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how to calculate the R-2R ladder

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tony_wu_ad

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Deal all:

Today, I study the R-2R DAC, I find that I can not calculate the voltage by hand.
I draw a pic show below.
If S4 is high, it is easy to calculate that vout is 1/2 vref, but if S3 is high and the other is zero, how can calculate the vout by hand? I calculate it and vout is 1/4.
but if S2 is high, how to calculate? it is too difficult by hand.

Pls help me , thank :)
 

use the delta-star transformation
 

it would need assumption to solve... because each value can be either 5V or 0V.... it involves solving in a cascaded way... i have tried before and got exact result...
 
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    kopi

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I think u may apply the prinnciple of superposition i.e. assume one source is high and the others are low then sum the outputs to get the value of Vout
 

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