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Precision infinite sample and hold circuit

Is it possible to couple some AD ADC directly to DAC without using microcontrollers or logic ICs? The goal is to make a single channel infinite sample and hold circuit with high resolution (at least 16 bits, preferably 18 or 20 bits). It should be able to sample a common-mode voltage in the range from -0.1V to +0.1V and reproduce it with no more than 100 uV error (preferably 10 uV). Found similar solution where 14-bit components were used, but don`t know how to select suitable ADC-DAC pair with higher resolution that will do the trick. Should I look for some specific features or just mindlessly read datasheets?

Thanks in advance.

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