# Analog dynamic range, accuracy and number of bits

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

1. ### Habib Bouaziz-VialletGuest

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 BartoliGuest

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 MacyGuest

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. ### Spehro PefhanyGuest

Or maybe 19, but if it's a test question, show your work.

6. ### Habib Bouaziz-VialletGuest

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 ?

Habib

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

8. ### rickmanGuest

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
yours.)

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...

Rick

9. ### Habib Bouaziz-VialletGuest

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
i do the hacks they pay for ... like everyone else ! the most important
is the next holidays in Greece or elsewhere with my wife !

Habib

10. ### Habib Bouaziz-VialletGuest

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 !

Habib

11. ### rickmanGuest

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?

Rick

12. ### Robert MacyGuest

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
period.

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 CargillGuest

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. ### Habib Bouaziz-VialletGuest

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. ### Habib Bouaziz-VialletGuest

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
sci.electronics.design a few months ago, so check groops.google.com

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 MacyGuest

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

19. ### Robert MacyGuest

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. ### Habib Bouaziz-VialletGuest

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.

H