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參數(shù)資料
| 型號(hào)： | AD-03 |
| 廠商： | National Semiconductor Corporation |
| 英文描述： | Effects of Aperture Time and Jitter in a Sampled Data System |
| 中文描述： | Aperture的時(shí)間和抖動(dòng)的影響采樣數(shù)據(jù)系統(tǒng) |
| 文件頁數(shù)： | 2/4頁 |
| 文件大?。?/td> | 43K |
| 代理商： | AD-03 |
http://www.national.com
2
The Effects of Non-zero Aperture Time
For the analysis of aperture time we will assume
ζ
to be
0. This is the case of no aperture jitter. We will, however,
consider the effects of
Ψ
≠
δ
. The error (as compared to
an ideal sampling process) will then be < f,
Ψ
> – < f, d >
This is equivalent to < f, (
Ψ
–
δ
) >. To progress we must
now make some assumptions about the nature of
Ψ
. If
we consider the physical process of sampling that takes
place within a sample-and hold amplifier we can make an
educated guess as to the shape of
Ψ
. Consider the
sample-and hold circuit shown in Figure 2. When the
switch is closed, V
OUT
takes the form of the equation
below:
Figure 2: Simplified Sample-And-Hold Circuit
The RC time constant of this circuit will be proportional
to the aperture time. This implies that
Ψ
has the form
indicated below:
t
RC
To get an idea of what effect this has on the sampling
process we will expand f as a Taylor series expansion
about the sampling instant: t. Once again we will
consider the first two terms of the expansion:
Now we can examine the value of < f, (
Ψ
–
δ
) >. < f,
δ
>
is by definition f(t
0
) and the other terms of the expansion
do not contribute to the result. Since
Ψ
has been
normalized, < f(t
0
),
Ψ
> is f(t
0
): the ideal result of the
sampling event. If we consider the next term: f'(t
0
) (t-t
0
)
this is a constant
( )
slope going through 0 at the sampling point. This,
expanded out gives us an approximation of the error
generated by the non-zero sampling time. This implies
that the error generated is proportional to the slew rate of
the input, multiplied by the aperture time. This result is
very similar to the result for aperture jitter.
Let us now look at the shape of
Ψ
that might be expected
in a CCD or SAW device where the sample consists of
the charge deposited in a bin as the bin passes beneath
an input terminal. In this case, due to the symmetry of
the sampling process, we can expect
Ψ
to be an even
function:
( )
≈
+
such as a gaussian, or a rectangular pulse then the
odd nature of (t-t
0
) will force < f'(t
0
) (t-t
0
),
Ψ
> = 0. Now in
order to determine the error generated by the non-zero
sampling time we must consider the next term in the
Taylor series expansion.
Now the expected error is:
If the input function f(t) is sinusoidal in nature, all of it’s
derivatives have approximately equal values so the
major difference between this case and the previous
case comes in the comparison of < t,
Ψ
> and 1/2 < t
2
,
Ψ
>.
How to Minimize Aperture Induced Errors
As we have seen in the preceding analysis the results of
both aperture time and aperture jitter is an error signal
which increases in amplitude as the slew rates at the
input terminal of the A/D increase. One set of strategies
that are used to reduce aperture errors therefore focus
on minimizing this input slew rate. In fact, from an
aperture error standpoint the only thing that is important
is that the slew rate be small at the instant that the
converter is sampling the input, rapid slewing between
samples does not contribute to aperture error. Another
tack that can be taken to minimize aperture related errors
is one which takes advantage of the fact that the noise
generated through aperture effects has a random
characteristic and therefore lends itself to reduction
through some standard signal processing techniques.
Reducing the Input Slew Rate
In some cases, the input slew rate is higher than it needs
to be to recover the information content of the signal to
be digitized. An example would be if an input signal were
being digitally down converted through aliasing. As an
example if a 100kHz signal, modulated on a 101MHz
carrier is to be digitized, then there are several possible
approaches:
1) Demodulate the signal and digitize the 100kHz base
band signal at a rate of 1MHz. This scheme results in
very low input slew rates and would be the preferred
method from an aperture error standpoint.
2) Digitize the modulated signal at a 1MHz rate, allowing
aliasing to perform the down conversion. In this method
the usual mixers are eliminated and the digitized signal
is identical to that obtained in method 1 above. The
problem is that the input slew rates seen by the
converter are over one thousand times greater than
those seen in the above example and aperture related
errors may dominate.
V
t
V
e
d
out
in
t
RC
t
( )
=
( )
τ
∞
∫
τ
τ
V
out
R
C
V
in
V
in
ψ
ψ
=
<
=
>
e
,t
0
0,t
0
f t
( )
≈
+
f t
f' t
(
t
0
0
)
f
t
error = f' t
te
dt
s
0
0
t
RC
0
( )
∞
∫
f t
f t
f' t
t
t
f" t
t
t
2
0
0
0
0
0
2
(
)
+
(
)
f
t
error
f' t
( )
<
2
t
t
,Y
s
0
0
0
2
( )
≈
(
)
>
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