Undersampling average

If it were me, I would use the basic PWM clock signal as a trigger, and make sure my 10 us samples were on the peaks. You can do this using a 74123 dual one-shot. Then, knowing the duty cycle, (from the trigger signal), you could calculate the average, or direct current.

emc_c

That actually would work, but I'm looking for a more general purpose solution. I have 12 motors, each operates at a different PWM frequency (I do this to reduce EMI).

If your signal is 30kHZ and you are taking a 10uS sample every millisecond, you don't really have a way of knowing whether you are sampling during the "on" or "off" phase of the pulse. Whichever it is, since your signal frequency is an integer multiple of your sample frequency, the sample will continue to occur at the same part of the signal wave: in this case, for every 30 signal pulses you are taking one sample. If the very first sample occurs while the pulse is "on" then every subsequent pulse will also occur when the pulse is "on" and you won't have an average.

If you want to be more accurate with no ripple, then you need to sample at a rate greater than 60kHZ. Google "Nyquist rate" for more info.

If a sample rate that high is not an option, then at least change your sample frequency to a rate--say, 0.91ms--for which the signal is not an integer multiple. That way you would be sampling at different parts of the waveform. Then you simply need to calculate how many samples you could take to get an even distribution across the waveform. If you used a 0.91ms sample rate, then each sample would be shifted by 3/10 of a wavelength; so after 30 samples you would have cycled through (so of course your ripple frequency would be 1/(.00091*30)=36.6Hz. If you want more accuracy, use a 0.909ms sample rate (100 samples to cycle through). That gives you a ripple frequency of 11Hz. The more irrational your sample rate is, the lower your ripple frequency, but you really want a ripple of zero, which can only be achieved by using a frequency more than twice the signal frequency.

I'm sorry you didn't read my original post better. The assumption is that the sampling frequency is not synchronous with the switching frequency, and of course, 30KHz and 10uS are not integrally related, and the idea is to employ undersampling, not Nyquist or Shannon sampling.

But thanks for taking the time to respond.

Here's a simplistic thought--if your samples are asynchronous to the PWM output, run samples through a FIFO pipeline (dynamically configurable?) of length greater than a number of PWM cycle times.

Then calculate running averages based on strings of samples that overlap in the pipeline (maybe 10-25% overlap?). These will be out of phase with the motors' current.

Compare the n-th average with previous averages and call it valid when the rate of change of averages slows down "sufficiently".

Like ending a software iteration when the successive results differ by a sufficiently small amount from the previous value.

Long term the DC average, as you said, should be stable. So the average of samples should stabilize too shouldn't it?

Yes - this approach would work, as would just averaging the samples. The question I'm asking is, how to relate the number of samples to when the rate of change of averages slows down "sufficiently". After studying the problem for an evening, I've about decided that whatever the answer is, it's many more samples than I'm prepared to take.

Thanks.

What kind of motors are they? steppers, sych, induction motors?

If they were for example squirrel cage running on VFDs, you could add a capacitor to your shunt resistor's output and measure a simple sine wave, thus being able to calculate RMS or whatever current values you need? Maybe?

Yahlasit

They are brush DC motors.

Guest #1 has a good plan. Since you said the V signal (proportional to current) looks like the PWM waveform, you must be using a scope. Trigger the scope on the PWM clock as Guest #1 suggested, and use the scope's delay control to assure you are sampling on the peaks of each pulse. You can use the scope's AVERAGE measurement for the final result. Many scopes have a statistical distribution routine so that you can see the mean and standard deviation to help decide when to take the average reading.

ummm - thanks.

Do you know the mux switch resistance (when ON) and the sample and hold capacitance of the A/D?

Are you using a PIC micro A/D for this application?

We ran into several interesting problems with multiplexed A/D conversions that were all easily solved by the addition of simple, and properly scaled, RC filters. That is NOT the answer to your question, but it may be the answer you need to get accurate measurements.

Oh sure - and that's what we'll end up doing. The signals will be passed through active lowpass filters and what we'll end up sampling is very close to DC. This was just an interesting (to me) question that came up, and I was curious if anyone had any insight into this kind of undersampling technique, since I've only ever been able to find one other instance of it being used.

OK... First thought was to use a resistor/capacitor low pass filter to do the averaging. BUT since you are going to run it directly to an A/D, I would run the digital words through a FIR (Finite Impulse Response) averaging filter. This is like a shift register say N samples long. Ignoring word size for the moment, each section of shift register is multiplied by 1/N and the output of the multiplications are all summed (accumulated). If you get tricky and use binary N, 1,2,4,8... the multiplys can be done by shifting only.

Bill

.5, .25, .125, .0625... etc.

I don't know your experience with DSP, but a book on the subject might make my comments more meaningful.

This gives what is known as a running average which means that samples which run off the end of the shift register are no longer part of the average.

Have fun...

Bill

An FIR, or more likely a simple averager is what we would run the samples to. My question is, how many samples are required to reduce the ripple in such a measurement to an acceptable level, based on the undersampling conditions listed in my original post. Undersampling is not something that's described much in the literature, as least not in this context of recovering DC information, hence my question.

I have faced a similar problem with trying to remove noise from an undersampled data stream- although the data was probably far noisier than what you are dealing with. I went through a period where I would strip spikes from the data, then pass it through an FFT and strip whatever frequency spikes I could find, then repeat the process until I got close to what I was looking for- which was the underlying signal that I wanted to strip from the noise until I had nothing but gaussian noise left. Ultimately, I found that, for my case, I needed about 38 time-synchronized samples to generate the same underlying signal from the data. Any more had no detectable effect on the finesse of the final results, and 35 averages still left recognizable ripple in the data (note that the underlying signal was repeating, but not DC, not sinusoidal and drifted somewhat over time). The rule held for data extracted from two totally different systems with the same measurement equipment.

Unfortunately, I have not been able to discover anything in the literature that will give me a relationship that would help me predict how many sample streams need to be averaged as a function of undersampling frequency, noise level (in my case, on the order of 5% of signal magnitude), or any other deterministic measure. There must be some ideas out there, but I haven't found them. I have encountered quite a bit on aliasing, and there should be some way to account for this, or extract higher-frequency information from the "folding" nature of the spectrum, but I haven't discovered anything yet.

But I ramble. The number you are looking for is 38. Or, that was the number that worked in my case. I suspect each system will have it's own number...

Thanks.

Did you think about using analog approach? At 33 usec rate you can get a very smooth variable (and pretty fast proportional with your dc) voltage which, sampled at 1 msec rate give you the necessary data.

Yeah - analog works great. I was looking for a digital approach. BTW, where is Sour Lake?

I escaped from Houston, two years ago. Sour Lake is 10 miles west of Beaumont, on hwy 105. Some 2000 souls, a golf course (I've never been on it), in a part of the Big Thicket Forest. If you want to receive radio waves, you need to rise an antenna over the trees (100 ft or so).

About the digital approach, I would need more than one sample each 1 msec, unless the values fluctuate with a frequency less than 500 Hz. And I would do (digitally) a moving average (ten samples, averaged than discard the oldest of ten and add a new sample and average them then discard again the oldest and add a new one and so on). But I am sure that you have already thought of that.