Sampling oscilloscopes 103
amplitude. The smoothing technique reduces noise to a value
corresponding to the reduction in loop gain; in the above
example with a loop gain of one-third, the noise is reduced by
9}/2 dB. The important point is that if the dot density is sufficient,
this noise reduction can be achieved without affecting the shape
of the signal - in other words, without reducing the bandwidth of
the system. We have to pay a price, of course, and in this case the
noise reduction is bought at the expense of time. With the great
dot density needed in this mode, a flickering display or even a
slow-moving spot may result. Nevertheless, it shows how a
technique which is easy in the digital world was in the past
achieved in the purely analogue sampling scope. In a modern
digital sampling scope, the same effect could be achieved by
acquiring the trace twelve times over and storing the average of
the twelve samples for each given point as the result for that
point. Here again, the noise reduction is bought at the cost of
increased time.
Whether you are observing a squarewave, a sine wave, or any
other shape, it is important to make sure that the dot density is
sufficient to produce a true display. If a front panel dot density
control (on some instruments labelled 'scan') is available, the
simplest way to obtain this condition is to increase the density
until no further change of amplitude or shape occurs. Insufficient
dot density, even without smoothing, can sometimes lead to a
'false display'. One example of how this could occur is shown in
Figure 6.9.
Looking first at the 1 MHz signal, with the At selected in the
illustration five samples will be taken, one-fifth, two-fifths .... up
the slope and the fifth sample at the top. When displayed on the
c.r.t, screen, these dots will give the appearance (quite correctly)
of five points on a slope with a 250ns risetime, and further
samples (not shown in the illustration) would complete the
picture of a 1 MHz trapezoidal waveform. Thus a true display of
the 1 MHz signal is built up on the screen. But looking at the
lower waveform, it can be seen that the same samples could have
been the result of sampling a faster (21MHz) signal of similar
shape with the same At, and merely by looking at the screen
display we would have no way of knowing this. In this case, the
104
Oscilloscoprs
{
ri
set
i
rn
e
250
ns)
Period
1
ps
At
50
i
I
i;n
4
M!
4
I
I
I
-
4
.-period
47.6
ns
4
21
MHz
(risetime
12
ns)
If
the
tinw
inlrrval
?.I
hetwrt.n samples exceeds
the
period
of
The
Figure
6.9
input
waveform.
aliasing
can
result
in
a
misleading display
1
MHz
trapezoidal display created by
the
sampling process
wodd
he
a
falsc
display,
an
‘aliascd’ display.
The
cause
of
the
tmuhlc
is
that for the faster signal
the
At
is
far
too
large, lirnc~
thr
clot
densily rriuch
too
low,
to build
up
a
proper picture
of
the individual signal cycles.
(Tlierc
is,
in
lacr,
less than one
dot
per cycle of the 21
MHz
signal.) False displays
can occur with
a11
waveshapes; an aliased display
of
a
sine
wave,
for exampIe,
will
look
like another lower frequency
4ine
wave.
But they are freaks. The slightest change in
At
in Figure
6.9
would immediately
cause
violent changes in the
false
display,
causing an incoherent jumble
of
dots, with perhaps successive
samples taken
on
rising and falling slopes. The term ‘false display’
applies only
to
situations shown in Figure
6.9
in which the
display looks misleadingly coherent and could be taken
for
that
of
a similarly shaped Iower frequency signal.
As
with incorrect
loop
gain, to
guard
against falsr displays thc gcncral rule
is
that thc dot
density
should
hc
incrcascd until no further change
of
waveshape
or arIipli~.udt.
can
be
obsri-vrd.
Of
course, we would
not
need
to
LIS~
a
sampling
scope
io
look
at
a
2
1
MHz
wavcIorrn,
let
alonc
a
1
MHz waveform,
but
it
illustrates thc
principle
and emphasizes how t.he
user
must.
bewarc
of
’aliasing’. After all,
if
you
wcrc using a sampling
scopc
Sampling oscilloscopes 105
to view very high-frequency phenomena and needed inciden-
tally to check out a lower frequency waveform in the process,
you might well use the sampling scope, simply to save the time
and bother of fetching a real-time scope.
The whole purpose of sampling is to look at or measure very
fast waveforms. What determines the maximum frequency or
minimum risetime that a given sampling system can handle? In a
fast signal the voltage level changes very rapidly, and if it is
desired to reproduce these changes on an oscilloscope display, the
sampling bridge must be capable of taking discrete samples
representing the various points on the ascending or descending
portions of the waveform. This is only possible if the time
duration during which the sample is taken is much shorter than
the slope to be measured. Hence the importance of providing
extremely short sampling pulses, and using the fastest available
diodes, but further circuit details are not appropriate in a general
book on oscilloscopes, such as this. The various techniques in use
in sampling scopes and, nowadays, in digital sampling scopes,
achieve sample times short enough to provide a bandwith of up
to 50GHz and a risetime as short as 7ps (see Figure 8.19).
Incidentally, in sampling scopes (whether of the older analogue
sort, or modern digital sampling scopes) the number of circuit
elements affected by these design considerations is relatively
small, so the price of a sampling scope is mainly determined by
other considerations.
Sequential sampling scopes share one problem with ordinary
analogue scopes. The trigger circuit cannot respond instantly to a
changing signal level, such as the leading edge of a pulse, and the
sweep circuitry (or in this case the fast ramp and comparator)
cannot start instantly when the trigger does occur. Therefore if
we attempt to trigger on, and then observe, a fast signal slope,
that slope will have ended before the sweep or sampling process
has commenced.
The solution in real-time oscilloscopes is to insert a delay line
(typically 200ns long) into the vertical signal path, with the
trigger pick-off point located ahead of it. In this way, the slope of
a signal can initiate the trigger before entering the delay line, and
when it emerges from the far end of the delay line and reaches
106
Oscilloscciprs
the vertical deflection plates the sweep will have started and the
slope can be observed.
The same technique can be used in sampling scopes. The delay
line must be ahead
of
the sampling gate (see Figure
6.4)
so
that
the first samples can be taken on the just-emerging beginning of
the signal slope.
But
delay lines have three great disadvantages
in
sampling systems:
1.
As
they
are situated at the
input
of
the scope circuit, their
characteristic impedance (usually
50
(I)
prevents
us
Irom
designing input circuits
of
higher input impedance.
2.
The
prcscnt state-of-the-art delay lines have bandwidt.hs
of
,jiisl.
a
few
GHz,
and
su
in the fastest instruments. prcciscly
whcrc the need
Inr
delay
is
greatesi.,
[.hey
caIilio~
be
used.
3.
They
are
heavy,
costly
and
bulky. Modern sampling equipment
is often designed
in
niodular form: in
a
sampling plug-in
there
is
often
just
no
room
for
a
delay line
of
adcquatc pcrfnrmance.
In sampling systems, then. delay lines often cannot be fitted for
physical reasons, but
if
they are used, their presence will
constrain the system bandwidth
to
a
few
GHz
and
the input
impedance to
50n."
If
you need
to
observe the point on the waveform on which
you are triggering and cannot use
a
system with
a
delay line.
you
will either
haw
to
provide a source of 'pre-trigger' (a pulse
occurring
ahead
of
the point of interest),
or
you wilI have to resort
to the use
of
'random sampling'.
Random sampling
Sincc.
after
recognizing
a
trigger, thcrc
must
he
some
finite
time
before the firsi.
sarnplr
ran
he
iaken,
ihen
exan1inin.g
thc
lcading
r
d
gc
w
h
i
ch
1
rigg
c.
r
c
d
t
11
c
sa
nip1
c
scc
ms
a
n
i
11s
I
I
r
in
n
iah
I
e
proh1c.m
if
a
&lay
liric
is
iriarlrnissiblc.
111
lacl,
iI
is
i~isurrIiourit.ablc.
*For
itw
Tc.ktronix
11801R
sarnpling
oscilloscope,
a
47.5
[is
delay
line
Is
availahlc,
with
a
bandwidth
of
5G11z.
'l'his
is
achicwrd
hy
hiiilding
imt
rhr
linc's
freqiicricy-clcI)eii~leii~
loss
to
a
'flat'
(0-5
GHz)
loss
of
6
dB.
Without
the
dday
line.
thc
instrument
priwidcs
a
bandwidth
of
up
to
50
GHz,
depending
upon
the
plug-
in
selected
Sampling oscilloscopes 107
Some unique leading edge of a waveform that caused the trigger
will have irretrievably passed before the sample can be taken, and
we shall never see it. What comes to our rescue is the fact that, in
sampling, we are dealing with repetitive waveforms. We shall
never see that leading edge, but if repetitive means what it says
there will be plenty more identical-looking ones coming along.
The basic idea in random sampling is not to take the samples
extra fast, trying to win the race with the first leading edge, but
on the contrary to delay them until just before the
next
leading
edge is due. The circuit in fact attempts to predict the arrival of
the next leading edge and takes the next sample a little ahead of
it. And then, of course, on subsequent signal cycles, further signal
samples will be taken At later to build up the complete
reconstructed image just as in sequential sampling. The reason
for the term 'random' will become apparent after the system has
been fully described. Random sampling is available on some
Tektronix 7000 series instruments, e.g. using the 7T11 plug-in,
and currently on the 11403A Digitizing Oscilloscope, the 6GHz
TDS820 Digitizing Oscilloscope and the 50 GHz CSA803 Commu-
nications Signal Analyser.
In the simplified block diagram shown in Figure 6.10 the
vertical circuitry is the same as in Figure 6.4 except for the
omission of the delay line. Blanking, gating and resetting circuits
which are the same as in Figure 6.4 have, for clarity, been omitted
in Figure 6.10.
The first important difference between Figure 6.4 and 6.10 is
that there is now no link between the trigger block and the fast
ramp. If the fast ramp started at the time that the trigger pulse
occurred (here designated to) it would be too late to catch the
elusive leading edge on which we are triggering. The circuitry
immediately underneath these blocks is designed to produce a
substitute pulse which arrives ahead of the trigger pulse at the
time tl, sometimes known as 'prediction time' because the circuit
predicts the time of arrival of the next leading edge.
The heart of the random mode circuits is the ratemeter ramp,
which is a slow ramp reset by the trigger hold-off circuit at a fixed
time (t5) after the trigger pulse has occurred, and the ramp then
begins to run down as shown by waveform 6. It will depend on
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