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One option is to employ a digital potentiometer, use 5V voltage reference and reduce the digital potentiometer output from 0-5V to 0-20mV by 2-resistor voltage divider ..
Another option is to use a digital to analog converter and again reduce its output voltage form whatever it produces (0-5V, for example) to 0-20mV using 2-resitor voltage divider ..
In both cases, if required, you can use a rail-to-rail voltage buffer-follower to ensure that your 0-20mV voltage source behavies like a voltage source ie. it has very low output impedance ..
use a microcontroller and a dac.....u can controll voltage from 0 to 5 volts....
then use a resistor divider network to get 20mV at full 5V input....then use a voltage follower if u want.....
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