1. Digital to Analog Converters
Tyler Smith
Brent Nelson
Jerry Jackson
10/14/04

2. Topics Discussed What is a DAC? Choosing a DAC Resistor String DAC
Weighted Resistor DAC
R-2R DAC
PWM
DAC associated errors
Applications
Conclusion

3. What is a DAC
A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output.

4. Choosing a DAC
There are six main parameters that should be considered when choosing a DAC for a particular project.
Reference Voltage
Resolution
Linearity
Speed
Settling time
Error

5. Choosing a DAC Reference Voltage
To a large extent the output properties of a DAC are determined by the reference voltage.
Multiplier DAC – The reference voltage is constant and is set by the manufacturer.
Non-Multiplier DAC – The reference voltage can be changed during operation.

6. Choosing a DAC Resolution
The resolution is the amount of voltage rise created by increasing the LSB of the input by 1. This voltage value is a function of the number of input bits and the reference voltage value.
- Increasing the number of bits results in a finer resolution
- Most DACs in the bit range

7. Choosing a DAC Linearity
The linearity is the relationship between the output voltage and the digital signal input.

8. Choosing a DAC
Speed
Usually specified as the conversion rate or sampling rate. It is the rate at which the input register is cycled through in the DAC.
High speed DACs are defined as operating at greater than 1 millisecond per sample (1MHz).
Some state of the art bit DAC can reach speeds of 1GHz
The conversion of the digital input signal is limited by the clock speed of the input signal and the settling time of the DAC.

9. Choosing a DAC Settling Time
Ideally a DAC would instantaneously change its output value when the digital input would change. However, in a real DAC it takes time for the DAC to reach the actual expected output value.

10. Choosing a DAC
Error
There are multiple sources of error in computing the analog output.

11. Example of a DAC - AD7224
An example of a DAC would be the Analog Devices AD 7224 D/A Converter. The AD7224 is a precision 8-bit, voltage-output, digital-to-analog converter with an output amplifier.
Specifications:
DAC Type – R-2R Voltage Out
Input – Dual 8 Bit
Reference voltage – Non-Multiplier
2v – 12.5v
Settling Time - 7μs
Cost - Under $4.00

12. Example of a DAC - AD7224

13. Types of DAC Circuits 1. Resistor String
2. N-Bit Binary Weighted Resistor
3. R-2R Ladder
4. PWM DAC

14. Resistor String DAC 3 Bit Resistor String DAC
Components of a String DAC
Resistor String
Selection Switches
Opamp

15. Resistor String DAC
How many internal components would be needed to create an 8 bit resistor string DAC?
Number of Resistors =
Number of Switches =
Impractical for a DAC with more than a couple bits input.

16. Weighted Resistor DAC Basic Idea: Use a summing op-amp circuit
Use transistors to switch between high and ground
Use resistors scaled by two to divide voltage on each branch by a power of two - + R 2R 4R
2nR
R/2
Vout

17. Weighted Resistor Example
Summing op-Amp:
Vref = -2V
Digital word = 1010
V1 = -2V
V2 = 0V
V3 = -2V
V4 = 0V
Rf = R/2 V1 R Rf 2R V2 4R V3 -
Vout + V4 8R

18. Weighted Resistor Summary
Advantages
Simple
Fast
Disadvantages
Need large range of resistor values (2000:1 for 12-bit) with high precision in low resistor values
Need very small switch resistances
Summary
Use in fast, low-precision converter

19. R-2R DAC Basic Idea: Use only 2 resistor values
Use equal resistances in parallel to halve the resistance
Creates a series of voltage dividers cutting voltages in half
Another summing op-amp

20. R-2R Example Digital word = 001
V0 has two 2R resistances in parallel connected to ground
Equivalent of R between V0 and ground
V1 now has a resistance R to V0 and R to ground
V0 = V1/2
V1 has two 2R resistances to ground
Equivalent of R between V1 and ground
V2 now has a resistance R to V1 and R to ground
V1 = V2/2
V2 = Vref
V0 = V2/4
V0 = Vref/4
Vout = -V0/2
Vout = -Vref/8

21. R-2R Summary Advantages Summary Only 2 resistor values
Better than weighted resistor DAC

22. Pulse Width Modulation
Approximate analog signal by switching on/off at high frequency
Integral of output voltage from PWM ideally is the same as integral of desired output voltage
N-bit digital words updated at rate f
DAC clock must run at rate 2n*f
Example:
Desired output = 7V, supply voltage = 10V
Operate 10V at 70% duty cycle to approximate 7V
In practice: use counter, comparator, clock, integrator

23. PWM Summary Advantages Disadvantages Summary All digital Cheap
High sampling rate required
Sensitive to clock variations
Summary
Best when load is a (relatively) slowly responding system

24. Errors

25. Errors Gain Error Offset Error Full Scale Error Linearity
Non-Monotonic Output Error
Settling Time and Overshoot
Resolution

26. Gain Error Slope deviation from ideal gain
Low Gain Error: Step Amplitude is less than ideal
High Gain Error: Step Amplitude is higher than ideal

27. Offset Error
The voltage is offset from zero when all input bits are low

28. Full Scale Error
Combination of gain error and offset error

29. Non-Linearity
The linearity error is due to the fact that the resolution of the converter is not constant.

30. Non-linearity
The largest difference between the actual and theoretical output as a percentage of full-scale output voltage

31. Non-linearity
It is the difference of tension obtained during the passage in the next digital code.
Should be 1 LSB in theory.

32. Non-monotonic Output Error
A form of non-linearity due to errors in individual bits of the input

33. Settling Time and Overshoot
Changes in input are not reflected immediately in the output
Lag times result

34. Resolution Errors Inherent errors associated with the resolution
More Bits = Less Error and Greater Resolution
Less Bits = More Error and Less Resolution

35. Applications

36. Programmable gain OpAmps
Voltage controlled Amplifier (digital input, Vref as control)
Digitally operated attenuators (Vref as input, digital control)

37. Programmable Filters Integrate DACs in filters
Variable cutoff frequency commanded by a digital signal

38. DAC Applications
Used at the end of a digital processing chain when analog signals are required
Digital Audio
CD Players, digital telephones, etc.
Industrial Control Systems
Motor speed, valves, etc.
Waveform Function Generators
Cruise Control

39. References
Alciatore, “Introduction to Mechatronics and Measurement Systems,” McGraw-Hill, 2003
Horowitz and Hill, “The Art of Electronics,” Cambridge University Press, 2nd Ed
Analog Devices AD 7224 DAC General Overview and Specifications
D/A Converter  Fundamentals and Definition Of Terms
Data Converter  Fundamentals