Noise Figure expressed in dB instead of nV/√Hz (noise density)?

[Tormy]

Several times I get this indication from datasheets:
but it's not the common case.

Normally I get nV/√Hz (noise density in the bandwidth range).
And when I need to compare 2 or more devices, if some of them has the NF in dB, I can't. It is like to compare apples with oranges.
The dB value is referred to what? Since dBs in voltages are always 20 times logarhythms of ratios.
The goal i to convert form one format to another, to be possible to compare stuff.

 

[RoadrunnerOZ]

NF - noise figure is the change/difference between input signal/noise ratio and output signal/noise ratio due to noise contribution by components in the circuit chain. If S/N is 90dB at the input and 88.5dB at the output then the NF is 1.5dB

 

[gyraf]

Yes, it's a measure of "distance from theoretically possible"

 

[Tormy]

NF - noise figure is the change/difference between input signal/noise ratio and output signal/noise ratio due to noise contribution by components in the circuit chain. If S/N is 90dB at the input and 88.5dB at the output then the NF is 1.5dB

Ok it means that the noise output is 1.188 times higher than the input noise. But this doesn't return how big the generated noise is.
I mean I can have a huge noise in input and a 1.5dB huger noise at the output. Having no noise in the input, I get 1.5dB noise at the output but what's it's density? Again: I can't compare dB with nV/√Hz May be 1.188 nV/√Hz? Should I read it in this way or should I interpret the 1.188 times as the RMS value? Or the pp value above the 0?

 

[gyraf]

The trick is: there is no such thing as "no noise"

 

[Tormy]

The trick is: there is no such thing as "no noise"

Right, indeed was an assumption. So I still can't compare 2 devices where in one case I get V/√Hz and the other cas I get dB values.
It seems that the answer to my question is: there is not any way.

NOTE: In physics we have the "ridig body" which it's not either a thing. It's just a concept. But it's used as commodity. Hence I was picturing that the "no noise" could be such thing as well

 

[RoadrunnerOZ]

Comparing two devices that have different scales is possible if you have common factors. Have a look at this calculator it may be of use:

https://3roam.com/dbm-hz-to-nv-sqrt-hz-calculator/
There is no piece of gear with no noise so everything has a signal to noise ratio which is what the noise factor reduces - the normal good stuff has signal to noise ratios of way better than 100dB but never infinity. Adding 1.5dB of noise to a noise floor of absolute 0 (which is impossible except in space) is in effect subtracting from a signal to noise ratio of infinity which is still infinitydB - 1.5dB below nominal 0dB.

I mean I can have a huge noise in input and a 1.5dB huger noise at the output. Having no noise in the input, I get 1.5dB noise at the output

When you say a huge noise at input I think you’re mixing up noise with signal - the noise floor in a piece of equipment is the amount of noise that is inherently present, not part of the signal itself which does not modify the noise floor (except by heating components) and this noise is compared to signal only at the output, at the nominal gain setting of the amplifier by use of a test signal to obtain a signal to noise ratio - at whatever is nominated test signal frequency/level and amp gain control setting used for specs.
If there is no signal input to an amplifier there will still be noise which is measurable - but this is an amount not a ratio and also not a true representation of the inherent noise which comes from gear running at its expected temperature, frequency and operating signal level, being the sum of the noise contributions of all components in the signal path. With a test signal being run the components which can contribute noise will heat up and generate their typical mount of noise - if you then measure the signal level and also the noise level at the output you will be able to get a ratio. If you just measure the noise level cold you don’t get a true figure.
Individual components have their own noise level but will have a specific frequency range, impedance and temperature gradient spec for maximum noise, op-amps will also have gain dependent noise as well as inherent quiescent noise.
The noise factor of a component is how much it will decrease the signal to noise ratio by when included in a circuit.

 

[Newmarket]

Probably a good idea to read this:
https://www.analog.com/media/en/training-seminars/tutorials/MT-052.pdf

And bare in mind that nV/√Hz defines only voltage noise so is independent of source impedance.
And nV/√Hz is often only stated in data sheet at one (typ 1kHz), or maybe two values. In reality and in general it varies with frequency.
NF defines the noise performance of an amplifier in a specific case and measurement bandwidth of the output signal needs to be defined.

 

[Tormy]

When you say a huge noise at input I think you’re mixing up noise with signal

Not really what I meant I mean: I didn't confuse the noise with the signal.
I just expressed a condition by using an "absurd" one.

If there is no signal input to an amplifier there will still be noise which is measurable -

Exactly. And we don't know the intensity of it just by the 1.5dB figure.

My understanding is: the input noise has a X value.
The output noise is added to the one present to the input.
So the output has Y value
In this case, 20 times the Log(10) of Y/X, returns the 1.5dB into the datasheet it means that Y/X = 1.188

so: the input noise can be extremely small or not so small (here my term: huge) ... it's however measurable, but we don't know which level it has. We only know that the added noise is 1.5dB. It's known the ratio.

Note: the datasheet reports dB and not dBm (which are dB referred to mW), While the site offers to convert from dBm to nV/√Hz

 

[Tormy]

Probably a good idea to read this:
https://www.analog.com/media/en/training-seminars/tutorials/MT-052.pdf

Thanks for the excellent documentation.

And bare in mind that nV/√Hz defines only voltage noise so is independent of source impedance.
And nV/√Hz is often only stated in data sheet at one (typ 1kHz), or maybe two values. In reality and in general it varies with frequency.
NF defines the noise performance of an amplifier in a specific case and measurement bandwidth of the output signal needs to be defined.

Well, I knew that the √Hz is referred to the bandwidth not to a specific frequency, since the nV/√Hz is a measure of noise density in the bandwidth rather than a measure of noise at a specific one.

 

[MicUlli]

The noise figure in dB says how much excess noise is present in comparison with the input resistor. In your example we see that the source resistor is 10 kOhm.
1,5 dB noise figure means that the total noise is that of a 14,1 kOhm resistor. Therefore the transistor is as noisy as a 4,1 kOhm resistor. A 4,1 kOhm resistor produces a voltage noise density of 8,1 nVs^(-0,5).

 

[Newmarket]

Thanks for the excellent documentation.

You're more than welcome

Well, I knew that the √Hz is referred to the bandwidth not to a specific frequency, since the nV/√Hz is a measure of noise density in the bandwidth rather than a measure of noise at a specific one.

Yes. But what I meant is that the nV/rt Hz figure itself changes with frequency. Eg a NE5534 opamp datasheet indicates a higher typical figure @ 30 Hz cf 1kHz (from memory but in any case the idea holds). To account for these changes we would split the frequency range into relevant zones and make straight line approximations.

 

[Tormy]

The noise figure in dB says how much excess noise is present in comparison with the input resistor. In your example we see that the source resistor is 10 kOhm.
1,5 dB noise figure means that the total noise is that of a 14,1 kOhm resistor. Therefore the transistor is as noisy as a 4,1 kOhm resistor. A 4,1 kOhm resistor produces a voltage noise density of 8,1 nVs^(-0,5).

thank you really very much. believe me or not, this detail was under my nose and I was not reading it. And I had to.
I feel myself an idiot. Thank you for the highlight. Indeed having these parameters, everything is calculable as you did and it makes sense.
This slap-on-my-face will be very useful any next time.
Yes the NF then is in dB power since the formula form the document is 10 * Log10(Noise Factor) and not 20 * Log10(Noise Factor) as I was supposing (since it was expressed in nV I got in confusion).

 

[Tormy]

You're more than welcome


Yes. But what I meant is that the nV/rt Hz figure itself changes with frequency. Eg a NE5534 opamp datasheet indicates a higher typical figure @ 30 Hz cf 1kHz (from memory but in any case the idea holds). To account for these changes we would split the frequency range into relevant zones and make straight line approximations.

Ok now we're re-aligned. Thank you so much

 

[JohnRoberts]

I prefer NF specs because it is independent of qualifying terms (like bandwidth) that can distort metrics. Of course it is just another way to say/measure the same characteristic (equivalent input noise). One important qualifier is the @X ohms impedance.

I killed a lot of brain cells doing deep dives into this stuff back in the 70s/80s. Now we have better discreet devices and better op amps. enjoy

JR

 

[moamps]

This is a great article on the subject.

 

[Tormy]

Thank you very much to all of you guys.
I've also created an Excel file where I put the dB value, the test conditions and I get the nV/√Hz. Once forever this thing is solved