How does a delta sigma DAC work?

[HeadSh0T]

i can't help with the origins of the name but i know it's used for marketing.. product brochures will advertise "delta-sigma" like it's the key to good sound..

what i don't get is if multi-bit dacs are superior then why bother creating delta-sigma dacs anyhow? seems like a wasted time and effort.

[Bricolo]

Originally posted by HeadSh0T
i can't help with the origins of the name but i know it's used for marketing.. product brochures will advertise "delta-sigma" like it's the key to good sound..

what i don't get is if multi-bit dacs are superior then why bother creating delta-sigma dacs anyhow? seems like a wasted time and effort.

if I understood correctly, multi bit dacs are still delta sigma, with noiseshaping

[Christer]

I am perhaps on deep water here since I haven't read up on
these techniques, but Kueis explanation puzzles me a bit (joke
unintentional). I have always thought that delta-sigma is some
variation/extension on delta modulation, but now kuei says it
is actually PWM, which is not the same thing, at least it wasn't
20 years ago when I took the telecom course and we had
labs on delta modulation. So if it is PWM, where does the
name delta-sigma come from?? And in the case it is actually
some form of delta modulation, and not PWM, what does the sigma refer to?

[mikewu99]

Origin of the term "delta-sigma"

In the most basic form, a delta-sigma modulator consists of a subtractor (delta) followed by an integrator (sigma) followed by a quantizer. The input signal is connected to the positive input of the subtractor and the quantizer output connects to the negative input. This forms a servo loop that tries to drive the signal at the quantizer output to match the input signal. Since the loop has high gain at low frequencies (due to the frequency response of the integrator) the error in the quantized signal (quantization noise) is greatly attenuated at low frequencies, but can be quite large at high frequencies.

FWIW, for years there was a debate over whether the correct name is "delta-sigma" or "sigma-delta", owing to the tradition among control theorists to name their systems from the inside out instead of from front to back.

[Kuei Yang Wang]

Koinichiwa,

Originally posted by Bricolo

That's very well explained (I suspect Kuei Yang Wang for being the writer from the books called "Idiots guide for ..." )

Please note that the explanation was EXTREMELY simplified, mostly to drive the basic points home.

Originally posted by Bricolo

As delta sigma DACs are a kind of PWM, where does theyr name come from?

I seem to remeber that it was based on the Delta (Difference) of Sigma (Time). Note that I said that DS DAC's CAN be viewed as PWM/PDM, the operation is not exactly identical, especially not once multi-level modulators are included.

Originally posted by Bricolo

"The strong ultrasonic content in the output of a Delta Sigma DAC makes many a non-oversampling DAC look quite decent"
Wouldn't it be the opposite? Since you have HF output, non os would not be a good idea.
Where does this ultrasonic content come from? Isn't the 5-7th order lowpass enough to filter it?

As siad, all this ultrasonic noise is basically the result of reducing the bit-depth. Only, instead of being liberally smeared across the
Audio Range it is instead "pushed" outside the audio band.

Originally posted by Bricolo

Does this say that R2R DACs haven't any HF on the output? Making them more suitable to a non os DAC?

I would not want to try to make a non-oversampling Delta Sigma DAC, unless the sample rate is very high (DSD/SACD is an example of Non-Ovesampling Delta-Sigma).

So for CD, if you don't want the Digital Filter - Multibit only.

Originally posted by HeadSh0T
what i don't get is if multi-bit dacs are superior then why bother creating delta-sigma dacs anyhow? seems like a wasted time and effort.

A decent quality Multibit DAC costs a lot of money to make.

The Burr Brown PCM1704 is rated as 24-Bit/96KHz DAC. It requires two DAC Chips and an external digital filter. Total cost in qanteties of 1000 around USD 40. It also needs a complex analogue stage, with a high performance Op-Amp as I/V converter and another as Filter and several seperate, well filtered and regulated powersupplies.

If you do it well I'd think the cost to implement a conventional 96/24 DAC subsystem using PCM1704 will be near $ 100 US for a manufacturer who makes at least 1000pcs annually.

The Burr Brown PCM1728 is also rated as 24-Bit/96KHz DAC. It is a single chip including Digitial filter, 2 channels of DAC, part of the Analogue filtering, needs a single supply and a single Op-Amp as Buffer/Filter per channel. Budgetary pricing is 3 Bucks for the DAC Chip and maybe another 6 Bucks for the needed passive parts, analogue stage with regulators etc.

So the price differential between shipping your "Gizmo" with a 96/24 DAC based on DS and a proper Multibit DAC is around 1:10. Or to turn this around, the contribution to the endcustomer retail for the "Gizmo" (Say a "High Perfomance DVD/CD Player) will be around $80 - $160 for the DS DAC but $800 - $1,600 for the multibit, assuming they sell in equal quanteties.

Does that answer this question?

Originally posted by Bricolo

if I understood correctly, multi bit dacs are still delta sigma, with noiseshaping

You understand incorrectly. You CAN combine Dleta/Sigma technology and Noiseshaping with Multibit DAC's. Commonly the low level linearity of Delta/Sigma is better than in multibit DAC's and more consistently so with production, at the same time multibit has less out of band noise and seems to do better at higher levels.

The best modern DAC Chip's (according to specifications anyway) usally combine the two fundamental technologies. I have heard the Burr Brown PCM1738 sounding rather decent, in fact about as good with CD as a fullblown implementation of the PCM1704 with Parallel DAC's and HDCD Filter.

Originally posted by Christer
I am perhaps on deep water here since I haven't read up on
these techniques, but Kueis explanation puzzles me a bit (joke
unintentional). I have always thought that delta-sigma is some
variation/extension on delta modulation, but now kuei says it
is actually PWM, which is not the same thing, at least it wasn't
20 years ago when I took the telecom course and we had
labs on delta modulation. So if it is PWM, where does the
name delta-sigma come from?? And in the case it is actually
some form of delta modulation, and not PWM, what does the sigma refer to?

Actually, PWM is a little easier to understand than Delta/Sigma, so I used it as the explanation. While different in certain aspects, in the end you end up with a pulse width or pulse density modulated signal that look very similar on the 'scope and achieve very similar results in similar ways.

Other than for certain practical application issues and academia I would lump PWM, PDM, DS and co all together as special cases of the same principle in DA (or AD) conversion, as distinct to PCM conversion, which also has several subclasses of operation.

Okay?

I did warn in the beginning that I had to brutally simplify for clarity and understandability to "Joe average" (sorry Joe, nothing demeaning is implied - we all are specialists in something).

Cool Dudes?

Sayonara

[phase_accurate]

A better expression would be PDM (for pulse density modulation).
While PWM uses a fixed frequency rectangular output waveform whose duty-cycle is signal dependant.
D-S modulation uses a signal representation with a constant sample-rate. This results in an output switching waveform whose transitions take place at integer multiples of the sampling frequency. But you don't have a constant switching frequency anymore.
It is high for low output voltages and low for high output voltages.

I have attached an example of a 20 kHz signal. The green trace shows the unfiltered D-S output. One could theoretically see that all the transitions take place at integer multiples of 250ns. The red trace shows the signal after passing a 2nd order 120 kHz "reconstruction filter". The switching residual can be clearly seen as high-frequency noise.

Regards

Charles

[Christer]

Originally posted by mikewu99
Origin of the term "delta-sigma"

In the most basic form, a delta-sigma modulator consists of a subtractor (delta) followed by an integrator (sigma) followed by a quantizer. The input signal is connected to the positive input of the subtractor and the quantizer output connects to the negative input. This forms a servo loop that tries to drive the signal at the quantizer output to match the input signal. Since the loop has high gain at low frequencies (due to the frequency response of the integrator) the error in the quantized signal (quantization noise) is greatly attenuated at low frequencies, but can be quite large at high frequencies.

FWIW, for years there was a debate over whether the correct name is "delta-sigma" or "sigma-delta", owing to the tradition among control theorists to name their systems from the inside out instead of from front to back.

Well, then it is identical to what was called delta modulation
when I took the telecom course long ago. It seems delta-sigma
(or sigma-delta) is just a more modern term for the same thing.
That clears up the issue for me. Thanks.

[Christer]

Kuei,

OK, it seems you did not really mean that delta-sigma is PWM,
only that it is similar in some sense. I agree to that, but I don't
think it appropriate to mix them up to the point of saying that
delta-sigma "is" PWM even in a simplified presentation as you
did, which is why I was confused.

Anyway, issue cleared.

[phase_accurate]

There is a significant difference between delta-modulation and delta-sigma (or sigma-delta) modulation.

The delta modulator has the integrator in the feedback path whereas the delta-sigma modulator has the integrator(s) in the forward path.

The result is that with delta modulation the pulse density is proportional to the signal slew-rate, where the pulse density is proportional to the signal amplitude for delta-sigma modulation.

Regards

Charles

[Christer]

Originally posted by phase_accurate
There is a significant difference between delta-modulation and delta-sigma (or sigma-delta) modulation.

The delta modulator has the integrator in the feedback path whereas the delta-sigma modulator has the integrator(s) in the forward path.

The result is that with delta modulation the pulse density is proportional to the signal slew-rate, where the pulse density is proportional to the signal amplitude for delta-sigma modulation.

Regards

Charles

I have been thinking about this now and then, trying to figure
out what you mean, but I don't get it. This is my understanding
of it. In both cases we have analog in and binary out. In the case
of delta modulation the input goes to in+ of a comparator, the
output from the comparator is clocked and used as output. This
output is also fed back to in- via an integrator. This seems to
agree with what you say. However, for delta-sigma you say
the integrator is in the forward path, and I fail to see where
to put it unless the whole design is fundamentally different.
Since we want binary out, I cannot quite envision any other
place to put the integrator than in the feedback path. What do
I miss? Or are my fundamental assumptions wrong??