Agilent Spectrum Analysis Basics - Agilent Technologies

We have already seen that both video filtering and video averaging reduce
the peak-to-peak fluctuations of a signal and can give us a steady value.
We must equate this value to either power or rms voltage. The rms value
of a Gaussian distribution equals its standard deviation, σ.
Figure 5-6. Random noise has a Gaussian amplitude distribution
Let’s start with our analyzer in the linear display mode. The Gaussian noise
at the input is band limited as it passes through the IF chain, and its envelope
takes on a Rayleigh distribution (Figure 5-7). The noise that we see on
our analyzer display, the output of the envelope detector, is the Rayleigh
distributed envelope of the input noise signal. To get a steady value, the
mean value, we use video filtering or averaging. The mean value of a Rayleigh
distribution is 1.253 σ.
But our analyzer is a peak-responding voltmeter calibrated to indicate the
rms value of a sine wave. To convert from peak to rms, our analyzer scales
its readout by 0.707 (–3 dB). The mean value of the Rayleigh-distributed
noise is scaled by the same factor, giving us a reading that is 0.886 σ (l.05 dB
below σ). To equate the mean value displayed by the analyzer to the rms
voltage of the input noise signal, then, we must account for the error in the
displayed value. Note, however, that the error is not an ambiguity; it is a
constant error that we can correct for by adding 1.05 dB to the displayed
value.
In most spectrum analyzers, the display scale (log or linear in voltage)
controls the scale on which the noise distribution is averaged with either
the VBW filter or with trace averaging. Normally, we use our analyzer in the
log display mode, and this mode adds to the error in our noise measurement.
The gain of a log amplifier is a function of signal amplitude, so the higher
noise values are not amplified as much as the lower values. As a result, the
output of the envelope detector is a skewed Rayleigh distribution, and the
mean value that we get from video filtering or averaging is another 1.45 dB
lower. In the log mode, then, the mean or average noise is displayed 2.5 dB
too low. Again, this error is not an ambiguity, and we can correct for it 8 .
8. In the ESA and PSA Series, the averaging can be
set to video, voltage, or power (rms), independent
of display scale. When using power averaging, no
correction is needed, since the average rms level is
determined by the square of the magnitude of the
signal, not by the log or envelope of the voltage.
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