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I would like to modelize my whole system into the S-domain. This is a mixed system, there a numerical part (corrector, ADC, DAC) and an analogic part (plant transfer function, sensors, etc...). I know that it is possible to transform a DAC (Digital to Analog converter) or a ZOH into the s domain thanks to the Padé's approximation. Nevertheless I do not know how to do for the ADC as it is non linear like the DAC. Is it possible to do the same with the Padé approximation. Does anyone know the transfer function in the S domain or the approximation of the transfer function of the ADC ?

Thank you and have a nice day !

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    $\begingroup$ ADCs don't have a transfer function. An ideal ADC is an ideal sampler with a sampling period T. Real ADCs are not ideal, they have some sampling delays, jitter, quantization noise, thermal noise, etc. Usually the sampling delays are really small compared to the dynamic of the systems, so we don't model them. Quantization noise and thermal noise should not be a factor unless the signal you measure is really small. And jitter is not an issue unless the signal frequency is really high. $\endgroup$
    – Ben
    Jan 19, 2021 at 14:48
  • $\begingroup$ However, sampling delays could be modeled using the Padé approximation. $\endgroup$
    – Ben
    Jan 19, 2021 at 14:48
  • $\begingroup$ @Ben Thank you for your answer. What is the transfer function of sampler with a sampling period T in the s domain ? $\endgroup$
    – Jess
    Jan 19, 2021 at 14:52
  • $\begingroup$ If you sample with an ideal sampler you move the continuous domain s to the discrete domain z. $\endgroup$
    – Ben
    Jan 19, 2021 at 14:53
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    $\begingroup$ How fast is your ADC ? If your ADC is really fast compared to the dynamics of your system, you could pretend that the ADC is not there. $\endgroup$
    – Ben
    Jan 19, 2021 at 15:34

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ADCs don't have a transfer function. An ideal ADC is an ideal sampler with a sampling period T.

Real ADCs are not ideal, they have some sampling delays, jitter, quantization noise, thermal noise, etc. Usually the sampling delays are really small compared to the dynamic of the systems, so we don't model them. Quantization noise and thermal noise should not be a factor unless the signal you measure is really small. And jitter is not an issue unless the signal frequency is really high.

So bottom line, if your ADC is really fast compared to the dynamics of your system and if the measured signal is inside the dynamic range of your ADC, you could pretend that the ADC is not there.

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