
The AD Tutorial (page 3: http://www.analog.com/media/en/training-seminars/tutorials/MT-033.pdf) says that: "Noise gain is equal to the signal gain of a non-inverting amp. Noise gain is also the same for either an inverting or non-inverting stage. ".
So, in case I am designing an inverting op amp, by which gain do I need to multiply the noise? Non-inverting gain?


Thank you

[awallin]

Try this video series by Analog Devices:
https://www.youtube.com/playlist?list=PLBD1F10D92010F8D7

[Marco]

But what if I work only at one specific frequency f*?

At one specific frequency the noise is zero, it just takes longer than the universe exists to measure it. Or in other words, there is no such thing as one specific frequency outside of mathematics.

[David Hess]

1) Given the input noise voltage n (typically in [nV/sqrt(Hz)] )  if I want to know the noise voltage in output, I calculate:
n*sqrt(Bw)*A
where Bw is my bandwidth and A the closed loop gain.
But what if I work only at one specific frequency f*? Is it simply n*A?

Yes, at one frequency, the output spot noise is just the input spot noise times the noise gain.

2) If n is not constant but changes with the frequency (for example see Figure 11: https://www.apexanalog.com/resources/products/pa90u.pdf), and I work in the range, say from 10 Hz to 1kHz then I need to integrate the input Noise Voltage curve given in the datasheet over the operating frequency range, correct?

That is correct.  You can integrate either the input noise and multiply by the noise gain or integrate the output noise to get the same result.

3) The noise gain.
The AD Tutorial (page 3: http://www.analog.com/media/en/training-seminars/tutorials/MT-033.pdf) says that: "Noise gain is equal to the signal gain of a non-inverting amp. Noise gain is also the same for either an inverting or non-inverting stage. ".
So, in case I am designing an inverting op amp, by which gain do I need to multiply the noise? Non-inverting gain?

Equations 2, 3, and 4 on page 3 of MT-033 cover this.  For a non-inverting amplifier, the closed loop gain and noise gain are the same.  For an inverting amplifier, the noise gain is 1 plus the signal gain.  I usually ignore this difference but it can matter at low inverting gains.