The basic DAC transfer function is a straight line with output values between a lower (negative) and upper (positive) reference.
All DACs have a Top (or Positive) Reference and a Bottom (or Negative) Reference. We do not often hear or think about a bottom or negative reference because it is usually ground potential (0.0V) in a DAC with a voltage reference and we generally ground (sometimes through a resistance) the negative reference of a DAC with a current reference.
- The analog output range for a DAC with a voltage reference and voltage output is
Where VRP is the positive or top reference voltage, VRN is the negative or bottom reference voltage and "G" is the DAC gain factor. Also, the total reference is VREF = VRP - VRN.
Assuming a gain (G) of one, the output range formula reduces to
- Further assuming that VRN is 0V, as in the example of the figure above, these two relationships reduce to
- So, with a gain of G = 1, a VRN of 0V and an input code of 0000 0000, the output of an ideal 8-bit DAC is 0V. With an input code of 1111 1111, the output voltage is
VOUT= G x (28 - 1) x VREF / 28 = G x 255 x VREF / 256, which is the full-scale output value. With an input code of 1000 0000, the output voltage = G x 27 x VREF / 28 = G x 128 x VREF / 256 = G x VREF / 2, which is the half-scale output value.
- So, with a gain of G = 1, a VRN of 0V and an input code of 0000 0000, the output of an ideal 8-bit DAC is 0V. With an input code of 1111 1111, the output voltage = G x (28 - 1) x VREF / 28 = G x 255 x VREF / 256, which is the full-scale output value. With an input code of 1000 0000, the output voltage = G x 27 x VREF / 28 = G x 128 x VREF / 256 = G x VREF / 2, which is the half-scale output value.
- While the basic DAC input/output transfer characteristic is a straight line, some DACs have been produced with other characteristics. A Logarithmic characteristic is an example.
