Bipolar DAC output and 3-bit transfer curve

A bipolar DAC produces both positive and negative output voltages. It adds a constant offset current equal to half of full scale, with opposite sign, to the current of a normal R-2R DAC.

Circuit

 Vref -->[ R-2R ladder ]--I_D----+
                                |   Rf=2R
 -Vref -----[ 2R ]----I_os------+--/\/\/--+
                                |         |
                              (-)\        |
                                  >-------+--> Vo
                              (+)/
                               GND

Derivation

1. The R-2R ladder (current mode) sends this current into the virtual ground:

I_D = (Vref/R)(b(n−1)/2 + b(n−2)/4 + … + b0/2ⁿ)
    = (Vref/R) · D/2ⁿ

2. The offset branch from −Vref through 2R gives:

I_os = −Vref/(2R)

3. The inverting summer output with Rf = 2R:

Vo = −Rf (I_D + I_os)
   = −2R [ (Vref/R)(D/2ⁿ) − Vref/(2R) ]
   = −Vref (2D/2ⁿ − 1)

Taking the polarity after an output inverter (or reversed references), the standard bipolar (offset binary) result is:

Vo = Vref (2D/2ⁿ − 1) = Vref (D − 2ⁿ⁻¹) / 2ⁿ⁻¹

• D = 0 gives −Vref
• D = 2ⁿ⁻¹ (MSB only) gives 0
• D = 2ⁿ − 1 gives Vref(1 − 2/2ⁿ)

Step size = 2Vref/2ⁿ.

Transfer curve for 3-bit bipolar DAC (n = 3)

Vo = Vref(2D/8 − 1), step = Vref/4.

 Vo/Vref
 +0.75 |                            +---
 +0.50 |                        +---+
 +0.25 |                    +---+
  0.00 |----------------+---+-----------
 -0.25 |            +---+
 -0.50 |        +---+
 -0.75 |    +---+
 -1.00 +----+
       000 001 010 011 100 101 110 111

The staircase goes from −Vref at 000 up through zero at 100 to +0.75 Vref at 111. Zero output falls at mid-code, which shows the bipolar nature of the output.