Anti-aliasing filtering for interleaved sampling approach

Started by Alexz February 12, 2008
Hello guys and girls, my first posting here.
On some other, hardware design-related forum there was a question raised
by someone whose goal is to built a sampling system to achieve 500 MHz
sampling rate by means of two 250 Msps ADCs while driving them with
samlping closk featured by 180 deg. phase shift. So that in time domain
would be sampling by two channels in interleaved manner. Then the entire
sampled sequence is to be composed from two memory buffers for further
processing.
My question is as follows: as we all know, sampling theory requires
anti-aliasing filtration (an LPF at half or lower of samlping rate) in
order to avoid distorting the sampled original spectrum by aliased
components.
If considering each cnannel (out of two) separately (as physycal sampling
is attained), it appears we need to have 125 MHz (half of 250 Msps rate)
LPF in analog domain prior to sampling to act as anti-aliasing filter.
However, that approach apparently defeats the whole purposes of the system
- to achieve effective rate of 500 MHz (i.e. effective bandwidth of 250
MHz).
On the other hand, if we assess the entire system in the whole, we know
that we intend to obtain 500 MHz samlping rate, so that the analog
anti-alias filtration should assume 250 MHz cut-off LPF rather then 125
MHz as if we would follow the previous approach. However, in such case we
may impact the spectral content of each separately sampled (physically)
channel.

So, what should be the recommended (or correct) aprpoach to anti-alias
filtration in that particular case ?

Thanks, Alex

Alexz wrote:
> > Hello guys and girls, my first posting here. > On some other, hardware design-related forum there was a question raised > by someone whose goal is to built a sampling system to achieve 500 MHz > sampling rate by means of two 250 Msps ADCs while driving them with > samlping closk featured by 180 deg. phase shift. So that in time domain > would be sampling by two channels in interleaved manner. Then the entire > sampled sequence is to be composed from two memory buffers for further > processing. > My question is as follows: as we all know, sampling theory requires > anti-aliasing filtration (an LPF at half or lower of samlping rate) in > order to avoid distorting the sampled original spectrum by aliased > components. > If considering each cnannel (out of two) separately (as physycal sampling > is attained), it appears we need to have 125 MHz (half of 250 Msps rate) > LPF in analog domain prior to sampling to act as anti-aliasing filter. > However, that approach apparently defeats the whole purposes of the system > - to achieve effective rate of 500 MHz (i.e. effective bandwidth of 250 > MHz). > On the other hand, if we assess the entire system in the whole, we know > that we intend to obtain 500 MHz samlping rate, so that the analog > anti-alias filtration should assume 250 MHz cut-off LPF rather then 125 > MHz as if we would follow the previous approach. However, in such case we > may impact the spectral content of each separately sampled (physically) > channel. > > So, what should be the recommended (or correct) aprpoach to anti-alias > filtration in that particular case ?
The individual channels will have aliasing just like any sampled signal will have aliasing if you only look at every other sample. Another way to look at it is that the aliases in your 2 channels will cancel each other out when you combine the 2 channels into one. That's because the aliased frequency content is identical in both channels except for being 180 degrees out of phase. -jim
> > Thanks, Alex
"Alexz" <alex@zabrovsky.com> wrote in message 
news:mamdnZdXYY8rlS_anZ2dnUVZ_qmlnZ2d@giganews.com...
> Hello guys and girls, my first posting here. > On some other, hardware design-related forum there was a question raised > by someone whose goal is to built a sampling system to achieve 500 MHz > sampling rate by means of two 250 Msps ADCs while driving them with > samlping closk featured by 180 deg. phase shift. So that in time domain > would be sampling by two channels in interleaved manner. Then the entire > sampled sequence is to be composed from two memory buffers for further > processing. > My question is as follows: as we all know, sampling theory requires > anti-aliasing filtration (an LPF at half or lower of samlping rate) in > order to avoid distorting the sampled original spectrum by aliased > components. > If considering each cnannel (out of two) separately (as physycal sampling > is attained), it appears we need to have 125 MHz (half of 250 Msps rate) > LPF in analog domain prior to sampling to act as anti-aliasing filter. > However, that approach apparently defeats the whole purposes of the system > - to achieve effective rate of 500 MHz (i.e. effective bandwidth of 250 > MHz). > On the other hand, if we assess the entire system in the whole, we know > that we intend to obtain 500 MHz samlping rate, so that the analog > anti-alias filtration should assume 250 MHz cut-off LPF rather then 125 > MHz as if we would follow the previous approach. However, in such case we > may impact the spectral content of each separately sampled (physically) > channel. > > So, what should be the recommended (or correct) aprpoach to anti-alias > filtration in that particular case ?
There are a number of issues in doing this - but it is done. The sample rate issue really isn't one of those issues. In effect, you're sampling at the required 500MHz rate - it's just *how* you're doing it that may be confusing. Think of it this way: A single signal being sampled at 500MHz resulting in a single sequence of samples at 500MHz. The fact that you have two "machines" that alternately do the sampling doesn't alter the fact that the sample rate is as required. Of course, you have to keep the clocks in control so that the samples are really equispaced in time. How you get there is unimportant as long as it's done adequately. Just don't think about "channels" in this case. There is but one. Now go worry about how to make that be the case. And, how you store things in memory is immaterial as long as you can access the 500MHz sequence in order. I guess to address your question in a more theoretical way: - Assume there are two sequences, sampled at half the intended rate and one of them delayed 1/2 sample interval relative to the other. - Now zero-stuff each sequence so the sample rate is doubled. - Now add the two sequences together. This yields the necessary sequence. But what about the spectra at each step? The first sequence potentially causes aliasing by adding unwanted components. The second sequence does the same. The sum of the two sequences doesn't have any unwanted components. This means that the unwanted components sum to zero when the two sequences are added together. That means that the unwanted components have the opposite sign - which must come as a result of the "quadrature" nature of the sampling. But ... I like the first treatment better. Much more direct and less involved. The second treatment may be useful if one needs to analyze the errors of quadrature jitter, etc. Fred
Alexz wrote:
> Hello guys and girls, my first posting here. > On some other, hardware design-related forum there was a question raised > by someone whose goal is to built a sampling system to achieve 500 MHz > sampling rate by means of two 250 Msps ADCs while driving them with > samlping closk featured by 180 deg. phase shift. So that in time domain > would be sampling by two channels in interleaved manner. Then the entire > sampled sequence is to be composed from two memory buffers for further > processing. > My question is as follows: as we all know, sampling theory requires > anti-aliasing filtration (an LPF at half or lower of samlping rate) in > order to avoid distorting the sampled original spectrum by aliased > components. > If considering each cnannel (out of two) separately (as physycal sampling > is attained), it appears we need to have 125 MHz (half of 250 Msps rate) > LPF in analog domain prior to sampling to act as anti-aliasing filter. > However, that approach apparently defeats the whole purposes of the system > - to achieve effective rate of 500 MHz (i.e. effective bandwidth of 250 > MHz). > On the other hand, if we assess the entire system in the whole, we know > that we intend to obtain 500 MHz samlping rate, so that the analog > anti-alias filtration should assume 250 MHz cut-off LPF rather then 125 > MHz as if we would follow the previous approach. However, in such case we > may impact the spectral content of each separately sampled (physically) > channel. > > So, what should be the recommended (or correct) aprpoach to anti-alias > filtration in that particular case ?
I don't understand your confusion. After you have collected your 500M samples in a second and arrayed them in time-serial order, it doesn't matter a whit (in theory) how they were obtained. For all that matters, there could be 500 samplers, each collecting one sample per second. For the sequence to be free of aliases, there can be no components as high as 250 MHz. Practical considerations impose several constraints. In order to ensure that components at and above 250 MHz are suitably diminished, the practical upper limit of the analog anti-alias filters' cutoff will be about 200 MHz. The signals captured by the several samplers must not have any differential lag. That is easily achieved by using a single filter and making the leads from it to the samplers about the same length. The clock phases must be accurately enough spaced so that the signal changes a small fraction of a LSB. Clock jitter is bad enough. Periodic clock jitter will produce aliases that may be troublesome. Moreover, the samplers must be closely matched for response time, analog frequency response, offset, gain, and linearity. Obviously, fewer samplers minimize the difficulty. Two are used when there is no alternative. Back when ADCs were trimmed by hand, one system using four was built and made to work in the laboratory. Even matching two samplers is not a project to be undertaken lightly. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;