98 Oscilloscopes
/l
|
' )'/ signal-
---~ k,
sampling gate pulses
_,.__ ~-~ sampling gate output with feedback '
i
I
I
----1 memory gate pulses
I
memory output l
. t
Figure 6.5 Showing how the a.c. amplifier compensates for the typically low
efficiency of the sampling gate
(Typical values might even be as low as 2 per cent.) The a.c.
amplifier is a slowly responding one with the aim of getting from
it an amplified and 'time stretched' version of the input. The
memory gate pulses, although initiated from the strobe compar-
ator, are also made comparatively long (typically 300ns). The
memory is acting as an integrator, and its output is the
cumulative result of successive inputs. This output drives the c.r.t.
display amplifier. It is also fed back to the input via a very slow
time constant network where it will take nearly 10 p~s to raise the
input capacitor of the a.c. amplifier to the level that the signal had
when the sample was taken. The slow time constant explains
why the sampling system cannot take samples faster than at a
100 kHz rate.
Why use such a slow time constant? As can be seen, the
feedback used is in fact positive feedback (in the same direction as
the original signal), and if it arrived while the
memory
gate (not
the sampling gate) was still conducting, the loop gain would
exceed unity and the system would be unstable.
The gradual raising of the voltage on the input capacitor to the
correct level of 2 vertical units is of course also amplified by the
Sampling oscilloscopes 99
a.c. amplifier, which explains the second, longer, lower bulge in
its output waveform. But as the memory gate is not conducting
during this period, it is of no significance. It is worth noting that
the combination of a.c. amplifier (acting as a differentiator) and
memory (acting as an integrator) ensures that the d.c. compo-
nent of the signal will in fact be passed by the circuit.
Figure 6.5 shows a second sample then being taken, and since
at this time the signal is at 3 vertical units and the sampling gate
output already sits at 2 vertical units, the circuit sees a potential
difference across the gate of only 1 unit. With a sampling
efficiency of 25 per cent, the output moves only a quarter of a
unit before the sampling pulse ends, but with the same circuit
gains as before this results in just the right amount of change to
bring the memory output to the correct level.
Looking now at the solid-line drawing of Figure 6.6, the more
common case is shown where, at the time of the second sample,
the signal is still at the same voltage as on the first. There is
therefore no voltage across the sampling gate when it conducts,
no energy need be transferred, no kickout occurs, the a.c.
amplifier sees no change at its input and thus produces no
output, and the memory remains at the same level. All is well in
the best of all possible worlds.
But Figure 6.6 also illustrates with dashed lines how the
feedback loop takes care of departures from this ideal. As an
example, it has been assumed that the a.c. amplifier gain is
excessive. This means that the memory output will be too high,
and the dot will appear too high on the c.r.t. Because, in Figure
6.6, the signal level for the second sample is unchanged, the
action of the feedback loop can be seen very readily. When this
second sample is taken, the voltage at the gate output is in fact
(erroneously) too high, so energy will be transferred in the
opposite direction and the gate output voltage will drop down (by
the usual 25 per cent of the difference). This negative change is
seen and amplified and added to the memory, but since the a.c.
amplifier gain is excessive, it will again result in too much
movement. The original overshoot is overcorrected, giving an
undershoot of small amplitude. On the third sample the
overshoot is reduced still further and on successive samples the
100 Oscilloscopes
I - 1
1 !
1 I
'
f.
sig I-- 9
J,,
X
na , /t!
i sampling gate pulses
t
w,
II I I
I I
;
------ t--'----
~ ~ .sampling gate output with
feedback~
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ij~ ac amplifier
has excessive
gain i
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u kJ,~ a c amplifier ~ tv
I output '-
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,! ! memory gate pulses
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I -/f--r~emory output, -~,
Figure 6.6 Effectively a time-discrete servo loop, the sampling system corrects
for small loop gain errors, as shown
circuit settles to the correct level. If the samples were widely
spaced and individually discernible the appearance would be like
that of a damped oscillation (see Figure 6.7(a)). Thus whilst in the
short term, i.e. on a sample-by-sample basis, the feedback loop
provides positive feedback, in the long run it demonstrates the
self-correcting, distortion-reducing effects of negative feedback.
Exactly the same effect would occur if, instead of excessive a.c.
amplifier gain, the memory circuit had too much gain, the
9 w
(a) (I))
Figure 6.7 Sampling servo loop gain t()() high (a), ()r too low (b).
Sampling oscilloscopes 101
feedback path had less attenuation, or the sampling efficiency
increased. All these conditions are covered by expressions like
'the sampling system has too much loop gain'.
If, conversely, the a.c. amplifier gain had been too low, the first
sample would not have reached the correct level, and the
difference between ideal and actual level would again have been
seen by the circuit when the subsequent samples were taken. In
this case the result is a gradual approximation to the correct level,
giving the appearance of simple undershoot (Figure 6.7(b)), a
condition known as 'low loop gain'.
This section has described how, in a traditional analogue
sampling scope, positive feedback is used to boost the sampling
gate output from just a few per cent to effectively 100 per cent,
enabling the true signal amplitude to be measured at each
sample. A similar scheme is used in digital sampling oscilloscopes,
described in Chapter 8. In these, some manufacturers use an
analogue feedback loop similar to that described here, whilst
others use a feedback voltage derived from a DAC (digital-to-
analogue converter) fed with a scaled version of the digitized
sample just taken. A discussion of the relative merits of these two
schemes, and of measures to deal with 'blow-by' (capacitively
coupled breakthrough of the input signal whilst the sampling
gate is not conducting and thus supposedly blocking the input), is
beyond the scope (no pun intended) of this book.
Sequential sampling scope behaviour
It was mentioned in the last section that the results of incorrect
loop gain, and the action of the feedback loop in such cases, was
particularly well illustrated by Figures 6.6 and 6.7 because the
signal level on subsequent samples was unchanged. Now on
some instruments, a front panel control (usually labelled 'dot
response') will allow the precise adjustment of the loop gain, and
obviously the best kind of waveform to use during the adjust-
ment is one resembling Figure 6.7, such as a squarewave.
Conditions of incorrect loop gain will be masked if the signal level
changes from sample to sample, and in the most important
special case of sine waves (whose shape is mathematically almost
indestructible) low or high gain will simply result in a low or high
lO2 Oscilloscopes
amplitude sine wave display (unless there were an unusually
high 'dot density' or number of samples per cycle of the
waveform), which could totally mislead the unwary user.
A useful technique called 'smoothing', which is available on
most sampling instruments, deliberately reduces the loop gain to
a low figure, say one-third of normal. The result is that the first
sample rises to only one-third of the final signal amplitude, and if
the signal level remains unchanged, subsequent samples will
each rise by one-third of the remaining difference, giving the
usual exponential approach to the correct level. This is shown in
Figure 6.8 (a).
It can be seen that with a loop gain of one-third it takes twelve
samples for the display to reach a value within 1 per cent of the
final value. The rendition of a squarewave by such a series of dots
appears intolerable, but if the dot density is now increased
sufficiently (by reducing At to a really tiny increment), the twelve
samples that fell short of the correct level can be made to bunch
up so closely that the appearance of a squarewave is restored, as
in Figure 6.8(b). So what has been gained? Since it takes twelve
dots to reach the correct amplitude, only repetitive (signal)
waveforms which are present during twelve successive samples
will be displayed with full amplitude. Any random variations,
such as high-frequency noise, whose value varies from sample to
sample, will be displayed with only one-third of [heir true
9 ~p =~ 9 "=,. ~.~ ~ v.o
o>(?r
~
~
(a)
(b)
Figure 6.8 (a) Reduced sampling loop gain requires several samples to follow an
input signal change. (b) But can still accurately delineate a fast edge, if the dot
density is made high enough
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