Noise_Figure

Noise figure
Many receiver manufacturers specify the performance of their receivers in
terms of noise figure, rather than sensitivity. As we shall see, the two can
be equated. A spectrum analyzer is a receiver, and we shall examine noise
figure on the basis of a sinusoidal input.

Noise figure can be defined as the degradation of signal-to-noise ratio as a
signal passes through a device, a spectrum analyzer in our case. We can
express noise figure as:

If we examine this expression, we can simplify it for our spectrum analyzer.
First of all, the output signal is the input signal times the gain of the analyzer.
Second, the gain of our analyzer is unity because the signal level at the
output (indicated on the display) is the same as the level at the input
(input connector). So our expression, after substitution, cancellation,
and rearrangement, becomes:

We use the true noise level at the input, rather than the effective noise level,
because our input signal-to-noise ratio was based on the true noise. As we
saw earlier, when the input is terminated in 50 ohms, the kTB noise level at
room temperature in a 1 Hz bandwidth is 174 dBm.

Noise figure is independent of bandwidth 4 . Had we selected a different
resolution bandwidth, our results would have been exactly the same.
For example, had we chosen a 1 kHz resolution bandwidth, the measured
noise would have been 120 dBm and 10 log( RBW/1) would have been 30.
Combining all terms would have given 120 30 + 174 = 24 dB, the same
noise figure as above.

4. This may not always be precisely true for a given
analyzer because of the way resolution bandwidth
filter sections and gain are distributed in the IF chain.