Integration in analog and digital domains

Question

Integration in analog and digital domains

luben111 (Aerospace)

(OP)

5 May 11 09:34

Intergarting in analog and digital domians
Hi,

One theoreitical question about signal integration.

Imagine that you have 10 bit ADC which measures the changing voltage on some capacitor. The signal is quite noise so there are mainly two approaches:
1. Increase the RC constant on the system and measure the voltage (integration in digital domain)
2. Don't change the RC constant but make several samples and integrate the results digitally (integration in digital domain, for example simpel averaging).

The question is - do these two methods yeild the same result if both operations are executed for the same time - i.e. if the added time from increased RC constant in case 1 is equal to the time spent to get extra samples in case 2?

From oversampling theory is known that in order to get more bits and/or better SNR the input signal should be filtered from HF otherwise signal aliases will appear and will compromise the result.

Or I can redefine the question as: In which conditions the integration in digital and analog domain are equivalent?

Best regards
Luben

IRstuff (Aerospace) · Answer 1 · 2011-05-05 09:47:55

When they're done the same way, in the approximate sense. Say the time constant is 1 second. You take two digital samples over 1 sec. Is that equivalent to the RC filter? Take 200 samples. Is that equivalent?

TTFN

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luben111 (Aerospace) · Answer 2 · 2011-05-05 12:36:12

Hi,
I'll put it other words - say I have in one case 10x bigger capacitor 10*Cs where I accumulate 10 charge transfers and then measure the voltage. In other case I have small capacitor Cs and measure 10 times the voltage. In both cases the measured voltage like value is the same.

The question is - in which case I get better noise immunity. Notice that when I use small capacitor I don't have LP filtering on the input so all noises dirrectly impact the ADC.

MacGyverS2000 (Electrical) · Answer 3 · 2011-05-05 13:14:04

Noise immunity? Neither case provides noise immunity.

What you appear to be looking for is what is the level of noise compared to the level of measurement. Obviously if the magnitude of measurement increases compared to a stable magnitude level of noise, the signal-to-noise ratio goes up and the measurement looks better. But it's still the same noise level, and neither is less "immune".

Dan - Owner
http://www.Hi-TecDesigns.com

luben111 (Aerospace) · Answer 4 · 2011-05-06 01:20:32

Hi MacGyver,
Thank you for the response.
In oversampling the gain in the SNR and/or the additional bits comes after applying LP filtering on the measured samples. So my concerns are about the LP filtering

GregLocock (Automotive) · Answer 5 · 2011-05-06 01:25:25

I suggest you draw a diagram of your two proposals, that'll stop LP filters from appearing in the middle of the thread.

Cheers

Greg Locock

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luben111 (Aerospace) · Answer 6 · 2011-05-06 06:04:11

Hi,

Thank you for the idea - see attached the file where are shown 3 cases:

1. ADC with hardware LP filter on the input is acquiring multiple samples. The final result is the average value of all samples

2. ADC without hardware LP filter is acquiring multiple samples. The final result is the average value of all samples

3. ADC without hardware LP filter is acquiring multiple samples, each new sample is filtered in the software (IIR and/or slew rate). The final result is the average value of all samples

For sure the best way to measure the values is 1, but we can't implement LP on the ADC by many reasons.

The question is - if using software LP filtering (case 3) is it close like noise suppression to case 1? I guess one of the problems by not filtering the signal on the source (no hardware LP filter on ADC) is that we'll get aliases of the HF noises and hence this will compromise somehow the final result.

Also - case 2 (no hardware LP filter and no LP software filter - just averaging) what kind of noise levels we get?

regards
Luben

http://files.engineering.com/getfile.aspx?folder=4f37fd93-20c6-4559-acae-59

MacGyverS2000 (Electrical) · Answer 7 · 2011-05-06 07:13:29

Oversampling does not remove the need for a LP filter, it merely relaxes the requirements (e.g., you may get away with a 3dB/decade filter rather than a 6dB/decade).

Dan - Owner
http://www.Hi-TecDesigns.com

luben111 (Aerospace) · Answer 8 · 2011-05-06 07:25:55

Hi MacGyver,

So you think that case 3 is the best in my case - ADC sampling and LP on the acquired samples before they added in the accumulator for averaging.

regards
Luben

IRstuff (Aerospace) · Answer 9 · 2011-05-06 10:23:58

Perhaps, you should start with what your design requirements are, i.e., how much noise exists, how much you need remove, and how much latency you can tolerate.

Jumping into the middle of process and asking for comparisons of point designs without knowing the point requirements is a poor way to select the appropriate design. Moreover, in all 3 cases, you're already doing an average, which you yourself have noted has lowpass characteristics. In 2 of the 3 cases, you double band your latency, because you have both filter latency and averaging latency.

There are recursive filters that have better time series characteristics, and there are maximum likelihood filters that hage both better performance and lower latency.

TTFN

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MacGyverS2000 (Electrical) · Answer 10 · 2011-05-06 11:30:12

Quote (luben111):
So you think that case 3 is the best in my case...

I said nothing of the kind... according to the diagram text, both case 2 and case 3 do not use hardware LP filters on the input. Without a hardware LP filter of some form, how do you intend to get away from high-frequency signals that alias themselves down into your passband before software averaging ever touches them??

Dan - Owner
http://www.Hi-TecDesigns.com

Skogsgurra (Electrical) · Answer 11 · 2011-05-06 12:57:59

Dan, I wonder - what kind of filters are that? ("you may get away with a 3dB/decade filter rather than a 6dB/decade").

I can understand 6 dB/octave, but how do you get 3 dB/octave? And is there anything to gain from that?

Gunnar Englund
www.gke.org
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IRstuff (Aerospace) · Answer 12 · 2011-05-06 14:10:10

Isn't that just a function of whether we're talking power dB or voltage dB?

TTFN

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MacGyverS2000 (Electrical) · Answer 13 · 2011-05-06 14:12:41

In my fast finger fumbling typing, I was trying to say that oversampling will allow him to relax his transition band requirements on the hardware LP filter. A project that may have originally required a 24dB/octave LP filter at the input may be relaxed to 12dB/octave with enough oversampling. Much easier to make a 12 than a 24.

Dan - Owner
http://www.Hi-TecDesigns.com

Skogsgurra (Electrical) · Answer 14 · 2011-05-06 16:11:34

OK, I almost thought so. My fingers are also getting a little too thick for my keyboard.

Gunnar Englund
www.gke.org
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Integration in analog and digital domains