1. Digital to Analog Converters (DAC) 3
©Paul Godin
Created March 2008

2. R/2R DAC
The Binary-Weighted DAC limitations include the need for progressively larger resistors.
The R/2R ladder method eliminates the need for the variety of resistors required. It operates on a ratio between resistors.
The Op Amp is still an important component in the circuit.

3. R/2R Circuit
VDD
VEE Rf R 2R
LSB
MSB

4. What value of R does the op-amp input sence?
R/2R Circuit
VDD
VEE Rf R 2R
LSB
MSB 1
What value of R does the op-amp input sence?

5. Resistor Equivalent 1 2R R R R 2R 1 2R 2R 2R
REQ 2R R

6. Resistor Equivalent 1 1
REQ 2R R Rf 2R
VDD 2R
LSB
VEE
Note: The resistor that connects between the inverting input and ground serves no function. The inverting input of an op amp is already at a “virtual” ground.

7. R/2R Circuit – Current Perspective
VDD
VEE Rf R 2R
LSB
MSB
The resistance seen to the right of any vertical resistor is 2R.

8. Errors in DAC

9. Errors
Digital to Analog systems have several possible sources of error.
The errors can be the result of:
Binary Input
Non-linear input sequences or incorrect values
Voltage issues
Resistor network
Resistors out of specification
Noise
Op Amp output errors
Improper input voltage
Improper Offset
Delay

10. Gain Error
A Gain Error occurs when the Op Amp produces an output at a different voltage scale than desired. The output is linear but the steps are either larger or smaller than they should be. Output may appear clipped.
Red: Ideal
Blue: Error
Green: Error
Volts
Binary Code

11. Gain Error Typical Causes: wrong VDD/VEE at op amp wrong RREF value
wrong resistor network values
Red: Ideal
Blue: Error
Green: Error

12. Offset Error
An Offset Error occurs when the Op Amp output has the same voltage per step but the starting voltage is different.
Red: Ideal
Blue: Error
Green: Error
Volts
Binary Code

13. Offset Error Typical Causes: op amp improperly offset Red: Ideal
Blue: Error
Green: Error

14. Non-Linearity: Non-Monotonic
A Monotonic Error occurs when the individual voltage steps are non-linear.
Volts
Binary Code
Red: Ideal
Blue: Error

15. Non-Linearity: Non-Monotonic
Typical Causes:
incorrect input binary sequence caused by mix-up at binary input or a stuck input
Red: Ideal
Blue: Error

16. Non-Linearity: Differential
A Differential Error occurs when the output steps start to vary in size.
Red: Ideal
Blue: Error
Volts
Binary Code

17. Non-Linearity: Differential
Typical Causes:
resistor network unbalanced
binary input voltage values
Red: Ideal
Blue: Error

18. Other Types of DACs
MOSFET Current Scaling that use a configuration of MOSFETs in a similar manner to R/2R.
Voltage Scaled DACs employ a resistor string as a large voltage divider for reference voltage values, and use enable/disable circuitry for the output voltage.
Charge Scaling DACs utilize capacitors instead of resistors. Can be more accurate and potentially faster but are more difficult to implement.

19. END DAC 3
©Paul R. Godin
gmail.com