# Noise Spectral Density Standard

Is there an IEEE or other standard for how Noise Spectral Density is calculated? In particular, when they give a single figure (like $$\12.4\,\text{nV }/\sqrt{\text{Hz}}\$$) is that averaged over the whole spectrum, including the $$\1/f\$$ flicker noise, or is that only a measure of the noise floor?

A follow up to that would be, if that is the case what is the standard for the bandwidth range to use when measuring noise floor?

I have never heard of an IEEE standard regarding noise. I also think it isn't needed as a noise specification should be clear by itself.

A figure like $$\12.4 nV/\sqrt{Hz}\$$ doesn't mean anything on its own.

An example of a proper specification would be:

$$\V_{noise} = 12.4 nV/\sqrt{Hz}\$$ at $$\1 kHz\$$ (spot noise)

or

$$\V_{noise} = 12.4 nV/\sqrt{Hz}\$$ between $$\1 kHz\$$ and $$\1 MHz\$$ (flat noise)

or

the 1/f noise is:

$$\V_{noise} = 12.4 nV/\sqrt{Hz}\$$ at $$\1 kHz\$$

(spot noise, which is 1/f so halves at 2 kHz and doubles at 500 Hz)

Often the 1/f noise will "flatten out" at some higher frequency into a "flat" (thermal) noise. For example:

Above is all "spot noise" so the noise at a particular frequency and in a 1 Hz bandwidth. If you want integrated noise then you have to integrate the spot noise value over the frequency, this is easiest when the noise is flat over frequency as we can then just multiply it with the square root of the bandwidth.

For example let's take the flat noise from above:

$$\V_{noise} = 12.4 nV/\sqrt{Hz}\$$ between $$\1 kHz\$$ and $$\1 MHz\$$ (flat noise)

and let's say we want to integrate that over 100 kHz to 1 MHz = 900 kHz that will result in:

$$\V_{noise} = 12.4 nV/\sqrt{Hz} * \sqrt{900 kHz} = 11.7 \mu V\$$

Note the unit, it is Volts now!

More info in this TI Application Report.

• Ah, ok, that makes a lot more sense. Looking back over the datasheet for the MAX44263, it does say that the condition for the spot noise of 12.7 nV/sqrt(Hz) is at f=10kHz. Feb 28 '19 at 0:38

As far as I'm aware, there's no specific standard here, but that doesn't mean you can't make "sane" assumptions about it:

First of all, for really wideband observations, noise floor power isn't constant; physically, it can't be, with limited power in the universe and all.

So, any noise PSD is always w.r.t to some explicit or implicit bandwidth of interest. If you've got an amplifier spec'ed for 900 to 1800 MHz, it's fair to assume that the noise power spectral density isn't higher than the given density in any reasonably wide bandwidth (for extremely narrow bandwidths, that'd be a spur with some power, not very much something you'd give as PSD).

Remember that PSD is just the expectation of the Fourier Transform of the Autocorrelation function; fluctuations are in the random nature of noise!

By the way, flicker noise is a very specific type of noise and you'd normally see that specified separately, if it occurs in a device significantly often.