Electronic – Help me find DAC Output function

capacitorconverterdacoutputtransfer 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):
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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

Best Answer

With the 8C/7 capacitor splitting the the array in half, the total value of the left block of capacitors is made equal to the right block LSB-only capacitance by the inclusion of the series capacitor. Does this help?

C + C + 2C + 4C +8C/7 = C (LSB of right hand block)

This means that the left block LSB capacitor is weighted down appropriately.

Here's an interesting document on the theory. I was a bit disappointed more documents were not avaiable.

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