Delta-Sigma encoding

In the bipolar case, equal 1s and 0s is 0 volts = mid scale. That's how audio does it.

The unipolar case is positive voltage proportional to duty cycle.

A delta-sigma ADC will servo to get correct. The integrator integrates the difference between the input and the duty-cycle feedback.

A d-s DAC is really a lowpass filter, which also recovers from a disturbance. After a while, it forgets.

Some people like to use a sinc3 lowpass filter to recover the output of a d-s data stream. It has differentiators and integrators inside that will never recover from an error, the theory being that digital systems never make errors.

But the sinc3, being a lowpass, will recover from a temporarily trashed input data stream.

Delta-sigma is just duty-cycle modulation with some noise tricks.

There are some outrageous d-s ADCs and DACs. I don't understand how they can be so good; there must be hidden semiconductor tricks.

I have a Spice model of a d-s ADC and corresponding DAC. I can probably hunt it down if anybody is interested. I have a *lot* of Spice files!

I found out what was wrong with that reply. The keyboard wasn't plugged in.

You have an integrator at both ends, one for encoding one for decoding. For fidelity, make sure they're the same. For noise impulse recovery make sure they drift towards AC 0V

If you use an R-C lowpass as the integrator, then any noise that gets into the stream will decay exponetially. if you use FIR like boxcar or trapezoid as the intregrator the noise will dissapear after finite time.

No.

No. The offset generates a correction signal that pulps it back

The output will move to match the no-signal input.

No. It's feedback system. The integrator just integrates the error signal, which feeds back.

The literature has a nasty habit of skipping the fundamentals. Somebody taught a high level course on sigma-delta A/D conversion at Cambridge, and it's graduates thought that anybody who didn't use it's misleading jargon didn't know anything about the subject.

Happily, that didn't stop me from using a sigma-delta A/D converter because it was all buried inside the chip I bought.

So this is the reason why many digital audio systems haven a low frequency limit at about 3 Hz(and not DC) ?

D-S works fine down to DC. Audio systems are generally AC-coupled, one reason being not to fry speakers. The other reason is to be cheap.

We use d-s adc's and dac's in precision instrumentation, DC accurate.

I wonder why audio CDs weren't d-s encoded. It would have saved gigabucks.

Probably not. Manufactures don't specify or measure anything they don't have to, and nobody in the audio market is interested in what the system does at frequencies humans can't hear.

Bill Sloman, Sydney

Pretty much all of them were. How come you didn't know that?

only the special SACDs are D-S encoded, normal CDs are 16bit PCM, though a lot of CD players use a D-S DAC

Probably because CDs were developed in the late 1970s, long before digital ICs (or semiconductors in general) were remotely fast enough and cheap enough for a consumer mass-market product.

.

Joe Gwinn

I apologise for responding twice to same post, but John Larkin has made two mistakes here.

The audio data that was digitised and ended up on Compact Disks (and other digital media was mostly digitised by rather expensive sigma-delta A/D converters in recording studios. There weren't enough of them for anybody to save gigabucks by using them.

Compact Disk were just a means of distributing digital audio after the audio signal had been digitised.

The consumer electronics that played back the compact disks were produced in high volume, and using sigma-delta D/A converters in them probaby did save a lot of money.

The book "The Art of Digital Audio" by John Watkinson - ISBN 0-240-512270-7 first published in 1988, is a full bottle on the subject, and on digitisation.

It is still in print. I cited it in comment published in Rev. Sci. Instrum. in 1999

It was originally published as a series of articles in Wireless World (UK) and can be downloaded from:

I did read Wireless World back then - but from 1975 Byte was competing for my attention. My wife (not that I'd married her at that point) was doing a post-doc at MIT when Byte first started up and gave me an initial subscription, which I kept up until it folded in 1998.

I ran into the book when browsing Heffer's book-shop in Cambridge and promptly bought it. I got the 1989 revised edition.

Whilst looking up that reference I came across a Wireless World article 'explaining' Delta-Sigma modulation. On the first page the author erroneously equated an integrator with a low-pass filter - the rest of the article then just degenerated into incomprehensible maths.