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DSD vs PCM resolution


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The second part has error where it says multi-bit SDM DAC would use R2R ladder for conversion. This is not the case and would leave out one very important phase of the process - DEM.

 

I thought a multibit ladder DAC could use DEM - am I wrong about that, or am I misunderstanding you?

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Not really, there's nothing making it class-A. And you need to take into account different load situations such as inductive and capacitive loads (phase difference between voltage and current).

 

There was written "ideal class A".

 

Ideal class A (mode of class A) can have strongly linear amplitude responce.

 

Class D (in contrast) is a pure square. Such is "digital amplifiers" with sigma delta modulation.

 

Of course real amp that you modeling is non-linear and work in the range of most linearity. Without entering to saturation.

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There was written "ideal class A".

 

It is even too simplistic for that, since it doesn't model even ideal one. There are also ideal component models (FET, etc) in SPICE, but those are not really useful for modeling any real world hardware, only for theoretical schematics. For example teaching someone about https://en.wikipedia.org/wiki/Common_collector

 

Of course real amp that you modeling is non-linear and work in the range of most linearity. Without entering to saturation.

 

That's the only useful thing when you want to design something that can actually be realized in real hardware.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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Well, binary encoded ladder cannot, because each element has a different weight and cannot be interchanged with another one.

 

Ah, got it, thanks.

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical to EtherREGEN -> microRendu -> ISO Regen -> Pro-Ject Pre Box S2 DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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Well, binary encoded ladder cannot, because each element has a different weight and cannot be interchanged with another one.

 

DEM converts non-linearity into linearity plus noise. There are some ways to get similar results out of ladder DACs by using multiple DACs per channel and sending them randomly varying inputs. For example with two DACs: If R is a random value (per sample) and A is audio sample, send A + R to one DAC and A - R to the other DAC and sum the analog outputs.

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DEM converts non-linearity into linearity plus noise. There are some ways to get similar results out of ladder DACs by using multiple DACs per channel and sending them randomly varying inputs. For example with two DACs: If R is a random value (per sample) and A is audio sample, send A + R to one DAC and A - R to the other DAC and sum the analog outputs.

 

Tony, do you know of anyone currently doing this?

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical to EtherREGEN -> microRendu -> ISO Regen -> Pro-Ject Pre Box S2 DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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PCM is typically binary coded (two's exponent) Nyquist sampled values without significant noise shaping.

 

SDM is typically unary coded (thermometer code) non-Nyquist sampled values and relies on heavy noise shaping.

 

 

DSC1 uses scrambled 32-bit unary coded values for conversion, while being bit-perfect with DSD data input. Values converted to analog vary between 0 and 32, thus having total of 33 possible levels.

 

While PCM ladder DACs depend on binary coded values...

 

Thanks for spelling out these main differences between PCM and SDM DACs so clearly. Hopefully the message will now sink in.

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Tony, do you know of anyone currently doing this?

 

Not sure about which DACs. I first heard of this idea in the late 80's when Barry Blesser gave a talk at Lincoln Labs that I attended. Most of the recent work on dynamic element matching has been published in the chip design context where 1 bit switch elements are used with some kind of thermometer code. (Example: SABRE DAC).

 

See this post of mine:

Conclusive "Proof" that higher resolution audio sounds different - Page 147

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DEM converts non-linearity into linearity plus noise. There are some ways to get similar results out of ladder DACs by using multiple DACs per channel and sending them randomly varying inputs. For example with two DACs: If R is a random value (per sample) and A is audio sample, send A + R to one DAC and A - R to the other DAC and sum the analog outputs.

 

But it doesn't really work well there where the major R2R problem is - relative inaccuracy of the MSB elements. Going from LSB towards MSB, every element doubles the precision requirement. You would really need to randomize the MSBs and still it would be inefficient while at same time introducing major loss in SNR.

 

There are better ways to linearize R2R, but the overall relative effectiveness is anyway lower.

Signalyst - Developer of HQPlayer

Pulse & Fidelity - Software Defined Amplifiers

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Going from LSB towards MSB, every element doubles the precision requirement. You would really need to randomize the MSBs and still it would be inefficient while at same time introducing major loss in SNR.

 

What does you mean under precision? Resistor's nominal value precision (example: 100 kOhm +/- 1%)?

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Yes. For a 24-bit R2R DAC, the MSB resistor would need a precision of about 0.00000001% if the LSB is 1%.

 

As I know no 0.00000001% precision for resistors.

 

As example, us need provide 1% DAC value precision.

 

If we use about LSB only: we get 0 or X volt with precision of LSB resistor (1% as example).

 

If we use about MSB only: we get 0 or X^16 volt again with precision of MSB resitor (1% as example).

 

Summ of MSB and LSB also into 1% precision.

 

Therefore, enough same precision for all resistors.

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As I know no 0.00000001% precision for resistors.

 

As example, us need provide 1% DAC value precision.

 

If we use about LSB only: we get 0 or X volt with precision of LSB resistor (1% as example).

 

If we use about MSB only: we get 0 or X^16 volt again with precision of MSB resitor (1% as example).

 

Summ of MSB and LSB also into 1% precision.

 

Therefore, enough same precision for all resistors.

 

That's not how it works. If they are all 1%, the inaccuracy in the MSB contributes more to the output than the actual input 8 bits down. In other words, a uniform accuracy of 1% is enough for an 8-bit DAC.

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Mansr,

 

1% was taken as example ("As example, us need provide 1% DAC value precision.").

 

As I understood, you want provide precision no worse LSB for 8 bit DAC with 1% precision of resistors.

 

1. As initial conditions:

1.1. DAC has 8 bit

1.2. Density of the probability distribution of the error accept as normal.

 

2. Maximal absolute error is MAE=1.

 

3. Maximal voltage for bit number MSB-1 is MV=2^7=128. MSB used as sign and applied via inversion of voltage.

 

4. Must be provided error

 

E=MAE/(3*MV)=1/(3* 128)=0.26%

 

Coefficient 3 used for normal distribution (point 1.2)

 

I.e. for providing of precision no worse LSB for 8 bit DAC, resistor precision should be 0.26%.

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  • 2 years later...
  • 2 weeks later...

Hi @Miska

 

This is puzzling question I always wanting to ask… DSD is always converted to analogue at its native sampling frequency. In PCM, 44.1kHz is always over-sampled to 352.8kHz inside the DAC then convert to analogue, this provided excellent signal to noise ratio across the audio range.

DSD64 noise-shaping is only effective up to 22.05kHz, after that ultra-sonic noise will start to appear. If DSD64 is over-sampled to DSD256 or even DSD512 inside a DAC, the ultra-sonic noise will be shifted even further away by a few octaves! This means, DSD64 recording is all it needs to get a good signal to noise ratio above 22.05kHz if it is oversampled in a DAC. Native DSD128 and DSD256 recordings will shift the ultra-sonic noise further away by a factor of 2 to 4 times but the files sizes becomes too large.

 

Is there any reason why DSD is never over-sampled or up-sampled in a modern DAC?

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