# What's the Model for a DAC followed by a sampler

I have a situation where a sampled signal is passed through a DAC and re-sampled by a switched capacitor circuit.

I can't see a model for this in the literature.

The standard model of a DAC is the ZOH. But when it gets re-sampled by the switched cap circuit it seems to me that ZOH effect of the DAC disappears because of the re-sampling.

What does the Signal Processing SE community think?

Assume the re-sampling is at the same rate as the DAC.

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What kind of DAC is that? Standard instrumentation DAC (modeled by a ZOH, with a negligible settling time and no reconstruction filter) or something fancier?

What's happening could be described in the following terms: in the short analog land between the DAC and the rest of the circuit, you see your signal with mirror images of its spectrum above Nyquist frequency (amplitude decreasing with frequency, as your ZOH is equivalent to a multiplication of the spectrum by a sinc function). The switched capacitor circuit resamples this signal; but since its sample rate is the same as that of the original signal, there is no aliasing - the mirror images created by the DAC/ZOH will line up perfectly with the original harmonics.

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Standard DAC etc.. Good answer. What's your opinion if the sample rates are different? I think the delay would become apparent again for non-integer rate reduction between the DAC and the sampler. What do you think? –  akellyirl Mar 4 '14 at 16:33
If the sample rates are in non-integer ratios, all the mirror images created by the ZOH will cause problems, as they will be mirrored during sampling. In this case you need a very good anti-aliasing filter at the input of your switched capacitor circuitry. –  pichenettes Mar 4 '14 at 16:43

It depends on how acccurate your model is. For an ideal DAC with rectangular impulse response $g(t)$ followed by an ideal sampler your observation is true: the sampled signal is identical to the DAC input signal.

But as soon as some frequency selective element comes into play (e.g. anti-aliasing filter) the impulse repsonse $g(t)$ causes a droop in frequency domain.

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