This is a
minimal spectrum analyzer but has the essential components which illustrate the
basic operation. The preselector, if it is present, is a broadband
tunable filter that tracks the local oscillator and limits the RF signals which
can get to the mixer. In the MMS spectrum analyzers, the preselector bandwidth
is in the range of 20-70 MHz, depending on MMS model and center frequency.
The preselector bandwidth does not enter into sweep time calculations.
The local oscillator sweeps between two frequencies over a specified span, SP, in a certain sweep time, ST. While the sweep time can be specified, it is usually calculated by the spectrum analyzer as discussed below. Regardless, one should be aware of whether SP/Nsamples is less than or greater than RB, as illustrated by these figures:
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The ability of the spectrum analyzer to resolve two closely spaced signals is controlled by the intermediate frequency filter, which has an adjustable resolution bandwidth, RB. The price of higher RB is higher noise in the spectrum.
When baseline noise is not a consideration, one generally wants to minimize
the sweep time. Consider the time that the spectrum analyzer spends in each
resolution element:
The time which the spectrum analyzer spends in the passband must be
consistent with the RB: the filter must have time to charge up. If the
passband function is Gaussian:
where
f is the frequency relative to the band center and 
is a measure
of the width, then the Fourier transform, the time-domain response of the
filter, is
Figure 1:
Resolution bandwidth (RB) is defined as the width at which the filter
response falls to 50% of its maximum.
The 
is related
to through
eq.2
by noting that 
The
time it takes for the filter response to from 1/x of its maximum and then
fall again to 1/x is given by 
where (see
eq.3):
Figure 2: In
this illustration, the time interval shown is sufficent for the filter to rise
from 0.1 (x = 10 of its maximum response, and then fall to 0.1.
For example, to give the filter time to rise from 1% of its maximum response
and then to discharge to 1%, x=100, and 
. HP uses
a factor of 2.5, so that eq.1
leads to 
This
requires that the bandwidth of the video filter is wide enough to pass the
fastest signal fluctuations generated by the sweep. Using the same criterion as
for the IF filter time constant, 
This
is the default mode for HP spectrum analyzers, when VBW and ST are
set to AUTO.
When VBW is set to MAN and 
, extra
time must be allowed for the video filter to settle, and thus the sweep time
equation becomes 
Video
smoothing has the effect of reducing the noise in the baseline by increasing the
time in each resolution element by a factor of 
.
In addition to separately controlling both and 
, HP
spectrum analyzers allow the
ratio to be set so that it is kept fixed as is changed.
If 
is not set
to MAN, an HP spectrum analyzer will automatically calculate the minimum
sweeptime according to 
If the
sweep time is set manually to less than this value, the filters will not respond
correctly and the amplitude of the spectrum analyzer will not be correctly
calibrated. The UNCAL symbol will appear on the display.
The radiometer equation gives the noise in the spectrum:
where 
is the
time which the spectrum analyzer spends in the resolution element at the sample
point. If the sweeptime is automatically calculated using the above equations,
then we get 
using the
minimum sweep time. Increasing the sweep time further does not reduces the noise
because the video filter does not then average all the signal obtained while the
sweep is in a given resolution element.
Further noise reduction is possible using video averaging (see Reference 1, p. 17).