how to calculate the R-2R ladder

[tony_wu_ad]

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

 

[ho83]

use the delta-star transformation

 

[A.Anand Srinivasan]

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...

 

[Ghitani]

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