Agilent Spectrum Analysis Basics - Agilent Technologies

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:
F = S i /N i
S o /N o
where
F= noise figure as power ratio (also known as noise factor)
S i = input signal power
N i = true input noise power
S o = output signal power
N o = output noise power
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:
F = N o /N i
This expression tells us that all we need to do to determine the noise figure
is compare the noise level as read on the display to the true (not the effective)
noise level at the input connector. Noise figure is usually expressed in terms
of dB, or:
NF = 10 log(F) = 10 log(N o ) – 10 log(N i ).
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.
We know that the displayed level of noise on the analyzer changes with
bandwidth. So all we need to do to determine the noise figure of our
spectrum analyzer is to measure the noise power in some bandwidth,
calculate the noise power that we would have measured in a 1 Hz bandwidth
using 10 log(BW 2 /BW 1 ), and compare that to –174 dBm.
For example, if we measured –110 dBm in a 10 kHz resolution bandwidth,
we would get:
NF =
[measured noise in dBm] – 10 log(RBW/1) – kTB B=1 Hz
–110 dBm –10 log(10,000/1) – (–174 dBm)
–110 – 40 + 174
24 dB
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.
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.
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