caclulation of a R2R dac ladder

[jeremy_zhu]

r2r calculate

Is the equation below all right or are there any some mistakes?
From the pic, current flowing the feedback res is If
And the vout=vcm+If*R can we get: vout in the pic
and the digital input code is sequenced from 0000 0000 to 1111 1111,and what’s the output of the dac ?


pic is attached here:

 

[Areky_qin]

r/2r dac equation

could you re-upload a more clear pic?
in generally, the r2r calculate is easy, please from the terminal close the vref,then one by one to the termal close the opamp.

 

[jwfan]

Google it.

 

[tzg6sa]

I do not understand the analysis of the R2R ladders. My main concern is that the different bits are seeing different resistances. If we look downwards all the resistances are 2R, but not upwards! For example the weight of b(n-2) should be (R+2R)||2R/((R+2R)||2R+2R)=3/8
For a 2 bit DAC the outputs would be:
0, 3/8, 4/8, 7/8

So looking upwards from the right end of a 2R resistor we see a resistance which depends on the distance of the output node. Thus the bits are not binary weighted.
Could somebody resolve this?

Added after 2 hours 20 minutes:

I do not understand the analysis of the R2R ladders. My main concern is that the different bits are seeing different resistances. If we look downwards all the resistances are 2R, but not upwards! For example the weight of b(n-2) should be (R+2R)||2R/((R+2R)||2R+2R)=3/8
For a 2 bit DAC the outputs would be:
0, 3/8, 4/8, 7/8

So looking upwards from the right end of a 2R resistor we see a resistance which depends on the distance of the output node. Thus the bits are not binary weighted.
Could somebody resolve this?

I see now. I did not finished the calculation. There is a voltage divider to the output. Taken into account the dividing ratio I get the correct binary weight.