Processing math: 100%

Digital to Analog Converter

A digital-to-analog converter (DAC, D/A, D2A or D-to-A) is a circuit that converts digital data (usually binary) into an analog signal (current or voltage). One important specification of a DAC is its resolution. It can be defined by the numbers of bits or its step size.

Digital to Analog Converter using the Summing Amplifier

The following diagram shows a 3 bit digital to analog converter implemented using a summing opamp amplifer.

From the summing amplifier circuit (see equation 6), the output voltage is Vout=R(V2R+V12R+V04R) Simplifying, we obtain Vout=14(4V2+2V1+V0)

Output Table
V2 V1 V0 Digital Value Vout
0 0 0 0 0
0 0 1 1 -0.25
0 1 0 2 -0.5
0 1 1 3 -0.75
1 0 0 4 -1.0
1 0 1 5 -1.25
1 1 0 6 -1.5
1 1 1 7 -1.75

From the table, we can conclude the following

  • The inputs can be thought of as a binary number, one that can run from 0 to 7.
  • V2 is the MSB (most significant bit) and V0 is the LSB (least signifcant bit).
  • The output is a voltage that is proportional to the binary number input.
  • The resolution of this DAC is 3 (the number of bits) or -0.25V (the step size).
  • To have more bits, add an additional resistor for each additional bit. Note the relationship between adjacent resistor values.

R-2R Binary Ladder Digital to Analog Converter

The R-2R Digital to Analog Converter uses only two resistance values R and 2R regardless of the number of bits of the converter compared to the summing amplifier implementation where each bit resistor has a different value. The circuit shown is a 3 bit DAC.

Depending on the state of bit B2, B1 or B0, the respective current I2, I1 or I0 is switched either to ground or to V- of the op amp. Thus Iout=B2I2+B1I1+B0I0

To analyse this circuit, first we observe that since the output is connected to V- through Rf, the opamp is in a negative feedback configuration. Thus V=V+=0

Therefore the individual current values I2, I1, I0 are unaffected by the switch setting and the resistor network circuit can be redrawn to the following

Due to the nature of the resistance network and values, we can obtain the current values by inspection.

From ohms law, I0=Ic From KCL at node V0, Ib=I0+Ic=2I0 From KVL, V1=IbR+I02R Substituting equation 6 into equation 7 V1=4I0R Again applying ohms law to I1 and using equation 8, we obtain V1=I12R=4I0R or I1=2I0 From KCL at node V1, and using equation 6 and 10 Ia=Ib+I1=2I1 From KVL, Vref=IaR+I12R=4I1R We leave the reader to figure out how we obtain I2=2I1=4I0=Vref2R Thus the R-2R network can be seen to be like a current source whose output depends on switch setting B2, B1, B0 that controls I2, I1, I0 respectively Iout=Vref8R(4B2+2B1+B0)

Including the opamp which behaves like I-V converter, we obtain the voltage ouput (note the direction of the current source) Vout=VrefRf8R(4B2+2B1+B0) Letting Vref = 1 and Rf = 2R, we obtain the following output table

Output Table
B2 B1 B0 Digital Value Vout
0 0 0 0 0
0 0 1 1 -0.25
0 1 0 2 -0.5
0 1 1 3 -0.75
1 0 0 4 -1.0
1 0 1 5 -1.25
1 1 0 6 -1.5
1 1 1 7 -1.75