# Help me find DAC Output function

Please help me find the output function, with $V_{REF}$ as reference, and $b_5-b_0$ as the digital input for this circuit (1):

I'm kinda confused with this Series capacitor that's splitting the array. It it weren't for that capacitor and all parallel ones were scaled normally, the output would be:

$\displaystyle V_{OUT} = V_{REF}\frac{C\sum\limits_{b=0}^{B-1}b_i 2^i}{C_{TOT}}$,

I think, but with this series capacitor I'm really not sure.

Reference:

(1) DAC Design Lecture, EECS dept, UC Berkeley, CA, 2009

• Could you provide a citation for the figure, please? I'm assuming that you did not draw it yourself. Dec 22 '13 at 11:44

• Thanks, this is very cool :) Spent hours searching for a similar paper unsuccessfully. However, I still can't figure out the output function. I understand that $V_{out} = V_{ref}\frac{C_{eq}}{C_{tot}}$, where $C_{eq}$ is the sum of all capacitors connected to Vref, with regard to Vref, but I'm not sure how this works out in this case. Dec 22 '13 at 13:49