1. Digital to Analog Conversion
Heather Humphreys
Cheng Shu Ngoo
Woongsik Ham
Ken Marek

2. Topics Discussed Woongsik Ham What is a DAC? Applications
Types of DAC circuit
Binary weighted DAC
R-2R Ladder DAC
Specifications of DAC
Resolution
Reference Voltage
Speed
Settling Time
Linearity
DAC associated errors

3. Woongsik Ham
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.
Explain picture in detail. 1 min

4. Principal components of DAC
Woongsik Ham
Principal components of DAC
Explain picture in detail. 1 min

5. What is a DAC? Digital  Analog
Woongsik Ham
What is a DAC?
Digital  Analog
Each binary number sampled by the DAC corresponds to a different output level.
Digital Input Signal
Analog Output Signal
Explain picture in detail. 1 min

6. Ideally Sampled Signal
Woongsik Ham
Typical Output
DACs capture and hold a number, convert it to a physical signal, and hold that value for a given sample interval. This is known as a zero-order hold and results in a piecewise constant output.
Output typical of a real, practical DAC due to sample & hold
Ideally Sampled Signal
DAC
Explain graphs in detail min

7. Types of DAC Multiplying DAC* Nonmultiplying DAC
Woongsik Ham
Types of DAC
Multiplying DAC*
Reference source external to DAC package
Nonmultiplying DAC
Reference source inside DAC package
*Multiplying DAC is advantageous considering the external reference.

8. Common Applications Used when a continuous analog signal is required.
Woongsik Ham
Common Applications
Used when a continuous analog signal is required.
Signal from DAC can be smoothed by a Low pass filter
Piece-wise Continuous Output
Analog Continuous Output
Digital Input
n bit DAC
0 bit
Filter
nth bit

9. Common Applications: Function Generators
Woongsik Ham
Common Applications: Function Generators
Digital Oscilloscopes
Digital Input
Analog Ouput
Signal Generators
Sine wave generation
Square wave generation
Triangle wave generation
Random noise generation 1 2

10. Woongsik Ham
Applications – Video
Video signals from digital sources, such as a computer or DVD must be converted to analog signals before being displayed on an analog monitor. Beginning on February 18th, 2009 all television broadcasts in the United States will be in a digital format, requiring ATSC tuners (either internal or set-top box) to convert the signal to analog.

11. Common Applications Motor Controllers
Woongsik Ham
Common Applications Motor Controllers
Cruise Control
Valve Control
Motor Control 1 2 3

12. Types of DAC Multiplying DAC* Nonmultiplying DAC
Woongsik Ham
Types of DAC
Multiplying DAC*
Reference source external to DAC package
Nonmultiplying DAC
Reference source inside DAC package
*Multiplying DAC is advantageous considering the external reference.

13. Types of DAC implementations
Ken Marek
Types of DAC implementations
Binary Weighted Resistor
R-2R Ladder
Pulse Width Modulator (not covered)
Oversampling DAC (used internally in HCS12)

14. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Start with summing op-amp circuit
Input voltage either high or ground
Adjust resistor weighting to achieve desired Vout

15. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Details
Use transistors to switch between high and ground
Use resistors scaled by two to divide voltage on each branch by a power of two
V1 is MSB, V4 LSB in this circuit
Assumptions:
Ideal Op-Amp
No Current into Op-Amp
Virtual Ground at Inverting Input
Vout = -IRf

16. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Assume binary inputs B0 (LSB) to Bn-1 (MSB)
Each Bi = 1 or 0 and is multiplied by Vref to get input voltage B5 B4 B3 B2 B1 B0

17. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Example: take a 4-bit converter, Rf = aR
Input parameters:
Input voltage Vref = -2V
Binary input = 1011
Coefficient a = ½

18. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Resolution: find minimum nonzero output
If Rf = R/2 then resolution is and max Vout is

19. Binary Weighted Resistor
Ken Marek
Binary Weighted Resistor
Advantages
Simple
Fast
Disadvantages
Need large range of resistor values (2048:1 for 12-bit) with high precision in low resistor values
Need very small switch resistances
Op-amp may have trouble producing low currents at the low range of a high precision DAC

20. R-2R Ladder Each bit corresponds to a switch:
Ken Marek
R-2R Ladder
Each bit corresponds to a switch:
If the bit is high, the corresponding switch is connected to the inverting input of the op-amp.
If the bit is low, the corresponding switch is connected to ground.

21. Ken Marek
R-2R Ladder B2 B1 B0

22. Ken Marek
R-2R Ladder
Circuit may be analyzed using Thevenin’s theorem (replace network with equivalent voltage source and resistance)
Final result is: B2 B1 B0 Rf
Compare to binary weighted circuit:

23. R-2R Ladder Resolution If Rf = R then resolution is and max Vout is
Ken Marek
R-2R Ladder
Resolution
If Rf = R then resolution is and max Vout is

24. R-2R Ladder Advantages: Disadvantages Only 2 resistor values
Ken Marek
R-2R Ladder
Advantages:
Only 2 resistor values
Lower precision resistors acceptable
Disadvantages
Slower conversion rate

25. General comments Circuits as shown produce only unipolar output
Ken Marek
General comments
Circuits as shown produce only unipolar output
Replacing ground with –Vref will allow Vout to be positive or negative

26. DAC Specifications: Reference Voltages Resolution Speed Settling Time
Cheng Shu Ngoo
DAC Specifications:
Reference Voltages
Resolution
Speed
Settling Time
Linearity

27. Reference Voltage Determines Characteristic of DACs
Cheng Shu Ngoo
Determines Characteristic of DACs
Set externally or Generated inside DAC
Vref sets maximum DAC output voltage (if not amplified)
Full scale output voltage:
Vref determines analog output voltage changes to steps taken by 1 LSB of digital input signal (resolution)
To a large extent, the characteristics of a DAC are defined by its reference voltage, whether generated within the DAC or applied externally. First, the reference voltage (VREF) sets the DAC's maximum output voltage if the output signal is not amplified by an additional output stage. VREF also defines the voltage step by which the output changes in response to a 1-LSB transition at the input. One step equals VREF/2N, where N is the DAC resolution.
When connecting an external reference, you should consider not only the current required and the voltage range of the DAC's reference input, but also any dynamic effects produced by the DAC's inner structure. With variation of the applied digital value, the reference input resistance can also change. Thus, the reference selected must be capable of following each load step within the required time, or you must add a capacitor or an op-amp buffer.
X = analog output
k = Constant
A = Vref analog
B = Binary (digital) input 27

28. Reference Voltage Internal vs. External Vref? Internal External
Cheng Shu Ngoo
Internal vs. External Vref?
Internal
External
Non-Multiplier DAC
Vref fixed by manufacturer
Qualified for specified temperature range
Multiplying DAC
Vary Vref
Consider current required
Consider Voltage range
Consider dynamic effects of inner structure
Multiplying mode - The variable voltage is multiplied with the adjusted digital input value and transferred to the output, producing the effect of an accurate digital potentiometer.
For this operating mode you should consider the DAC's bandwidth and voltage range, as well as dynamic characteristics of the reference input; such as voltage feedthrough from the reference input to the output at a digital value of zero.
*Multiplying DAC is advantageous considering the external reference. 28

29. Resolution 1 LSB (digital)=1 step size for DAC output (analog)
Cheng Shu Ngoo
1 LSB (digital)=1 step size for DAC output (analog)
Increasing the number of bits results in a finer resolution
Most DAC - 8 to 16-bits (256 to 65,536 steps)
e.g. 5Vref DAC
1LSB=5/28 =0.0195V resolution (8-bit)
1LSB=5/23 =0.625V resolution (3-bit)
1 LSB
Smallest output voltage change for change in 1 LSB digital input
Diff between successive values

30. Speed (Max. Sampling Frequency)
Cheng Shu Ngoo
Speed (Max. Sampling Frequency)
The maximum rate at which DAC is reproducing usable analog output from digital input register
Digital input signal that fluctuates at/ has high frequency require high conversion speed
Speed is limited by the clock speed of the microcontroller (input clock speed) and the settling time of the DAC
Shannon-Nyquist sampling theorem  fsampling ≥ 2fmax
Eg. To reproduce audio signal up to 20kHz, standard CD samples audio at 44.1kHz with DAC ≥40kHz
Typical computer sound cards 48kHz sampling freq
>1MHz for High Speed DACs
Human hearing range - ~20Hz – ~20kHz

31. Settling Time
Cheng Shu Ngoo
The interval between a command to update (change) its output value and the instant it reaches its final value, within a specified percentage (± ½ LSB)
Ideal DAC output would be sequence of impulses  Instantaneous update
Causes:
Slew rate of output amplifier
Amount of amplifier ringing and signal overshoot
Faster DACs have shorter settling time
Electronic switching  fast
Amplifier settling time  dominant effect

32. Settling Time
Cheng Shu Ngoo
tsettle

33. DAC Linearity Cheng Shu Ngoo
The difference between the desired analog output and the actual output over the full range of expected values
Does the DAC analog output vary linearly with digital input signal?
Can the DAC behavior follow a constant Transfer Function relationship?
Ideally, proportionality constant – linear slope
Increase in input  increase in output  monotonic
Integral non-linearity (INL) & Differential non-linearity (DNL)
Linear
Non-Linear

34. Types of DAC Errors Gain Error Offset Error Full Scale Error
Heather Humphreys
Types of DAC Errors
Gain Error
Offset Error
Full Scale Error
Non-Monotonic Output Error
Differential Nonlinearity Error
Integral Nonlinearity Error
Settling Time and Overshoot Error
Resolution Error
Sources of Errors

35. Gain Error Slope deviation from ideal gain
Heather Humphreys
Gain Error
Slope deviation from ideal gain
Low Gain: Step Amplitude Less than Ideal
High Gain: Step Amplitude Higher than Ideal

36. Offset Error The voltage offset from zero when all input bits are low
Heather Humphreys
Offset Error
The voltage offset from zero when all input bits are low
*This error may be detected when all input bits are low (i.e. 0).

37. Full-Scale Error Includes gain error and offset error
Heather Humphreys
Full-Scale Error
Includes gain error and offset error
Occurs when there is an offset in voltage form the ideal output and a deviation in slope from the ideal gain.
Error at full scale – contrast with offset error at zero

38. Non-Monotonic Output Error
Heather Humphreys
Non-Monotonic Output Error
A form of non-linearity, due to errors in individual bits of the input
Refers to output that is not monotonic

39. Differential Nonlinearity Error
Heather Humphreys
Differential Nonlinearity Error
The largest difference between the actual and theoretical output as a percentage of full-scale output voltage.
Voltage step size differences vary as digital input increases. Ideally each step should be equivalent.
In other words, DNL error is the difference between the ideal and the measured output responses for successive steps.
An ideal DAC response would have analog output values exactly one code (LSB) apart (DNL = 0).

40. Integral Nonlinearity Error
Heather Humphreys
Occurs when the output voltage is non linear; an inability to adhere to the ideal slope.
INL is the deviation of an actual transfer function from a straight line. After nullifying offset and gain errors, the straight line is either a best-fit straight line or a line drawn between the end points of the transfer function.
INL is often called 'relative accuracy.'

41. Settling Time and Overshoot Error
Heather Humphreys
Settling Time and Overshoot Error
Settling Time: The time required for the voltage to settle within +/- the voltage associated with the VLSB. Any change in the input time will not be reflected immediately due to the lag time.
Settling time generally determines maximum operating frequency of the DAC
One of the principal limiting factors of any commercial DAC is the settling time of the op-amp
Overshoot: occurs when the output voltage overshoots the desired analog output voltage.

42. Resolution Errors Inherent errors associated with resolution
Heather Humphreys
Inherent errors associated with resolution
More Bits => Less Error & Greater Resolution
Less Bits => More Error & Less Resolution
Q: How does very high resolution affect measurements?
A: LSB may be in noise range and not produce an output; it may be difficult to find an op-amp to amplify such small current
Better Resolution (3 Bit)
Poor Resolution (1 Bit)

43. Sources of Errors Deviation of voltage sources from nominal values
Heather Humphreys
Sources of Errors
Deviation of voltage sources from nominal values
Variations and tolerances on resistance values
Non-ideal operational amplifiers
Other non-ideal circuit components, temperature dependence, etc.

44. Project Applications Motor speed controller
Woongsik Ham
Project Applications
Motor speed controller
Solenoid valves (pneumatics)
Digital Motor Control
Computer Printers
Sound Equipment (e.g. CD/MP3 Players, etc.)
Electronic Cruise Control
Digital Thermostat

45. References
Previous student presentations and…
Alicatore, David G. and Michael B Histand. Introduction to Mechatronics and Measurement Systems, 2nd ed. McGraw-Hill, 2003.
Maxim AN641 Glossary
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