digital to analog conversion
DESCRIPTION
Digital to Analog Conversion. Heather Humphreys Cheng Shu Ngoo Woongsik Ham Ken Marek. Woongsik Ham. Topics Discussed. 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 - PowerPoint PPT PresentationTRANSCRIPT
Heather HumphreysCheng Shu NgooWoongsik Ham
Ken Marek
Digital to Analog Conversion
Topics Discussed What is a DAC?
Applications
Types of DAC circuitBinary weighted DACR-2R Ladder DAC
Specifications of DACResolutionReference VoltageSpeedSettling TimeLinearity
DAC associated errors
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.
Woongsik Ham
Principal components of DAC
Woongsik Ham
What is a DAC?Digital AnalogEach binary number sampled by the DAC
corresponds to a different output level.
10111001 10100111 10000110010101000011001000010000Digital Input Signal
Ana
log
Out
put
Sig
nal
Woongsik Ham
Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold
Typical OutputDACs 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.
DAC
Woongsik Ham
Types of DACMultiplying DAC*
Reference source external to DAC package
Nonmultiplying DACReference source inside DAC package
*Multiplying DAC is advantageous considering the external reference.
Woongsik Ham
Common Applications
Used when a continuous analog signal is required.
Signal from DAC can be smoothed by a Low pass filter
0 bit
nth bit
n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111
Digital Input
Filter
Piece-wise Continuous Output
Analog Continuous Output
Woongsik Ham
Common Applications:Function GeneratorsFunction Generators
Digital OscilloscopesDigital InputAnalog Ouput
Signal GeneratorsSine wave generationSquare wave generationTriangle wave generationRandom noise generation
1 2
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.
Woongsik Ham
Common ApplicationsMotor ControllersMotor Controllers
Cruise ControlValve Control Motor Control
1 2 3
Woongsik Ham
Types of DACMultiplying DAC*
Reference source external to DAC package
Nonmultiplying DACReference source inside DAC package
*Multiplying DAC is advantageous considering the external reference.
Woongsik Ham
Types of DAC implementationsBinary Weighted ResistorR-2R LadderPulse Width Modulator (not covered)Oversampling DAC (used internally in
HCS12)
Ken Marek
Binary Weighted Resistor
•Start with summing op-amp circuit
•Input voltage either high or ground
•Adjust resistor weighting to achieve desired Vout
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
Ken Marek
Binary Weighted ResistorAssume
binary inputs B0 (LSB) to Bn-1 (MSB)
Each Bi = 1 or 0 and is multiplied by Vref to get input voltage1 2 01
out f f 2 n-1...
2 2 2n n
ref n
B B BBV IR R V
R R R R
B0
B5
B4
B3
B2
B1
Ken Marek
Example: take a 4-bit converter, Rf = aR
Input parameters:Input voltage Vref = -2VBinary input = 1011Coefficient a = ½
Binary Weighted Resistor
3 02 1out 1 2 4 8ref
B BB BV aV
out
1 1 0 1 1 112 1.375
2 1 2 4 8 8V V
Ken Marek
Binary Weighted ResistorResolution: find minimum nonzero output
If Rf = R/2 then resolution is
and max Vout is
f
min n-12refR V
VR
n2refV
max
11
2ref nV V
Ken Marek
Binary Weighted ResistorAdvantages
SimpleFast
DisadvantagesNeed large range of resistor values (2048:1
for 12-bit) with high precision in low resistor values
Need very small switch resistancesOp-amp may have trouble producing low
currents at the low range of a high precision DAC
Ken Marek
R-2R LadderEach 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.
Ken Marek
R-2R Ladder
B2
B1
B0
Ken Marek
R-2R LadderCircuit may be
analyzed using Thevenin’s theorem (replace network with equivalent voltage source and resistance)
Final result is:
1
out ref0 2
nf i
n ii
R BV V
R
Ken Marek
B2
B1
B0
Rf
Compare to binary weighted circuit:1
out ref ( 1)0 2
nf i
n ii
R BV V
R
R-2R LadderResolution
If Rf = R then resolution is
and max Vout is
Ken Marek
f
min n2refR V
VR
n2refV
max
11
2ref nV V
R-2R LadderAdvantages:
Only 2 resistor valuesLower precision resistors acceptable
DisadvantagesSlower conversion rate
Ken Marek
General commentsCircuits as shown produce only unipolar
outputReplacing ground with –Vref will allow Vout to
be positive or negative
Ken Marek
DAC Specifications: Reference Voltages Resolution Speed Settling Time Linearity
Cheng Shu Ngoo
Reference VoltageDetermines Characteristic of DACs
Set externally or Generated inside DACVref 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)
Cheng Shu Ngoo
BAkX X = analog outputk = ConstantA = Vref analogB = Binary (digital) input
n
nref
fso
VE
2
)12()(
Reference Voltage
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
Cheng Shu Ngoo
*Multiplying DAC is advantageous considering the external reference.
Resolution
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)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
58-bit Resolution
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
53-bit Resolution
1 LSB
nrefV
2Resolution
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
Cheng Shu Ngoo
Settling Time
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 amplifierAmount of amplifier ringing and signal overshoot
Faster DACs have shorter settling timeElectronic switching fastAmplifier settling time dominant effect
Cheng Shu Ngoo
Settling TimeCheng Shu Ngoo
tsettle
DAC Linearity
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)
010101000011001000010000Digital Input Signal
Ana
log
Out
put
Sig
nal
010101000011001000010000 010101000011001000010000Digital Input Signal
Ana
log
Out
put
Sig
nal
010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
010101000011001000010000 010101000011001000010000Digital Input Signal
Ana
log
Out
put S
igna
l
Cheng Shu Ngoo
Linear Non-Linear
Types of DAC ErrorsGain ErrorOffset ErrorFull Scale ErrorNon-Monotonic Output ErrorDifferential Nonlinearity ErrorIntegral Nonlinearity ErrorSettling Time and Overshoot ErrorResolution ErrorSources of Errors
Heather Humphreys
Gain ErrorSlope deviation
from ideal gainLow Gain: Step
Amplitude Less than Ideal
High Gain: Step Amplitude Higher than Ideal
Heather Humphreys
Offset ErrorThe voltage offset
from zero when all input bits are low
*This error may be detected when all input bits are low (i.e. 0).
Heather Humphreys
Full-Scale ErrorIncludes gain error
and offset errorOccurs 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
Heather Humphreys
Non-Monotonic Output ErrorA form of non-linearity, due to errors in
individual bits of the inputRefers to output that is not monotonic
Heather Humphreys
Differential Nonlinearity ErrorThe 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).
Heather Humphreys
Integral Nonlinearity ErrorOccurs 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.'
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.
Heather Humphreys
Resolution Errors• 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
bitsof#2
Voltage RefResolution
Poor Resolution (1 Bit)
Better Resolution (3 Bit)
Heather Humphreys
Sources of ErrorsDeviation of voltage sources from nominal
values
Variations and tolerances on resistance values
Non-ideal operational amplifiers
Other non-ideal circuit components, temperature dependence, etc.
Heather Humphreys
Project ApplicationsMotor speed controllerSolenoid valves (pneumatics) Digital Motor ControlComputer PrintersSound Equipment (e.g. CD/MP3 Players,
etc.)Electronic Cruise ControlDigital Thermostat
Woongsik Ham
References Previous student presentations and… http://en.wikipedia.org/wiki/Digital_to_analog http://www.allaboutcircuits.com/vol_4/chpt_13/index.html Alicatore, David G. and Michael B Histand. Introduction to
Mechatronics and Measurement Systems, 2nd ed. McGraw-Hill, 2003.
http://www.emersonprocess.com/fisher/products/fieldvue/dvc/ http://auto.howstuffworks.com/cruise-control.htm http://www.thermionics.com/smc.htm Maxim AN641 Glossary http://www.electrorent.com/products/search/
General_Purpose_Oscilloscopes.html http://www.bkprecision.com/
power_supplies_supply_generators.htmhttp://hyperphysics.phy-astr.gsu.edu/hbase/electronic/
dac.html#c4