I'm wondering if the internal clocks in these devices are active only for the
conversion or if it is possible to disable them using one of the operating
There is no internal clock for AD7689 and AD7949. You have to provide an
external serial clock and datasheet recommends a discontinuous SCK because the
part is selected with CNV low, and SCK activity begins to write a new
configuration word and clock out data.
So you can disable external clock as per your requirements.