Noise figure versus input referred noise

If we use the specification for a low noise amplifier, invariably the noise performance is a Noise Figure. However, in a particular system design we calculated the input referred voltage that could be a limiting factor for the very first stage LNA. The issue was how to convert from the noise figure of a selected LNA ( from Analog Devices no less) to the input referred noise voltage to make sure the amplifier was being chosen correctly. Well here is the conversion at least in one form.

Note: The noise factor is simply 1 + NA/Ni. Ni is the noise power coming in from a 50 Ohm matched source and is equal to -174 dBm/Hz. ( Pretty standard usage).

The noise voltage being generated by the 50 Ohm source is vni=4.46E-8 Vrms/Hz. This can then be used to compare whether the amplifer will work with a particular noise figure ( from the expression 1 + NA/Ni).

Check and see if the number NA, the noise input referred power generated by the amplifier itself, converted from a voltage to power is acceptable or not. Must remember to use the impedance level of 50 Ohm. Simple?


Example: If the NF is = 0.8, then 1+ NA/Ni = 10**0.08 = 1.2 ( approx). We can calculate vna as above for vni.

Here is a note on input noise. It has been found that the -174 dBm/Hz should be modified to -162 dBm/Hz for the rural environment in the US and to -98 dBm/Hz for the urban environment. The -174 dBm/Hz is therefore a theoretical figure used to specify and calculate noise figures and noise factors!

Yes, another thought; we need to make sure that the derivation for the noise factor is elaborated: Here it is:

Noise factor F = SNRi/SNRo where i stands for input and o stands for output.

So = Si X G ( G = Gain)
No = [Ni noise power from the 50 Ohm source + NA, noise power generated by the amp].

F = [Si/Ni] / [GSi/G(Ni+NA)] = 1 + NA/Ni.

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