鈥?/div>
味.
This is intuitively comfortable since it states
that the error is proportional to the slew rate multiplied by
the aperture jitter.
When a signal is sampled, the expected error that will be
generated will be the RMS value of the slew rate multi-
plied by the RMS value of
味
(the RMS value of
味
is what
is commonly specified as Aperture Jitter). Hence for a full
scale sinusoidal input signal of 10MHz, the RMS slew
rate is 0.02 full scale ranges/ns. If the Aperture Jitter is
10ps then the expected error would be 0.02 * 0.01ns
or 213ppm. This corresponds to a signal to noise ratio
of 73dB or approximately the same size error as the
quantization error from an ideal 12 bit converter.
In Figure 1 the Signal-to-Noise Ratio is plotted vs. the Input
frequency for various different values of aperture jitter.
SNR vs. Input Frequency
120
鈭?/div>
鈭掆垶
where
未(t-n蟿)
is a dirac delta distribution, f(t) is the input
signal and f
S
(n) is the sampled function. In practice the
sampling event is somewhat different, the instantaneous
sampling is replaced by an integration over a small
period of time, and there is uncertainty in the actual
instant at which the sample is taken. These two non-
idealities: the finite sampling time and the uncertainty of
the sampling instant can be accounted for by replacing
the delta distribution by another distribution
唯(t). 唯(t)
will be an ordinary, continuous function of time which
includes a random variable:
味
to denote the uncertainty in
sampling instant.
味
will not be explicitly written but it is
assumed that
唯(t)
is
唯(t+味). 味
represents the uncertainty
in the sampling instant or aperture jitter and is a random
variable with a mean value of 0. The RMS value of
味
is
what will be specified as aperture jitter. The result of a
sampling operation may now be written as:
f
s
=
f
鈭?/div>
鈭掆垶
(
t
)
蠄
(
t
鈭?/div>
n
蟿
)
dt
+鈭?/div>
100
SNR
80
1PS
60
5PS
10PS
15PS
20PS
25PS
100M
A shorthand way of expressing this is f
S
= < f,唯 >.
We are now in a position to evaluate the effects of
aperture non-idealities in the sampling process on the
sampled signal. One key is that since we are dealing
with a random process, the result of a single sample is
40
1k
10k
100k
1M
10M
Input Frequency (Hz)
Figure 1: SNR vs. Input Frequency for Various
Values of Aperture Jitter
漏 1994 National Semiconductor Corporation
Printed in the U.S.A.
http://www.national.com
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