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ADC and undersampling

Discussion in 'Electronic Design' started by Pawel, Jan 27, 2004.

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  1. Pawel

    Pawel Guest

    Hello,

    As a result of a measurement I obtain a bandlimited signal centered at
    144 kHz (12kHz Bandwidth). I was planning to use undersampling
    (Fs=192kHz) to fold this signal to 48kHz in the digital domain.
    I am having a difficulty to find an ADC for this purpose. The only
    ADCs I could find (I need at least 18 bit resolution) that support
    Fs=192kHz had too small analog bandwidth, f.ex. cirrus CS5361.

    Is there an ADC that could suit my application?

    Thanks!

    Pawel
     
  2. Zak

    Zak Guest

    Why not sample a much lower frequency? 48 will not work (the 0 frequency
    ends up in themiddle of your band of interest) but something a bit lower
    (6 KHz lower or so) should work.

    Take care that the quality of the sample-and-hold is more important with
    this input... the time of sampling is much more critical at high
    frequencies.


    Thomas
     
  3. Mac

    Mac Guest

    I think what he is saying is that the ADC frontend doesn't have enough
    bandwidth to do under-sampling. I know some high speed ADC's are designed
    for this, but I'm not too sure about these slower (192 kHz) ones.

    If he went to an even slower ADC, his problems would only get worse,
    presumably.

    Mac
     
  4. GPG

    GPG Guest

    ADS1625, ADS1626, ADS8383, AD7679 ??
     
  5. Fred Bloggs

    Fred Bloggs Guest

    Where are you getting that? The data sheet clearly states that the 0.1dB
    passband at "quad speed" sampling is 0.24 x Fs which puts you at 46KHz,
    your 48KHz is 0.25 x Fs - negligible additional attenuation 0.14dB? And
    this is the digital filter- not the analog passband.
     
  6. me

    me Guest

    If you use very low sample rates, remember to obey the nyquist rule for
    the highest (baseband?) output frequency.

    Jim Adamthwaite.
     
  7. The bandwidth is 12kHz, so Nyquist says 24kHz. Is that what you mean?

    -- glen
     
  8. GPG

    GPG Guest

    The INPUT is 144KHz
     
  9. Fred Bloggs

    Fred Bloggs Guest

    The analog input is aliased into 48KHz in the digital domain, it is
    the digital domain that is filtered, not the analog, and that passband
    spec refers to the digital domain .
     
  10. Rick Lyons

    Rick Lyons Guest

    Hi,
    here are the frequency ranges (in kHz)
    within which you can have your Fs sample rate:

    Fs_ranges =

    150.0000 -to- 276.0000
    100.0000 -to- 138.0000
    75.0000 -to- 92.0000
    60.0000 -to- 69.0000
    50.0000 -to- 55.2000
    42.8571 -to- 46.0000
    37.5000 -to- 39.4286
    33.3333 -to- 34.5000
    30.0000 -to- 30.6667
    27.2727 -to- 27.6000
    25.0000 -to- 25.0909

    Zak is right, 48 kHz won't work.

    Good luck,
    [-Rick-]
     
  11. Fred Bloggs

    Fred Bloggs Guest

    Ummm- maybe you are confused by the term bandwidth. This means Fc+/-6KHz
    and -3dB, and at quad speed this is 0.03 x Fs. Looking at the passband
    ripple graph which a nominal 0.03dB peak variation- your low sample
    rates mean the signal is spread over a correspondingly larger percentage
    of the passband- you see the *full* ripple error variation which is of
    the same order of magnitude as using the 192KHz Fs. Luck is for dummies
    and programmers, analysis is for engineers.
     
  12. Pawel

    Pawel Guest

    Hello,
    Thanks for the answers!
    I did not say I wanted to sample at 48 kHz. I said I have a 144 KHz
    analog signal that I want to alias to 48 kHz by sampling at Fs=192kHz.
    Therefore I was looking for an audio 192 kHz ADC for the application.
    The problem is that they ones I could find have too small analog
    passband so the udersampling trick would not work.

    Regards,

    Pawel
     
  13. Pawel

    Pawel Guest

    Hi!

    Thanks for the info GPG!
    Yes, I was condsidering to use an ADS1626 for my application and
    just sample faster to have my 144 kHz below Nyqvist frequency. It can
    be an alternative solution. But at faster sampling frequencies it has
    a high power consumption, which is a limitation for me.
    Lowering Fs would not help since the ADS1626 passband filter scales
    with Fs so the undersampling trick would not work either, would it?

    Regards,

    Pawel
     
  14. Jerry Avins

    Jerry Avins Guest

    I doubt that Rick is confused at all about acceptable sampling ranges.
    The best explanation I know of the constraints on sub-band sampling is
    given in the book "Understanding Digital Signal Processing" by Richard
    G. Lyons (ISBN 0-201-63467-8), Section 2.3. (Don't run out to buy the
    book now. There's a second edition coming out soon.) If you check with
    the equations there, you'll find that Rick is right on. :) I don't
    think he directly addresses Pawel's concern, though.

    Jerry
     
  15. What happens if you sample at something just under 138kHz as Rick suggested?
    You should end up with an image with bandwidth of 12kHz centered at +/-6kHz.
    Then you can immediately decimate (with proper filtering) from 138 to
    something like 30 like how about by a factor of 4 down to 34.5kHz? That
    leaves plenty of room for filtering between 12kHz and fs/2=17.25kHz.

    The only thing the digital filter in the ADC does is keep the bandwidth
    consistent with the sample rate. It doesn't change the input bandwidth, it
    controls the output bandwidth to be consistent with the output sample rate.
    So, if the sample rate is 1.25MHz, the bandwidth is limited to below 625kHz
    at actually 550kHz. If the sample rate is 138kHz, it limits the output
    bandwidth to (550/1250)*138 = 60.72kHz, which is what you want for that
    sample rate. The useful information is below 12kHz at this point - so you
    decimate by 4 thereafter.

    The other alternative is to go to a complex envelope representation by
    sampling at 144kHz in quadrature. Rick Lyon's book deals with that very
    nicely. In fact, the ADC's will do it for you by sampling at 144kHz and all
    you have to do is alternately grab the output words to get the quadrature
    results. It's either that or deal with the wider bandwidth as I have done
    above - and avoid having quadrature channels to deal with. The number of
    operations thereafter should be pretty close to the same either way because
    either you have two channels with 1/2 the bandwidth or one channel with full
    bandwidth.

    I think that's right.....

    Fred

    Fred
     
  16. Well, I didn't acknowledge here that Rick had suggested sampling at even
    lower frequencies - and I should have. The filtering necessary while
    decimating will change if you do that.

    Fred
     
  17. Jarmo R

    Jarmo R Guest

    Don't think so.
    The ADC samples at about 6 MHz.
    Then it filters so that aliasing will not happen when it decimates down
    to
    actual output rate. So 144 KHz will not alias.

    This is the fine point in oversampling converters with decimation.
    Analog antialias filter need only be effective for the actual high
    sample rate.

    Jarmo
     
  18. Rick Lyons

    Rick Lyons Guest

    Hi,
    Oh shoot, I misread your first post.
    Sorry.

    [-Rick-]
     
  19. Rick Lyons

    Rick Lyons Guest

    On 29 Jan 2004 11:33:44 -0800, (Pawel)
    wrote:

    (snipped)
    Hi,
    I was thinkin' some more about your question,
    and darn it, you make me ask a question.

    If we define:

    Fc = carrier freq (Pavel's 144 kHz)
    Fs = sample rate (Pavel's 198 kHz)
    Fi = the positive center freq of the aliased
    spectral replication nearest to zero Hz.

    In Pavel's case:

    Fi = Fs(1 + {Fc/Fs}) -Fc (1)

    where {Fc/Fs} means the integer part of Fc/Fs.

    Using that Eq. (1), Pavel's Fi (in kHz) is:

    Fi = 192(1 + 0) -144 = 48

    which is what he said.

    So now here's my question: At the risk of lookin'
    like (as Fred Sanford would say) a big dummy,
    is there a way to solve the above Eq. (1) for Fs
    in terms of Fc and Fi?

    For some reason (maybe Alzheimers) I can't
    figure out how to handle that {Fc/Fs} operation
    in algebra.

    Thanks,
    [-Rick-]
     
  20. Jerry Avins

    Jerry Avins Guest

    A big dummy doesn't know. A big idiot thinks he does but doesn't. I'll
    risk being branded with the latter title.

    Solve for {Fc/Fs} first. Then, given the known Fc, see what range of Fs
    makes that possible. I've introduced another variable, {Fc/Fs}, so it
    may take some trial and error anyway, but at least it's directed.

    Jerry
     
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