R-2R Ladder DAC

The following circuit diagram shows the basic 2 bit R-2R ladder DAC circuit using op-amp. Here only two values of resistors are required i.e. R and 2R. The number of digits per binary word is assumed to be two (i.e. n = 2). The switch positions decides the binary word ( i.e. B1 B0 )

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The typical value of feedback resistor is Rf = 2R. The resistance R is normally selected any value between 2.5 kΩ to 10 kΩ.
The generalized analog output voltage equation can be given as

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The operation of the above ladder type DAC is explained with the binary word (B1B0= 01)
The above circuit can be drawn as,

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Applying the nodal analysis concept at point (A), we gets following equations

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Applying the nodal analysis concept at point (B), we gets following equations

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Substituting the equation of VB in the above equation, we get

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The voltage at point A i.e. VA is applied as input to the op-amp which is in inverting amplifier mode as shown in figure below.

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The output voltage of the complete setup
∴Vo=-(2R/R) VA

∴Vo=-(2R/R)(-VR/8)

∴Vo=VR/4

Similarly for other three combinations of digital input the analog output voltage Vo is calculated as follows

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