Sampling Problems

From a practical point of view? Capacitor memory (dielectric absorption) and S&H leakage mess up the samples too. I'm sure there's more.

Jerry

Hadn't thought of those -- but if you sample fast enough leakage isn't much of an issue. Modern C-2C ADCs do have a problem which is that when the sampling switch is closed some of the charge can leak back into an insufficiently stiff driver so the new reading depends ever so slightly on the old.

The faster you want to sample, the smaller the capacitor you can afford, so leakage is pretty constant when scaled by sample time.

Jerry

Might want to discuss anti-aliasing filtering topics including, avoiding aliasing, phase effects, and possibility of compromises between filtering, signal bandwidth, and sample rate.

Might want to look at/discuss sigma-delta/delta-sigma converters.

Dirk

Tim Wescott wrote:

(top posting compulsively "corrected")

Yes, I'm introducing the concepts of aliasing, discussing anti-alias filters and their drawbacks, why you want your anti-alias filter to be of lower order and wider in a control context than you would in a pure signal processing context, etc.

I hadn't considered discussing converters at all -- perhaps if there's room I will discuss converters in general, however.

------------------------------------------- Tim Wescott Wescott Design Services

I did a detector noise limited design for IR detection back in the

80's. You could practically write a whole book on the sample and hold section. Nothing is "perfect". You have to choose an imperfect material for the capcitor and imperfect switches, and then work around the imperfections, deal with the response time of the circuit, the spectral content of the noise and signal. The problems and solutions just go on and on; totally satisfying as a design project :) In the end though we had a 100ppm precision, offset/leakage compensation, 1kHz sampling rate, 5 channels, and detector noise limited system. The first (and last) thing is learning how to do fast estimates, then you can proceed towards detailed calculations. All of the first order errors can be cancelled then you are left with the second order errors that typically must be esamined in detail, including interactions; then you have a stable good system you have control of. Believe it or not the second order errors hold surprises. It sounds hard but it is all standard Electronic theory applied in detail. The final sampling circuit only had about 4-5 parts; it's all in timing and process.

Ray

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It seems like a difficult job elegantly done. I don't know which is harder: cataloging (and maybe learning) the elements of good design, or deciding which of them to include in a beginning course.

Jerry

How about quantization by the resolution of the converter and the process of reconstruction of the original signal. I suppose the differences in zero and first order hold is inappropriate for the beginner.

As I understand it, no hold at all is a series of spikes, a zero-order hold creates a stair case, and a first-order hold is either a continuation of the previous section's slope, of linear interpolation. The only first-order hold I've ever seen was one I built myself to smooth the digitally generated carrier of a home-brew 212 modem.

A zero-order hold doesn't attenuate the high frequencies. It greatly amplifies the whole usable spectrum, just a little less at the high end.

Leave out the detail. It's not too deep, but it sidetracks the thought process. Describe the stepwise nature of the output, mention in passing (if you must) the high-end loss, but pass on. High-end attenuation is zilch anyway in servos with their necessary oversampling. MHO.

Jerry

I have that covered.

I hope so -- I'm only covering the zero-order hold.

Well, that depends on how you do your math in the first place. One way or another, however, the high-frequency energy ends up being much less than the low.

One of my goals is to explain why, if you're building a servo system and the guy next to you is working on a telephony application, he needs fancy anti-alias and reconstruction filters and you need "good enough" anti-alias and vestigal reconstruction filters.

...

Chris Bore used to be a regular contributor to comp.dsp. Explore his site, especially if you're putting together a course. It's copyrighted, but ideas are free. (Look at the on-line courses

He made a remark one time that I occasionally use as a sig. See below.

There's more than not _needing_ fancy filters, they hurt. A substantial delay when reproducing recorded music goes unnoticed, but even a faint artifact in the sound is intrusive. Real-time voice reproduction is more tolerant of artifacts, but less tolerant of delay -- more than 5 ms becomes uncomfortable. 5 ms will kill a servo, but if a motor doesn't like the buzz and whistle from the aliasing, it will never tell you.

Servo filters should be "prompt" (close to minimum phase) and as "light" (short) as possible. Servos are practically a different technology: higher sample rates for the bandwidth, different filtering goals, flash or parallel successive-approximation ADCs, and so on.

Jerry

Thanks for the link. The missing 'www' is interesting.

Well, that's why I said you need "good enough" filters -- I wanted to be stronger than to say you don't need fancy ones. This is one of the points that I intend to make -- while you do sometimes need anti-aliasing filters, particularly if you're in an electrically noisy environment, you also need to pay careful attention to your filter's phase delay, and with almost all plants you _don't_ need to worry about a bit of aliasing 'cause it all falls outside of the plant's passband anyway.

snip

I've had to spend significant time convincing folks of this, in the past. On one occasion I ended up just specifying the phase delay of the filter and letting the circuit designer go ahead and implement the extra

3 poles of anti-aliasing.

Yea verily.

------------------------------------------- Tim Wescott Wescott Design Services

Tim, For some content you may want to look at the book "The Art of Electronics". While the book may not go into the "WHY", you can probably extract that out. They most likely address some of the issues that are experienced in the real-world.

Cheers, David