Theoretical questions about A/D calculation

A/D calculation

Hi,
I think this would be the only question about Theory in this forum. But , I am stuk on it now :roll:
Please give me some hints ...

A strain gauge measures force up to 10MN with a precision of .08MN. What is the dynamic range in dB? What is the optimal size ADC to use without sacrificing resolution? Measurements of the transducer when installed show that there is .1V noise; the ADC operates on a 5V supply with 10MN corresponding to a 5V signal. Would you change your decision regarding the ADC and why? If so how many bits would you have in the ADC? Explain your answer. Note ADCs are available in multiples of 2 bits (4, 6, 8, etc).

Thanks

A/D calculation

range = 10/.08
range = 125.
ratio 125 : 1 = 42dB voltage ratio.

resolution = 5/125
resolution = 40mV

NOISE!
noise = 5/0.1
resolution with noise = 50. (get a bloody filter)

although a 6 bit convertor would do, I would choose an 8 bit because it more than satisfies the 125 degree resolution.

PS. This might be a load of crap, but thats how I would do it!

Re: A/D calculation

Be careful not to confuse resolution with accuracy or precision (accuracy and precision are the same). I can have 12 bits of resolution and only 8 bits of accuracy. Having said that, if your converter has .08MN of resolution then I agree with Btbass that the dynamic range is 42db [-20log1/125]. The second question is correctly phrased in terms of resolution instead of accuracy. It helps to have a calculator that can take the log with base 2, but I always use ln(x)/ln2 to get log base 2 of x. So, the minimum bits (or size of the ADC) for the required resolution (assuming again that .08MN is the resolution as well as the accuracy) is -ln(.08/10)/ln2 = 6.96. Since ADC's come modulo 2 bits, round up to 8 bits. Now look at the noise picture. Noise of .1V out of a possible 5V full scale limits the resolution to a maximum of -ln(.1/5)/ln2 = 5.64. So now you can get by with a 6 bit converter.

The noise question is actually a little bit tricky too as you really have to decide what level of confidence you want to have. Noise is a statistical phenomenon so you have to consider what confidence interval you want to consider. The RMS noise (you don't say, but if you use a voltmeter your .1V noise is the RMS noise) is the same as the noise standard deviation. With one SD you have a 68.27% chance of being within that limit, 2 SD gives you a 95.45% confidence, 4 SD gives you 99.9937%. So let's say you want to measure your signal with 99.9937% confidence in the presence of 0.1V RMS noise and using the smallest ADC possible. The resolution decreases to 4*0.1V = 0.4V (the new statistical noise level). -ln(0.4/5)/ln2 = 3.64. So you can reduce your ADC to 4 bits!

This is probably more detail than you want but there you go.

Re: A/D calculation

oh, thanks for your replies. I find this very useful. I will try and post up what I ve got here.
Pat

Re: A/D calculation

Hi, It is confusing to me between SNR and the dynamic range. Are they the same?
The ratio between Input/Precision is RANGE, or number of steps.
How about Inut/Noise ??? What does it imply to?
Also, which of the following is correct:
SNR = 20 Log10(SNR + 1)
SNR = 20 Log10(Input / nose)
Thanks
Patrick

Re: A/D calculation

Anyone please helps.... I am so confusing.
Thanks
Pat

Re: A/D calculation

Read this article about Signal to Noise Ratio (SNR):

What does the ADC SNR mean? www.reed-electronics.com/ednmag/article/CA419561?pubdate=5/27/2004
PDF version www.reed-electronics.com/ednmag/contents/images/419561.pdf

Re: A/D calculation

Dynamic range is about ADC.S/N ratio is about the signal.To convert without losses,Dynamic range must be greater than S/N.That's all.
I will give you a tip:since you evidently need some noise filtering (it will improve S/N dramatically) you can use one 8-bit, or better, 10-bit ADC and integrate the result from let's say 16 or 64 measurement.Just sum 64 samples and then ignore the 6 least significant bits.
If you use a processor,that is.
Otherwise use a simple RC low-pass filter with a cut-off frequency slightly higher than the maximum frequency of the signal.
Another thing:If the noise is not a noise but a 50Hz sine,then the measurement should be done and integrated for 20ms to completely get rid of it.

Re: A/D calculation

Patrick,

It is a little confusing and it is hard to find good overall info on data converters. Most explanations give you a large-signal view or the small-signal view, but not both.

First large signal properties (large signal means properties you can measure with a variable level DC input) are resolution, integral non-linearity (INL), and differential non-linearity (DNL). Large signal properties are of primary concern for data converters used in instrumentation applications. Precision, or accuracy, is dominated by INL. INL is the best fit straight line through a graph of all of the codes versus voltage. Accuracy has nothing to do with resolution. They are independent properties. DNL is what assures you that you have no missing codes. Most decent converters will have a DNL of less than 0.5 bits and you don't have to worry about it. As you say, range is the number of steps. Divide the maximum input voltage swing by the range and you have the resolution.

Now for small signal properties. These are properties that you can only measure by applying an AC signal like a sine wave. Small signal properties are of primary concern for data converters used in DSP applications. SNR is defined as 20*log10(rms signal/rms noise), which for a perfect converter, becomes 6.02N+1.76db where N is the number of bits. A nice article on this is **broken link removed**. This relationship is always true no matter what the input signal is, as long as the input signal is expressed in terms of an rms value. Why do I say ideal data converter? SNR should use the total input noise of the system, data converter, amplifiers, etc. If we assume the only noise source is the quantization noise , ie the noise due to the lsb quantization of the signal, then that is treating the converter as ideal and the above reltionship holds. Dynamic range is a little squishier, as dynamic range is just the ratio of the biggest and smallest signals. If the biggest signal is the input range and the smallest signal is the quantization noise, then dynamic range is the same as SNR. People tend to use dynamic range and SNR interchangably for that reason.

Note and caution: whenever you are talking about noise you are in the world of statistics. The math of statistics is your most powerful tool for analyzing noise. RMS noise is the same thing as one standard deviation for instance. How often will the peak-to-peak noise exceed the rms value? Only statistics can answer that question.

Hope that helps!

Duncan