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PROBLEM: enter image description here

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: enter image description here

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.

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    \$\begingroup\$ Google "superposition". \$\endgroup\$ – The Photon Dec 29 '15 at 16:58
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    \$\begingroup\$ also google" virtual ground". \$\endgroup\$ – JIm Dearden Dec 29 '15 at 17:43
  • \$\begingroup\$ or "Thévenin's theorem". \$\endgroup\$ – jippie Dec 29 '15 at 17:51
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    \$\begingroup\$ Your simplification doesn't account for inputs C and D being 0V. \$\endgroup\$ – jippie Dec 29 '15 at 17:52
  • \$\begingroup\$ 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. \$\endgroup\$ – robert bristow-johnson Dec 29 '15 at 19:17
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Start by redrawing your circuit:

  • 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.

If you show your intermediate results in your question, people will be more than willing to help you along.

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R1 and R2 are in parallel so that makes 1 Ohm. They are in series with R3 so that makes 2 Ohms. All that is in parallel with R4 which makes 1 Ohm. Finally, this is in series with R5 which makes 2 Ohms.

In your simplification you need a 2 Ohm resistor going from the junction of R6 and R7 to ground.

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