# Signal to noise degradation based on noise temperature vs noise figure

I have a question regarding the signal to noise degradation after a device with a known noise figure.

I must be wrong in some of the assumptions I'm making. As far as I know, the S/N degradation should be equal to the noise figure, but if I calculate it using noise temperatures, I get very different values.

Let:

SNidB: Signal no noise at the input, in dB
SNidB: Signal to noise at the output, in dB
Te: Excess temperature of the device at the input
T0: Reference temperature = 290 ºK
Ti: Noise temperature at the input = 10 ºK (e.g. an antenna pointing at the sky)
Nf: Noise figure of the device = 0.8 dB
Ps: Power of the input signal = -120 dBm
Pni: Noise power at the input
Pno: Noise power at the output
B: Bandwidth = 2.4 kHz


The noise power at the input is:

Pni = 10log10 (kTi*B / 10^-3) = -154.8 dBm

So, the signal to noise at the input:

SNidB = -120 + 154.8 = 34.8 dBm

If we calculate the noise power after the device in terms of it's noise temperature contribution:

Knowing that:

F=1+Te/T0

Nf = 10*log(1+Te/T0)

Then, with our given Nf of 0.8 dB:

Te = 58.7K

And the noise power at the output is

Pno = 10log10(k(Ti+Te)*B / 10^-3) = -146.4 dBm

So, the signal to noise at the output:

SNodB = -120 + 146.4 = 26.4 dB

Which gives us a degradation of 34.8 - 26.4 = 8.4 dB

But, according to the noise figure definition

** Nf = SNidB - SNodB, which should be our given 0.8 dB != 8.4 dB

¿What am I doing wrong?

• SNodB calculation omits the gain of this system.
– user16324
Commented Dec 10, 2020 at 13:32