16
APPENDICES
APPENDIX A. THE OSCILLOSCOPE DISPLAY
Single or dual cable connection
The DSA524 produces a multiplexed output which enables two
traces plus text to be displayed using only one channel of the
display oscilloscope. The multiplexed output also incorporates a
trigger signal. Consequently the DSA can be connected to the
oscilloscope via just one cable with triggering being sourced from
the input channel.
The disadvantage of single cable connection is that the trigger
signal is visible at the left hand edge of the screen as a very
narrow vertical pulse followed by a short bright line. Connecting a
second cable from the "Trig out" socket to the external trigger
input of the oscilloscope and setting the scope to external trigger
removes the visible trigger signal from the screen.
Triggering
Because the DSA524 produces a multiplexed output waveform,
trigger adjustment is very important particularly when text is
being displayed. If a satisfactory initial set-up display cannot be
obtained check the following points:
The 'scope must be set to single channel operation. The input
coupling must be DC and the sensitivity must be set to
100mV/div. The sweep hold-off and trigger delay (if present)
must be set to minimum. The sweep speed must be set to
50us/div. The trigger source must be from the input channel (not
vertical mode). The trigger slope and level must both be
negative.
Adjust the trigger level. If a satisfactory display can still not be
obtained try setting the sweep speed to 20us/div and then slow-
ing it down to 50us/div using the sweep variable control.
When using a single cable connection, some oscilloscopes (those
having a poor dynamic range on their trigger circuit) may give
unstable triggering when full screen height waveforms are being
displayed. Should this occur, first try careful adjustment of the
trigger level control but if the trouble persists change to a two
cable connection.
Vertical Size
The amplitude of the vertical output is factory adjusted to an
accuracy of + 1 %. The two horizontal lines of the set-up display
are intended to be exactly 6 divisions apart. The output level can
be adjusted to compensate for inaccuracies of the oscilloscope
using the rear panel preset adjustment marked "Set Height". If
the linearity of the oscilloscope is poor, however, it may not be
possible to set the two lines at exactly ±3 divisions from the
arrow tip. If so ignore the vertical position of the arrow tip and
set the two lines to be at ±3 divisions from the graticule centre
line.
The horizontal timing of the DSA524 is crystal controlled to an
accuracy of 0.01% (except for "repeat" mode operation) and
cannot be adjusted.
APPENDIX B. ALIASING
One problem that occurs with digital storage oscilloscopes that
does not occur with real-time oscilloscopes is aliasing.
Sampling theory dictates that any periodic waveform must be
sampled at more than twice the highest frequency component to
avoid aliasing. Aliasing causes the apparent waveform frequency
to be much lower than the real frequency. Thus if the timebase is
set too low an invalid display will result (see Fig a).
To avoid aliasing the timebase must be set as follows:
Minimum time/div = 50 divided by the maximum cyclic signal
frequency.
The difficulties occur when the signal frequency is unknown. In
this case it is safest to set a fast timebase speed initially and
work down.
A second form of aliasing that can occur is visual aliasing. This
occurs when the display is made up of bright dots and the
number of samples per waveform period is low (though greater
than two). The eye can be deceived into incorrectly linking the
dots to form a slower period waveform (see Fig b). The dot join
feature of the DSA524 greatly reduces the chances of visual
aliasing occurring.
Fig a. True aliasing -
waveform sampled at
less than twice the
signal frequency (in
this case
approximately at the
signal frequency).
Fig b Visual aliasing -
vertical separation
between samples
large in comparison
to horizontal separa-
tion, leading to incor-
rect interpretation by
the eye.
If the input signal is repetitive and the trigger repetition rate is
between 50Hz and 5MHz the AUTOSET function of the DSA524
can be used. Autoset resets the timebase to a speed suited to
the trigger rate and well above the point at which aliasing
effects can occur.
APPENDIX C. SINGLE-SHOT BANDWIDTH AND INTER-
POLATION
Probably the most important use of a digital storage instrument
is for the capture of single-shot waveforms (i.e. waveforms
which occur only once). The user will need to understand the
bandwidth restrictions which apply to this mode of operation.
Nyquist sampling theory dictates that a waveform can be per-
fectly re-constructed if sampled at more than twice the fre-
quency of the highest frequency component. Thus a 9.9 MHz
sinewave could be reconstructed if sampled at 20MHz. Unfortu-
nately this assumes that sampling can take place for an infinite
period of time. Clearly this is not possible with a single-shot
waveform.
In theory a single-shot waveform can only be perfectly recon-
structed using an infinite sampling frequency. This is because
the waveform has discontinuities at the start and end which
give rise to infinite frequency elements. Given a known
maximum sampling frequency we need to know how good a
representation of the original waveform can be achieved.
Because there can be no certainty of the existence of any cyclic
elements in a single-shot waveform, sampling theory must be
abandoned. Instead, a subjective principle must be used to
decide what constitutes an acceptable representation of a
waveform. This will depend on the information that the user
needs to obtain from the waveform.
Consider the waveform of Fig c which consists of a rapid
change of level, followed by an exponential decay of sinusoidal
oscillations. If the user requires only to know the settled
amplitudes before and after the change of level the sampling
frequency requirements are modest since a representation
which merely indicates the disturbance and the settled values
will suffice.
