| Mode | Span | RBW | VBW | ST | Effective Int.Time |
Notes |
|---|---|---|---|---|---|---|
| default | specified | specified | AUTO | AUTO | 2.5/RB | VB=RB; fastest possible ST; good for narrow signals |
| optional | specified | specified | MAN | AUTO | 2.5/VB | reduces noise power by sqrt(VB/RB) |
| optional | specified | specified | MAN | MAN | 2.5/VB | does not minimize noise effectively if ST > STmin; amplitude is uncalibrated if ST < STmin |
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:
|
|
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).