The fully integrated autocorrelator was fabricated several times, and
the best (so far) sample (chip number ``USB280'', HYPRES wafer number
``w2823d'') was almost completely operational. After preliminary
low-frequency tests of the circular shift register, we started the
on-chip clock and measured the ``I-V curve'' similar to the one
described in Chapter 
(see Fig. ), plotting
the average voltage on all outputs as a function of the ``SIG''
current through the comparator. There were no signals on outputs
``Q9'' and ``Q12''. After that we connected the autocorrelator
outputs to the oscilloscope and tested them one by one for the ``gray
zone'' behavior by varying the ``SIG'' current. After this experiment
we had to mark output ``Q10'' also as inoperational since in the
middle of the comparator ``gray zone'' it was toggling at a much lower
frequency than expected. All other outputs passed the ``gray zone''
test and also responded correctly when we applied a harmonic signal to
the ``SIG'' input (with amplitude bigger than the comparator ``gray
zone'') and varied its frequency in the 
interval. Finally, we connected the autocorrelator output to the
room-temperature data acquisition system and observed autocorrelation
functions (and their Fourier transforms) for harmonic inputs of
different amplitudes and frequencies. Figures , ,
and show the measured autocorrelation functions of
harmonic inputs. We would like to emphasize that the theoretical
curves (dashed lines in Figs. - ), calculated for
the ideal quantizer and noiseless harmonic input, do not have any
fitting parameters. The calculation was performed as follows. A
harmonic signal 
of period T was sampled at
equal time intervals 
, yielding a sequence 
. After that, we mapped x(n) into a(n) in the usual way (see
Eq. () in the Introduction), i.e.
The dashed lines in Figs. - are the autocorrelation
functions of a(n) calculated according to Eq. () in
Chapter . The ratio of the frequencies
is given by 
.
The clock speed in this experiment, from both oscilloscope
observations and voltage-to-frequency relation was consistently around
. Ideally, the observed characteristic autocorrelation
functions shown in Fig. , , and
should indicate harmonic input frequencies of 
and 
, respectively. For
example, the harmonic input with period 
, results in an
alternating sequence of 32 ``1'''s and 32 ``0'''s. That is, it fills
the entire shift register with ``1'''s and then clears it. This is
exactly the ``Christmas tree'' sequence discussed in Chapter
. The main property of this sequence is that the
channel outputs are linearly proportional to the channel numbers
(autocorrelation function is a ``ramp''). And this is exactly what we
observe in Fig. .
However, the observed ratios of clock and signal frequencies were
consistently higher by a factor of two. Currently, we do not have an
explanation for this difference, but it was observed in all
experiments and at different clock speeds and was independent of the
signal amplitude or offset. We conclude that the problem was of a
digital nature, possibly, an incorrectly operating one T flip-flop
stage in the clock path. The differences between theory and experiment
in Figs. - could be attributed to several
factors. First, behavior of channels ``Q9'', ``Q10'' ``Q12'' could be
indicative of the properties of the delay line in this region. We also
note that the difference between experiment and theory is also very
noticeable for channel ``Q11'' , which is geometrically close to the
inoperational channels. Low frequency dc bias margins of the circular
shift register were already very narrow, close to few per cent. At
speed, margins tend to become even more narrow, so probability of
digital errors in the delay line was high. We expect this defect to be
entirely eliminated in a better sample with wider dc bias margins. At
the same time, however, we would like to note that, since
autocorrelator is a ``statistical'' device, designed for processing
white noise inputs, some digital noise would be acceptable. For
example, if the total number of accumulated samples is 
per
channel (see Chapter ) with first 10 bits prescaled and
discarded, then an error rate of the order of 
would not affect the upper 16 bits, since on average only
samples would be distorted. This is a very
important observation, especially in the light of the experimental
results described in Chapter . From this point of view,
autocorrelator, unlike most other digital applications, is perfectly
suited for minimization of dc power dissipation, even up to the point
when it will result in a relatively high error rate at the optimal
bias. For T flip-flop prescalers, minimization of dc power
dissipation can be carried out to even further extremes, especially
for the ones operating in a quasi-static regime, i.e. below 1
GHz. Second, error was introduced when channel outputs were
synchronously read-out into the FIFO. Currently, a specialized
room-temperature interface with 
asynchronous counters is
being designed. We expect it to eliminate this second source of
errors. Errors were also introduced in the quantizer due to the
comparator ``gray zone'' and instability of the on-chip clock. The
amplitude of the harmonic signal in this experiment was 
. With
a 
load the current amplitude at the comparator was 
, which is bigger but comparable to the half-width of the
comparator gray zone which was estimated at around 
. Further increase in signal amplitude was impossible since it would
have overloaded the comparator. In our experiment the total number of
samples accumulated on- and off-chip was close to 4 million (4096
read-outs for every 1024 on-chip clock cycles), so the effect of the
comparator noise was scaled down by a factor of approximately
.
Another interesting experiment was the observation of a very small
(relative to noise) signal in the middle of the gray zone. Turning the
signal on and off and observing the Fourier transform of
the autocorrelation function we could see a small spike appearing and
disappearing even when the signal amplitude was down to 
,
i.e. 
for a load without attenuation. Comparing
it to the estimated half-width of the gray zone of we get
a signal-to-noise resolution at around 
. Ideally, from
contents of one full FIFO (total of 
samples), one would
expect a signal-to-noise resolution of approximately
. Apart from the errors
discussed above, in this experiment the correct evaluation of the
harmonic signal amplitude at the quantizer input (including
attenuation, etc.) as well as the correct evaluation and definition of
the width of the quantizer ``gray zone'' were important for an
accurate estimate of the signal-to-noise resolution.
Figure: Output of the autocorrelator fed by a harmonic
signal. Circles show experimental points, dashed line is theory for
. In this experiment we had 
and 
.
Figure: Output of the autocorrelator fed by a harmonic
signal. Circles show experimental points, dashed line is theory for
. In this experiment we had and 
.
Figure: Output of the autocorrelator fed by a harmonic
signal. Circles show experimental points, dashed line is theory for
. In this experiment we had and 
.
Figure: Output of the autocorrelator fed by a harmonic
signal. Circles show experimental points, dashed line is theory for
. In this experiment we had and 
.