In Reply to: R2R DAC posted by jason on 10/04/03 at 10:44 AM:
First you have to know how an op amp works. The op amp has high gain, ideally infinite, so the voltage diference at the inputs is zero for any output. There is no current flow into or out of the op amp input, therefore all the current must flow thru Rf. When current (I)is applied to the op amp input, the output (Vo) assumes a value that will produce I, otherwise the input would not be zero. Practical op amps are close enuf to this ideal that the equation:
Vo = -Rf*I
is valid.
When the first switch (b1) is closed all the current (I) flows thru RF because the node voltage is zero.
When the second switch (B2) is closed, some of the current flows thru R on the right side (and also thru Rf) and the remainder flows thru 2R in parallel with R+2R in parallel with 2R. If you work that out, the resistance on the left is equal to R, so the current divides equally and the current thru Rf is 1/2 I.
Now you should be able to work out the other two switches to verify that B2 switch produces 1/4 I thru Rf, etc.