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| 型號(hào)： | AD-03 |
| 廠(chǎng)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(yè)數(shù)： | 3/4頁(yè) |
| 文件大?。?/td> | 43K |
| 代理商： | AD-03 |
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http://www.national.com
3) Down convert to an I.F. of 1MHz then digitize at a rate
of 1MHz. In this method, some of the advantages of
digital down conversion can be retained - multiple
channels can be demodulated simultaneously - and
complexity is reduced from a system that down converts
to baseband. From an aperture standpoint we are still
seeing input slew rates an order of magnitude greater
than we did in example 1, but two orders of magnitude
less than those seen in example 2.
4) Place a sample and hold circuit, sampling at a rate
of 1MHz, in front of the A/D in scenario 2. This results in
the A/D converter seeing a very low slew rate, but the
aperture errors are shifted to the sample-and-hold circuit.
In many cases a sample-and-hold has much lower
aperture errors associated with it than a comparable
speed A/D converter.
In all of the above scenarios, the digital output from the
converter is at a 1 MHz rate and the digital output would
be identical if the A/D converter were an ideal converter
with no aperture jitter. With real world converters, there
will be a vast difference in the signal to noise ratio in each
of these three scenarios.
The solution involving placing a sample and hold circuit in
front of an A/D converter is especially interesting with many
high speed, high resolution, monolithic A/D converters.
Many of these devices have particularly poor aperture
performance and as a result even if the input frequencies
are reduced to sub-nyquist rates, the aperture error may
be the dominant error source. Use of a separate sample
and hold will allow for the burden of sampling the signal
to be shifted to the sample and hold, reducing the
sensitivity to aperture jitter in the A/D converter.
Reducing Noise Through Signal Processing
A/D converter outputs contain noise that has as its
origins quantization noise, noise that comes from
aperture related effects and noise from other sources.
Often it is desirable to lump all of these together and just
treat them as noise and work towards reducing them.
One technique that can be used for this is simply to over-
sample the input then digitally low pass filter the output.
If we take the example above, where we have a 100MHz
carrier modulated with a 100kHz signal, if we sample at
a rate of 2MHz instead of a rate of 1 MHz, the noise is
distributed over a band that is twice as wide. If the
digital signal is then filtered, and the half of the band that
does not contain the signal of interest is thrown away, the
result is a 3dB improvement in the signal to noise level.
This could be carried on as far as the speed of the
converter permits with the cost being carried mainly in
the power and complexity of the digital filtering hardware.
Imagine sampling the signal at 1GHz, then filtering out all
but the lowest 500kHz band to obtain the equivalent of
1MHz sampling: we would be able to obtain a 30dB
improvement in SNR over what we would have sampling
at 1MHz.
Another signal conditioning method that can be used
toreduce the noise both from aperture effects as well as
other sources is implemented in SD A/D converters. A
block diagram of a simple converter is shown in Figure 3.
Figure 3
If we replace the SD A/D and D/A pair with a simple
additive noise where this noise represents the noise
contributed by the sampling process, both quantization
noise and aperture jitter related noise, then the block
diagram is modified to look like that in Figure 4. The
transfer function for the signal in this system is given by:
Figure 4
It can be seen from this that if H(s) is large for the
frequency range in which the signal is, then the signal
transfer function is near unity.
The noise however, sees a different transfer function:
If H(s) is large in the area of interest then the noise is
attenuated in this same area. The result is that the
signal to noise ratio is increased.
If an analysis is done of this (which is beyond the scope
of this paper) it turns out that this is a much more effec-
tive method of reducing the noise than the simple over-
sampling and low pass filtering that is outlined above.
With a first order filter for H(s) then the SNR improvement
that can be realized with
Σ
techniques is 9dB per octave
of oversampling as compared to the 3dB that we
obtained above. As the order of the filter used increases
the gains can be increased as well.
Conclusion
As digitizing systems increase in speed, aperture effects
play a larger and larger role in the total error budget of
the system. Techniques for analysis and prediction of
the errors have been presented. Techniques for the
reduction of aperture related errors have been presented.
Signal
In
H(s)
A/D
D/A
Digital
Out
+
STF
H s
1 H S
=
Signal
In
H(s)
Sampling & Quantization
Noise In
Out
+
+
NTF
1
1 H S
=
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