Sigma-Delta DAC Noise Spectrum

[roadbuster]

 

I am trying to design a sigma-delta DAC. On page 40 of **broken link removed**, a figure of the in-band noise for various types of samplers is shown:

I understand that these spectrums are for ADCs. Do the same spectrums apply to DACs? That is, if I use a simple, oversampled DAC, will the quantization noise be spread between DC and Fs/2? Similarly, if I use a first-order sigma-delta DAC, is the quantization noise suppressed like in the figure?

As well, can anyone explain the math behind how oversampling spreads the quantization noise over a larger bandwidth?

Thank you for any help.

 

[FvM]

There is plenty of literature on this topic, the best basic books, also discussing DACs in detail, are to my opinion from Richard Schreyer et al, either Understanding Delta-Sigma Data Converters or the predecessor, Delta-Sigma Data Converters

 

[roadbuster]

Thank you for the links. I already own the Richard Schreier book. The chapter on DACs only goes over DAC architectures rather than the math involved with things like quantization.

Can you at least tell me if quantization noise is spread over the sampling frequency for oversampled DACs? I mean, if I have a baseband signal of 20KHz which I oversample to 2MHz, is the quantization noise spread between 0 - 20KHz, or 0 - 1MHz * \[ \left( 0 \ - \ \frac{F_s}{2} \right)\] ?

 

[FvM]

The mathematics is basically identical for AD and DA applications. From this prerequisite, both books discuss mostly particular structure aspects in the DA chapters, I think. In my understanding, the quantization noise is initially spread over the frequency range determined by the modulator respectively the oversampling frequency. This already reduces in-band noise by the square root of over sampling ratio. The art of SD noise shaping is in reducing it further in the signal band.