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Analog dynamic range, accuracy and number of bits

Discussion in 'Electronic Design' started by Habib Bouaziz-Viallet, Nov 2, 2012.

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  1. Hi all,

    Anyone could tell me what are the relations between Analog dynamic range
    (figure with no dimension), accuracy over this range and number of bits ?
    In other words, how to compute the number of bits of an ADC knowing the
    analog range and the accuracy wanted over this range.

    Ex :
    Analog range = 1:500
    accuracy over this range : +-0.1%
    number of bits = ?

    Best Regards, Habib
  2. Guest

    I do not know how you define dynamic range, but the old rule of thumb
    is that the signal to noise ratio SNR (signal power to quantization
    noise power) expressed in decibels, can be calculated simply as

    SNR = 6 x number_of_bits
  3. Fred Bartoli

    Fred Bartoli Guest

    Habib Bouaziz-Viallet a écrit :
    Depending on what you want/have to do there are a lot of parameters that
    can enter into the equation.

    Better to tell us what you want to do.
  4. Robert Macy

    Robert Macy Guest

    Sounds more like a 'test' question, but here goes:
    if accuracy is +/- 1/1000 and the smallest range to largest implies
    500X, 1/500000; which is a little more than 19 bits, so therefore you
    need AT LEAST 20 bits.
  5. Or maybe 19, but if it's a test question, show your work.
  6. Le 02/11/12 15:36, Robert Macy a écrit :
    In fact i'm far from a test question ... it's real life and i've got the
    same approach.

    Energy Watt-Meter 0,1% accuracy, 230Volts/50Hz. I range (0,02In .. In,
    10 In)), U range (0,8Un .. Un .. 1,5Un)

    --> 24bits on ADC for currents measurements.

    Any objection from gurus of the analog ?

  7. Guest

    While adding dithering noise, oversampling and postprocessing low pass
    filtering will certainly give you some extra bits, at least if the
    actual ADC is monotonous, I am a bit suspicious of the accuracy of
    that meter (I am not claiming that it would be worse than traditional
    electromechanical kWh meters).

    The situation would be easy if only resistive loads existed, but in
    the real world, the voltage waveform contains a lot of distortion,
    current drawn by a non-PFC electronics loads (such as "energy saving"
    lamps) complicate the situation further.

    However, if it can be assumed that the load remains constant for
    several cycles (e.g. 1 s) averaging will help and less bits are needed
    in the ADC.
  8. rickman

    rickman Guest

    To know how many bits you need to use in the converter, you have to
    define if you want to calculate the power to 0.1% or if you want to
    measure the voltage and the current to 0.1% and you need to know if the
    0.1% accuracy is applied to the full range of measurement or if it is
    relative to the largest value measured.

    If you need to calculate the power to 0.1%, then you need each
    measurement to 0.05% since the percentage errors will add as you
    multiply to get power. If you want to know the total energy consumed to
    0.1% you also need to be accurate over the full range since a given user
    may only consume at lower levels.

    So the lsb of your converter must be no larger than 0.05% of your lowest
    current measurement in addition to the 500:1 current range or 1 part in
    1,000,000. (excuse my use of periods and commas being different from

    This would imply a 20 bit converter for the current, but don't assume a
    converter with 24 bits is accurate to 24 bits. There are mostly two
    types of converters with 24 bit results, slower ones for scales and
    other measurements at rather low sample rates which I don't think you
    can use. Then there are audio type converters which will sample at
    higher rates, but are specified for AC performance mostly. The useful
    number of bits (ENOB - effective number of bits) is sometimes given, but
    usually they spec SNR which is a similar number in dB. You will get 1
    bit for each 6.02 dB of SNR minus a small factor to account for
    quantization noise (~1.5 dB IIRC).

    So 24 bits may be good enough, but make sure you have at least 122 dB of
    SNR ((20 * 6.02) + 1.5). This is not so easy in a small, low power chip.

    How fast do you plan to sample? You will get some improvement in SNR by
    averaging multiple measurements, either over a cycle or over multiple
    cycles of the power line. Random errors will average out (or more
    "accurately" they average down since they never go away). "Accuracy" is
    also impacted by systematic errors which won't average out.

    One thing that bugs me is that they measure the current of the meter so
    you pay to power the durn measuring device! I would expect the power
    company to treat that as part of it's own operating costs...

  9. Le 02/11/12 21:12, rickman a écrit :

    Yes most of ADC 24bits are nearly 18bits ENOB but they (AD, TI, Cirrus
    ....etc) claims that Gaussian noise gives the major part in the SINAD.
    Gaussian noise on I and U would canceled themselves on the power
    calculation (mean (discrete sum (U, I)) on 1s) because the two
    acquisitions sequences are not correlated each other ... we will see
    even if with GNU-Octave (awgn() ....) the results are something like
    spectacular !
    We plan to get 8Ksamples/s (out of the FIR filter after the Delta-Sigma
    modulator of the ADC)
    i do the hacks they pay for ... like everyone else ! the most important
    is the next holidays in Greece or elsewhere with my wife !

  10. Le 02/11/12 16:46, John Larkin a écrit :
    Pardon me John but i really doubt that you could achieve to implement
    any power meter with even a real 12 bits ADC over the 1:500 range of
    current, no offense John.
    Hey John, some guys are paying me to implement a good IEC62053-21 class
    0.2S power meter ... they will whip me out if i repeat you words ...
    Please John don't try to ruin my next Holidays !

  11. rickman

    rickman Guest

    To get good accuracy you also need the two converters to be very well
    synchronized. You can do the calculations to see just *how* synchronized.

    Where are you from that you use U for voltage? I haven't seen that
    before. I thought this was something standardized by SI? I also saw
    you use In and Un. What does that mean?

    How will you verify the accuracy of the meter? Using a simple resistive
    load is pretty easy, but how can you verify its accuracy in a real world
    situation with spikes and inductive loads?

  12. Robert Macy

    Robert Macy Guest

    I don't recommend counting on dithering and such, better to just do
    straight forward ADC. else certain waveforms will cause strange power
    measurements. I highly recommend TI's ADC used in the soundcards. I
    get 22.5+ bits out of them and sometimes better.

    There is a company in South Africa I use to compare my power meter
    design to, both cost and performance. They were good, low cost AND
    accurate, really tough competitor, but memory is not so good and lost
    the name with those pesky 8 hard drive crashes ALL in a two year

    From memory, we did the power meter esign with an analog multiplying
    chip AND my current transformer was a different design so didn't take
    any metal. I used air core, almost, just a small bit of core whose
    permeability could be initially over 10 to 1 and when operating change
    30 to 1 and still keep in spec.pretty forgiving current sensor.

    Don't forget to put in 'exterior' field sensors to cause the meter's
    reading to skyrocket if some one tries to use a magnet to disable your
    meter. That's what we did to punish those who attempted to saturate
    the current sensor core to lower the power reading. I'll bet they were
    surprised the first time they tried that and had to pay more!
  13. Les Cargill

    Les Cargill Guest

    The disk meters are really good. Very clever transducer, IMO.
    I believe the disk meters are more or less integrating current meters
    ( the movement is actually proportional to power, but voltage will
    converge on a constant fairly quickly for a good network ).

    That's not quite the same thing as "digital"/TOD meters, where you
    basically pull a data stream from them. I don't recall what those
    actually measure. I'd want to basically do a histogram
    of the phase angle & amplitude myself, but I don't think
    that's what they really do.
    Right - the ... momentum of the meter helps.
  14. Le 03/11/2012 01:33, John Larkin a écrit : I like VMEBus, i remember i have been designing VME IO's cards interface
    with VME a controller named VIC (Cypress) ... it was about 20 years ago !
    Oh yes with a re&l 16bits we can expect the IEC tests benches.
    For currents it will be CT with a ratio 1:100 and furthermore we have to
    design the interface to support Rogowski Transformers.
    VT for voltages.

    Accuracy is specified the interface only. A procedure to calirate and
    zeroing the interface *with* the sensor (all over the range) will be
    done by software.

    Best Regards, Habib.
  15. Guest

    I have only seen V used for voltage in anglo-saxon literature, in many
    other cultures (notably German) , U has been used.

    n = nominal
  16. Le 03/11/2012 01:28, rickman a écrit :
    Right. U and must be synchronized of course (each sync signal every 1s)
    in order to re-synchronize the two ADC's)! Remember i have to compute
    Power/Energy. each U, I sampled *synchronously* and make the
    sum/mean/square/product ... over 1s.
    I live in France. U (or sometimes V) is for Voltages. Un stands for V
    rated and In stands for I rated. Excuse my English ...
    Good point. The bench for IEC6.... -21 conformance will be done by an
    independent agency. Some sort of test equipement (PPS400.3 and PRS ...)
    will be used. I don't know exactly how and what these guys will handle
    any test protocol :-(

    Best Regards, Habib.
  17. Guest

    That would make 160 samples/cycle at 50 Hz, ie. a sample every 2.25
    degrees of the mains cycle. The conduction angles can be quite short
    in power supplies, so one might ask, does it make sense to use
    sampling rates that are exact multiple of the mains frequency.

    There has been a similar discussion about energy metering here in a few months ago, so check

    As a general plea to all posting information request to this group,
    provide as much as possible information about the problem (limited by
    any NDAs) and you will get much better responses immediately.

    In the worst case, some requests look like "do my home works,
    please":) and the responses will reflect that.
  18. Robert Macy

    Robert Macy Guest

    not in the countries they deploy these meters. The govt and industry
    are all pwerful there.
  19. Robert Macy

    Robert Macy Guest

    Don't they test up to PF of 6? or is that 10? Digital has a it of
    trouble there since we're starting to subtract to large numbers to
    find the power. Those 'disk' meters have an incredibly good accuracy
    curve thatconverges down to 'almost' zero.
  20. Le 03/11/2012 17:13, John Larkin a écrit :
    In fact there are two type of daughter board, one for currents (CT,
    Rogowski) and the other for voltage. I have to synchronize the
    delta-sigma modulators of each Delta-Sigma ADC's, 1 time per second to
    avoid false measurements based on each local quartz drifting ... That's
    the meaning of synchronizing.

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