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My PCB consists of multiple ADC chips (AD7685) connected in a daisy-chain mode with STM32F303 as MCU and SPI communication. As far as I know, increase in the number of chips in the system results in decrease of the sampling rate per channel. So if I use twenty ADCs, the max sampling frequency can be 75kSPS, considering the data rate of STM32. One AD7685 chip can operate at max 250kSPS, according to the datasheet. My question is can I use only one chip to its fullest (250kSPS) in some cases when I do not need all twenty ADCs?

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My question is can I use only one chip to its fullest (250kSPS) in some cases when I do not need all twenty ADCs?

Yes you can but, it is limited to the first in the daisy-chain closest to the MCU. If you wanted to use the next chip, then you would process chip 1's result and discard it and keep chip 2's result. Clearly this takes about longer and, chips further down the daisy-chain take even longer. Then begin a new conversion.

So if I use twenty ADCs, the max sampling frequency can be 75kSPS

All ADCs simultaneously produce their conversions in a maximum time of 2.2 μs. Then, you have to clock all twenty serially at the maximum rate of the AD7685 (50 MHz). So, if you want 20 × 16 bit results, it will take 320 serial bits to complete the task.

That's 2.2 μs + 6.4 μs = 8.6 μs or, an overall sample frequency of 116.28 kSps. It looks like the MCU is the limitation here. It also sounds like you are assuming a clock rate of 24 MHz but, don't forget to take into account the conversion time of 2.2 μs. That would make an equivalent sample time closer to 64 kSps if you are running SPI at a clock of 24 MHz.

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The communication rate, of course, is not directly related to the sample rate, but it may limit it.

If you are only interested in the ADC or ADCs nearest to the data input of the MCU you can trigger a conversion and just read the ADCs of interest, then trigger a new conversion. As shown in the datasheet

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