Example circuit equation derivation – level shift and scaling circuit

Generally voltage DAC output will be [0V : +VREF ], where VREF is the reference voltage to the DAC. But sometime you would like to have a bipolar signal out of DAC for your use. In this case, you would need to level shift and scale the signal accordingly. Shown below is a circuit that level shift the DAC output from [0V : +VREF ] to [-VREF : +VREF]

To derive the equation, first is to identify from y = mx + c, y = vout, x = Gdac. In actual application, when you program DAC to half its range, Gdac = 0.5, and the number can be controlled from 0<=Gdac <=1 by changing DAC data input.