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Sigma Delta DAC

celebrevida

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I am studying Sigma Delta modulation. I believe I understand the first order basics for both ADC and DACs.

However in the case of Digital to Analog Converter, I am confused. Since you are generating a digital bitstream pattern from a binary input, why do you need the whole Sigma Delta scheme?

I guess my question is for every digital input pattern, why can't you just just use combinational logic or lookup table to generate the pattern and then just stream it one bit at a time for Sigma Delta DAC?

Also, and this applies to both ADCs and DACs, does the actual bit pattern matter or is it just the number of 0s and 1s that you get in a full frame cycle?
For instance in DAC bitstream output, would thermometer code bitstream work just as well as the bitstream that comes out of sigma delta DAC (which tends to NOT be like a thermometer code, the 1s tend to be more "dispersed"). Wouldn't the spectral content be the same either way?

Thanks for any insight.
 

Dominik Przyborowski

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Maybe I am wrong or my knowledge is outdated. However, I am not sure whether such animal like Delta-Sigma (or Sigma-Delta) DAC exists.
Oversampled DACs uses noise shaping technique (and at least I know this term - Noise Shaping DAC).

They are a cascade of N-bit interpolator, followed by noise shaper (it is basically a digital filter with N-bit input and M-bit output M<N and usually M=1), low resolution DAC (usually 1bit) AND analog LPF.

I believe that your concern is on noise shaper. We need it to process high resolution and low frequency N-bit digital signal into high frequency (oversampling ratio times Sampling freq) and low resolution (1 bit) digital signal for output DAC.
 

celebrevida

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Maybe I am wrong or my knowledge is outdated. However, I am not sure whether such animal like Delta-Sigma (or Sigma-Delta) DAC exists.
Oversampled DACs uses noise shaping technique (and at least I know this term - Noise Shaping DAC).

They are a cascade of N-bit interpolator, followed by noise shaper (it is basically a digital filter with N-bit input and M-bit output M<N and usually M=1), low resolution DAC (usually 1bit) AND analog LPF.

I believe that your concern is on noise shaper. We need it to process high resolution and low frequency N-bit digital signal into high frequency (oversampling ratio times Sampling freq) and low resolution (1 bit) digital signal for output DAC.
Here's a TI document on a Sigma-Delta DAC:
Implementation of 12-bit delta-sigma DAC with MSC12xx controller

Apparently they are very popular for audio applications. The are low speed but high resolution apparently.

If you look at the TI doc, on Table 2, they spell out the DAC output stream for a 3-bit DAC.


At least for this trivial example, it seems like you could just use logic and stream out those bit patterns explicitly. Of course 3-bits is trivial. Real Sigma Delta DACs are like 16 to 24 bits and maybe the complexity of doing that (having the output patterns hardwired with logic rather than a Sigma-Delta Feedback loop) is actually greater than just doing the Sigma Delta modulator. I mean the for a DAC, the modulator part isn't THAT complex to begin with.
 

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SD is a synonym for noise shaping, SD DAC is commonly used term.

Although it's possible to implement SD DAC with simple first order modulator you'll realize that modern 24 bit audio converters are typically higher order and multilevel modulators. The difference matters regarding achieved noise shaping respectively in-band SNR.
 

celebrevida

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SD is a synonym for noise shaping, SD DAC is commonly used term.

Although it's possible to implement SD DAC with simple first order modulator you'll realize that modern 24 bit audio converters are typically higher order and multilevel modulators. The difference matters regarding achieved noise shaping respectively in-band SNR.
Fair point. With higher order SD DAC, the concept of using using logic or lookup table is probably not possible. It seems like you could do it with just first order SD DAC. But it sounds like in real life first order SD modulation is not commonly used so whether you could do it that way or not is a moot point I guess.
 

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First order SD ADC and ADC are used, but not for high performance applications. Surely suited for 12 bit.
 

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