Alexander Gurney Alexander Pitt Gautam Puri 1 Digital to Analog Converters Alexander Gurney What is a DAC Applications of DACs Alexander Pitt Types of DACs Binary Weighted Resistor ID: 356738
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Slide1
Digital to Analog Converters
Alexander Gurney
Alexander PittGautam Puri
1Slide2
Digital to Analog ConvertersAlexander Gurney What is a DAC? Applications of DACsAlexander Pitt Types of DACs Binary Weighted Resistor
R-2R LadderGautam
Puri Specifications Resolution Speed Linearity Settling Time
Reference Voltages
Errors
2Slide3
What is a DAC?A DAC converts a binary digital signal into an analog representation of the same signalTypically the analog signal is a voltage output, though current output can also be used
0101
0011
0111
1001
1001
1010
1011
DAC
What is a DAC? – Alexander Gurney
3Slide4
Reference Voltage
DACs rely on an input Reference Voltage to calculate the Output Signal
What is a DAC? – Alexander Gurney
4Slide5
Binary to Analog Conversion
1011
1001
1010
0111
1000
0110
0101
0100
0011
0010
0001
0000
Digital Input Signal
Analog Output Signal
Each sample is converted from binary to analog, between 0 and
Vref
for
Unipolar
, or
Vref
and –
Vref
for Bipolar
What is a DAC? – Alexander Gurney
5Slide6
Sampling FrequencySampling frequency is the number of data points sampled per unit timeSampling frequency must be twice the frequency of the sampled signal to avoid aliasing, per Nyquist criteriaA higher sampling frequency decreases the sampling period, allowing more data to be transmitted in the same amount of time
What is a DAC? – Alexander Gurney
6Slide7
Output is a Piecewise FunctionThis is due to finite sampling frequencyThe analog value is calculated and “held” over the sampling periodThis results in an imperfect reconstruction of the original signal
Ideally Sampled Signal
Output typical of a real, practical DAC due to sample & hold
DAC
What is a DAC? – Alexander Gurney
7Slide8
An Example4 Bit signalUnipolarVref = 7V8 Sample PointsSample Frequency = 1 hertzDuration 8 seconds
0001 0011 0110 1100 1011 0101 0010 0111
What is a DAC? – Alexander Gurney
8Slide9
FilteringThe analog signal generated by the DAC can be smoothed using a low pass filter
This removes the high frequencies required to sustain the sharp inclines making up the edges
0 bit
n
th
bit
n bit DAC
011010010101010100101
101010101011111100101
000010101010111110011
010101010101010101010
111010101011110011000
100101010101010001111
Digital Input
Filter
Piece-wise Continuous Output
Analog Continuous Output
What is a DAC? – Alexander Gurney
9Slide10
DACs in Audio Digital Analog MP3s ->3.5mm Audio Out HD Radio ->Signal received by speaker CDs ->RCA Audio Out
What is a DAC? – Alexander Gurney
10Slide11
DACs in Video Digital Analog DVDs ->Composite Output OTA Broadcast ->Converter Box Output Youtube
->Analog Monitor Input
What is a DAC? – Alexander Gurney
11Slide12
Types of Digital to Analog ConvertersBinary Weighted
Explanation
Advantages and disadvantages R-2R Ladder
Explanation
Example
Advantages and disadvantages
DAC Types – Alex Pitt
12Slide13
Binary Weighted DAC
Use transistors to switch between open and close
Use a summing op-amp circuit with gain
Adds resistors in parallel scaled by two to divide voltage on each branch by a power of two
DAC Types – Alex Pitt
13
V
out
= Analog OutSlide14
Binary Weighted DAC
Circuit can be simplified by adding resistors in parallel to substitute for
Rin. *Values for A, B, C and D are either 1 or 0.
DAC Types – Alex Pitt
14Slide15
Binary Weighted DAC
MSB
LSB
General equation
B
0
B
1
B
2
B
3
DAC Types – Alex Pitt
15Slide16
Binary Weighted DACAdvantagesWorks well up to ~ 8-bit conversions DisadvantagesNeeds large range of resistor values (2048:1 for a 12-bit DAC) with high precision resistor values
Too much or too little current flowing through resistorsMinimum/maximum
opamp current Noise overwhelms current through larger resistance values
DAC Types – Alex Pitt
16Slide17
R-2R Ladder DACRequires only two resistance values (R and 2R)
V
ref
4 bit converter
Each bit controls a switch between ground and the inverting input of the op amp.
The switch is connected to ground if the corresponding bit is zero.
DAC Types – Alex Pitt
17
R
FSlide18
R-2R Ladder Example
Convert 0001 to analog
V
0
V
1
V
2
V
3
V
1
V
ref
V
0
DAC Types – Alex Pitt
18
R
FSlide19
R-2R Ladder Example19Convert 0001 to analog
2R
R
V
0
V
ref
DAC Types – Alex Pitt
R
F
R
FSlide20
R-2R Ladder By adding resistance in series and in parallel we can derive an equation for the R-2R ladder.
DAC Types – Alex Pitt
20Slide21
R-2R LadderBy knowing how current flows through the ladder we can come up with a general equation for R-2R DACs.
MSB
LSB
DAC Types – Alex Pitt
21Slide22
R-2R Ladder
R
f
4-Bit Equation
Substituting
General Equation
DAC Types – Alex Pitt
22Slide23
R-2R Ladder DACAdvantagesOnly two resistor valuesCan use lower precision resistors
DAC Types – Alex Pitt
23Slide24
Specifications of DAC Lets discuss some terms you’ll hear when dealing with DACsReference VoltageResolutionSpeed LinearitySettling TimeSome types of Errors
Specifications -
Gautam
Puri
24Slide25
Reference Voltage VrefThe reference voltage determines the range of output voltages from the DACFor a ‘Non-Multiplying DAC’, V
ref is a constant value set internally by the manufacturerFor a ‘Multiplying DAC’,
Vref is set externally and can be varied during operationVref also affects DAC resolution (which will be discussed later).
Specifications -
Gautam
Puri
25Slide26
Full scale voltageFull scale voltage is the output voltage when all the bits of the digital input signal are 1s.It is slightly less than reference voltage Vref
Vfs =
Vref - VLSB
Specifications -
Gautam
Puri
26Slide27
Resolution of a DAC is the change in output voltage for a change in the least significant bit (LSB) of the digital inputResolution is specified in “bits”.
Most DACs have a resolution of 8 to 16 bits
Example: A DAC with 10 bits has a resolution of
Higher resolution (more bits) = smoother output
A DAC with 8 bits has 256 steps whereas one with 16 bits has 65536 steps for the given voltage range and can thus offer smoother output
Resolution
Specifications -
Gautam
Puri
27Slide28
Speed (Sampling frequency)Sampling frequency is the rate at which the DAC accepts digital input and produces voltage outputIn order to avoid aliasing, the Nyquist criterion requires thatSampling frequency is limited by the input clock speed (depends on microcontroller) and the settling time of the DAC
Specifications -
Gautam
Puri
28Slide29
Settling TimeIt takes the DAC a finite amount of time to produce the exact analog voltage corresponding to the digital inputThe settling time is the time interval from when the DAC commands the update of its output to when the voltage actually reaches ± ½ VLSB.A faster DAC will have a smaller settling time
t
settle
Specifications -
Gautam
Puri
29Slide30
LinearityIf the change in analog output voltage per unit change in digital input remains constant over the entire range of operation, the DAC is said to be linearIdeally the DAC should have a proportionality constant which results in a linear slopeNon-linearity is considered an error, and will be further discussed in the errors section
Linear
Non-linear
Specifications -
Gautam
Puri
30Slide31
Types of DAC ErrorsNon-monotonic output errorNon-linear output errorDifferentialIntegralGain errorOffset errorFull scale error
Resolution errorSettling time and overshoot error
Specifications -
Gautam
Puri
31Slide32
Non-monotonic Output ErrorA monotonic function has a slope whose sign does not changeNon-monotonic error results when the analog output changes direction for a step or a few steps of digital inputIn a closed loop control system this may cause the DAC to toggle continuously between 2 input codes and the system will be unstable.
Specifications -
Gautam
Puri
32Slide33
Differential non-linear output errorFor a change in the LSB of input, the output of an ideal DAC is VLSBHowever in a non-linear DAC the output may not be exactly the LSB but rather a fraction (higher or lower) of it
Specifications -
Gautam
Puri
33Slide34
Differential non-linear output errorBasically “differential” non-linearity expresses the error in step size as a fraction of LSB
The DNL is the maximum of these deviations over the entire transfer function
One must choose a DAC with DNL less than 1 LSB. A DNL > 1 LSB will lead to non-monotonic behavior. This means that for certain steps in digital input, the output voltage will change in the opposite direction. This may cause a closed loop control system to become unstable as the system may end up oscillating back and forth between two points.
Specifications -
Gautam
Puri
34Slide35
Integral non-linear output errorThe integral non-linearity error is the difference between the ideal and actual output. It can also be defined as the difference between ideal and a best fit lineINL occurs when the output is non-linear and thus unable to adhere to a straight line.The maximum deviation from this line is called INL.
Specifications -
Gautam
Puri
35Slide36
Integral non-linear output errorINL is expressed as fraction of LSB.INL cannot be calibrated out as the non-linearity is unpredictable and one does not know where the maximum deviation from the ideal line will occur. One must choose an ADC with an INL (maximum deviation) within the accuracy required.
Specifications -
Gautam
Puri
36Slide37
More important - DNL or INL ?The DNL and INL are both important non-linear errors to be aware of.
In the case of an application such as an imaging one, where slight differences in color densities are important, the “differential” non-linearity error is more important.
In an application where the parameters vary more widely, such as speed of a vehicle, the “integral” non-linearity error may be of greater importance
Specifications -
Gautam
Puri
37Slide38
Gain ErrorThe difference between the output voltage (or current) with full scale input code and theideal voltage (or current) that should exist with a full scale input code
2 Types of Gain Error
Low Gain: Step Amplitude Less than IdealHigh Gain: Step Amplitude Greater than Ideal
Gain Error can be adjusted to zero by using an external potentiometer
Specifications -
Gautam
Puri
38Slide39
Offset ErrorIt is the difference in ideal and actual output voltage at a digital input of zeroAll output values will differ from the ideal values by that same amount, hence the output is “offset” from the inputOffset can be ‘positive’ or ‘negative’It can be fixed by adding/subtracting the difference to the digital input before passing through the DAC
Specifications -
Gautam
Puri
39Slide40
Full Scale ErrorIt is a combination of gain and offset errorIt is measured at the full scale input
Specifications -
Gautam
Puri
40Slide41
Resolution ErrorIf the resolution is not high enough, the DAC cannot accurately output the required waveformLower resolution results in higher resolution error
Low resolution (1 bit)
Higher resolution (3 bits)
Specifications -
Gautam
Puri
41Slide42
Settling Time and Overshoot ErrorIf settling time is too high, the DAC will not produce the ideal output waveform fast enough and there will be a delay or lag. This will also lower the maximum operating frequency of the DAC.
Specifications -
Gautam
Puri
42Slide43
ReferencesPrevious semester lecture slideshttp://www.hitequest.com/Hardware/a_dac.htm http://www.national.com/appinfo/adc/files/ms101157.pdf
http://www.noise.physx.u-szeged.hu/DigitalMeasurements/ADConversion/ADSpecs.pdf
Scherz, Paul. Practical Electronics for Inventors. 2nd Edition,
McGraw
Hill. 2007.
http://masteringelectronicsdesign.com/an-adc-and-dac-differential-non-linearity-dnl/
http://masteringelectronicsdesign.com/an-adc-and-dac-integral-non-linearity-inl/
43Slide44
Questions ? Alexander Gurney What is a DAC? Alexander Pitt Types of DACs
Guatam Puri
Specifications 44