R-2R ladder D/A converter with mutilple non-zero inputs

PROBLEM:

So I am not used to r-2r ladders where 3 out of 4 inputs are 0V. Here both A and B are 5V, so I don't know how to approach this problem.

This is what i get when i simplify the ladder:

I think there is a virtual short at the terminal between R7 and R8, so current through Rf = current through R8. But I don't know what to do after this.

I haven't had much practice with these types of questions, so any help would be appreciated.

• Google "superposition". – The Photon Dec 29 '15 at 16:58
• also google" virtual ground". – JIm Dearden Dec 29 '15 at 17:43
• or "Thévenin's theorem". – jippie Dec 29 '15 at 17:51
• Your simplification doesn't account for inputs C and D being 0V. – jippie Dec 29 '15 at 17:52
• Also, even though the circuit will work as it is, it would be simpler to understand the R-2R concept if there was another 2$\Omega$ resistor placed between the node joining $R_7, \ R_8$ and the virtual ground of the "-" terminal of the op-amp. call that resistor "$R_9$" and notice it is a reflection in the topology of $R_1$. with all inputs equal to zero, look at each of these R-2R nodes, left and right of the node, and tell us what resistance to ground that you "see" going into the node. – robert bristow-johnson Dec 29 '15 at 19:17

• Draw a horizontal line for 5V power at the top of the circuit.
• Draw a horizontal line for GND at the bottom of the circuit.
• Move the resistors connected to 5V up and connect them to the 5V rail.
• Same for the resistors connectd to 0V, but now down to ground.

• Take a sheet of paper and cover the circuit.

• Move the sheet right in such a way that only R1 and R2 show.
• Calculate the node voltage of the sub-circuit.
• Calculate the output impedance of the sub-circuit.

• Knowing the node voltage and output impedance of sub-circuit R1-R2 move the sheet of paper right so R3 shows.

• Redo the calculation with the previous result and move R3 into the equation.

• Repeat .. until all you have is a single resistor and a single voltage source for the ladder network.

• Now finally take the opamp and its feedback resistor into account.