Noise voltage and Noise figure relationship

[Leiser]

Hi,

does anyone know if there is any equation that relates noise voltage (dBuV) with noise figure (dB) and viceversa for an amplifier?

For exemple, a noise voltage =0dBuV for a 12dB gain FM amplifier , measured in 120KHz BW, what would be the noise figure in db?

Thanks a lot.

 

[logbook]

Well now that is a potentially tricky area.

You are quoting a very narrow bandwidth for an RF device which makes me suspicious.

For low frequency amplifiers you do not quote noise figure, but input referred voltage and current noise. For an RF amplifier with 50 ohm inputs and outputs you do quote noise figure, but you do not measure the output noise voltage, you measure the output noise power. Of course if you are using an RMS voltage measuring device then that is acceptable. Interestingly a spectrum analyser does not measure RMS values, although it is correctly calibrated for RMS values of sinusoidal tones.

You then need to decide it you want to make a spot noise measurement or an averaged value over the whole band (probably the whole band for such a narrow band device). Then figure out how the “noise bandwidth” relates to the 3dB bandwidth.

Like I said, there is a lot of tricky stuff in this area to catch you out. Be very specific about your amplifier and test equipment and we can be more specific. Otherwise we have to present a lot of “if” clauses. There is lots of data on noise figure measurements on the web for you to read up on including app notes from Agilent.

 

[logbook]

The available noise power from the input termination at 290degK is kTB

=1.38E-23 * 290 * 120E3 = 4.8E-16 W

The power gain is 12dB, giving x15.85 power gain
and 7.607E-15 W ideal output. The RMS voltage into a 50 ohm load that would cause this much power is sqrt (50* 7.6E-15) = 0.617µV RMS.

In this case we have 1µV output so the noise figure is 20*log10(1/0.617) = 4.2dB

Or we could try it another way just for interest!
We have kT watts/Hz noise power density at the input.
That is 4.0E-21 W/Hz or -174 dBm/Hz.
We then expect (-174+12) dB/Hz at the (12dB) amplifier output = -162dBm/Hz.
The bandwidth of 120kHz contributes 10*log10(120E3)= 50.8dB, giving -111.2dBm at the output. 1µV into 50 ohms gives 2E-14W = -107dBm.

The noise figure of the amplifier is therefore
-107 - -111.2 = 4.2dB.


This should be enough to get you started. You should now go off and crack open a text book or surf the wikipedia and the RF Café etc to get the formulae and more info.

 

[Leiser]

Hi Logbook!

Thanks a lot for your explanation, quite ilustrating and useful and for your time.

I find this web very interesting. I am designing LNA´s for the automotive market and I am finding lots of doubts in my way, I´m having a good time though!.

Thanks a lot again.

 

[zappedagain]

Logbook,

I'm taking this thread a bit off topic - you said "Interestingly a spectrum analyser does not measure RMS values, although it is correctly calibrated for RMS values of sinusoidal tones."

So what/how does a spectrum analyzer measure? I started thread236-186261 looking to quantify the RMS of a pulse. You have me thinking that may have been the wrong track...

Thanks,

z

 

[logbook]

It is difficult to generalise, or at least it is inaccurate to generalise. Older spectrum analysers were easy. They peak-detected within the IF bandwidth, hence “peak reading rms calibrated”. Recent (expensive) spectrum analysers have multiple selectable detectors which can measure some out of the selection mean (average), peak, rms, quasi-peak, and more specialist variants used for comms. They would all read the same for a single tone within the IF band. The differences would occur due to pulse repetition frequency and number of tones within the IF bandwidth. Noise would be the ultimate in number of tones within the IF bandwidth. You might then be interested in measuring noise with a discernable slope characteristic within the IF bandwidth.