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Digital to AnalogConverters (DAC)

Adam Fleming

Mark Hunkele

3/11/2005

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Outline

Purpose

Types

Performance Characteristics

Applications

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Purpose

To convert digital values to analog voltages

Performs inverse operation of the Analog-to-

Digital Converter (ADC)

DACDigital Value Analog Voltage

Reference Voltage

ValueDigitalOUTV

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DACs

Types Binary Weighted Resistor R-2R LadderMultiplier DAC

The reference voltage is constant and is set by the manufacturer.

Non-Multiplier DAC The reference voltage can be changed during operation.

CharacteristicsComprised of switches, op-amps, and resistors Provides resistance inversely proportion to

significance of bit

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Binary Weighted ResistorRf= R

8R4R2RR Vo

-VREF

iI

LSB

MSB

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Binary RepresentationRf= R

8R4R2RR Vo

-VREF

iI

LeastSignificant Bit

MostSignificant Bit

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Binary Representation

-VREF

LeastSignificant Bit

MostSignificant Bit

CLEAREDSET

( 1 1 1 1 )2 = ( 15 )10

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Binary Weighted Resistor

Rf= R

8R4R2RR Vo

-VREF

iI

LSB

MSB

Weighted

Resistors

based on bit

Reducescurrent by afactor of 2 for

each bit

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Result:

Bi = Value of Bit i

RB

R

B

R

B

R

BVIREF 842

0123

842

0123

BBBBVRIV REFfOUT

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More Generally:

Bi = Value of Bit i n = Number of Bits

ResolutionValueDigital

2 1

REF

in

iREFOUT

V

B

VV

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R-2R LadderVREF

MSB

LSB

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R-2R Ladder

Same input switch setup as BinaryWeighted Resistor DAC

All bits pass through resistance of 2R

VREFMSB

LSB

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R-2R Ladder

The less significant the bit, the more resistors the signalmuss pass through before reaching the op-amp

The current is divided by a factor of 2 at each node

LSB MSB

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R-2R Ladder The current is divided by a factor of 2 at each node

Analysis for current from (001)2 shown below

0I

VREF

RR R R 2R

2R2R2R

Op-Amp inputGround

B0

2

0I

4

0I

8

0I

R

V

RRR

VI REFREF

32220

B1B2

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R-2R Ladder

Result:

Bi = Value of Bit i

842

012 BBBVR

RV

REF

f

OUT

Rf

8423

012 BBB

R

VI REF

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R-2R Ladder

If Rf = 6R, VOUT is same as Binary Weighted:

Bi = Value of Bit i

12 ini

REFOUT

BVV

in

iREF B

R

V

I 23

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0I

VREF

RR R R 2R

2R2R2R

Op-Amp inputGround

B0 B2

0I

VREF

R-2R Ladder

Example:

Input = (101)2

VREF = 10 V

R = 2 Rf = 2R

mA67.13222

0

R

V

RRR

VI REFREF

mA04.128

00

III

ampop

V17.4 fampopOUT RIV

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Pros & Cons

Binary Weighted R-2R

Pros Easily understood

Only 2 resistor values

Easier implementation

Easier to manufacture

Faster response time

Cons

Limited to ~ 8 bits

Large # of resistors

Susceptible to noise

Expensive

Greater Error

More confusing analysis

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Digital to Analog Converters

Performance Specifications

Common Applications

Presented by: Mark Hunkele

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-Performance Specifications

Resolution

Reference Voltages

Settling Time

Linearity

Speed Errors

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Resolution: is the amount of variance inoutput voltage for every change of the LSB

in the digital input. How closely can we approximate the

desired output signal(Higher Res. = finerdetail=smaller Voltage divisions)

A common DAC has a 8 - 12 bit Resolution



-Resolution

NLSB

VV

2

ResolutionRef N = Number of bits

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-Resolution

Better Resolution(3 bit)Poor Resolution(1 bit)

Vout

Desired Analog

signal

Approximateoutput

2Volt.Levels

Digital Input0 0

1

Digital Input

Vout

Desired Analog signal

Approximate

output

8Volt.Levels

000

001

010

011

100

101

110

111

110

101

100

011

010

001

000

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Reference Voltage: A specified voltageused to determine how each digital input

will be assigned to each voltage division. Types:

Non-multiplier: internal, fixed, and defined by

manufacturerMultiplier: external, variable, user specified



-Reference Voltage

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-Reference Voltage

Assume 2 bit DAC

Non-Multiplier: (Vref = C)

Digital Input

Multiplier: (Vref = Asin(wt))

0

Voltage

00

01 01

00

10 10

11

0

Voltage

Digital Input00 00

01 01

10 10

11

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Settling Time: The time required for theinput signal voltage to settle to the

expected output voltage(within +/- VLSB). Any change in the input state will not be

reflected in the output state immediately.

There is a time lag, between the twoevents.



-Settling Time

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-PerformanceSpecifications-Settling Time

Analog Output Voltage

Expected

Voltage

+VLSB

-VLSB

Settling timeTime

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Linearity: is the difference between the desired

analog output and the actual output over the

full range of expected values. Ideally, a DAC should produce a linear

relationship between a digital input and the

analog output, this is not always the case.



-Linearity

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-Linearity

Linearity(Ideal Case)

Digital Input

Perfect Agreement

Desired/Approximate Output

An

alogOutputVolta

ge

NON-Linearity(Real World)

AnalogOutputVolt

age

Digital Input

Desired Output

Miss-alignment

Approximateoutput

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Speed: Rate of conversion of a singledigital input to its analog equivalent

Conversion RateDepends on clock speed of input signal

Depends on settling time of converter



-Speed

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Non-linearity

Differential

Integral

Gain

Offset

Non-monotonicity



-Errors

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Differential Non-Linearity: Difference in voltage step sizefrom the previous DAC output (Ideally All DLNs = 1

VLSB)



-Errors: Differential Non-Linearity

Digital Input

Ideal Output

AnalogOu

tputVoltage

VLSB

2VLSB Diff. Non-Linearity = 2VLSB

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Integral Non-Linearity: Deviation of the actualDAC output from the ideal (Ideally all INLs = 0)



-Errors: Integral Non-Linearity

Digital Input

Ideal Output

1VLSB Int. Non-Linearity = 1VLSB

Analog

OutputVoltage

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Gain Error: Difference in slope of the idealcurve and the actual DAC output



-Errors: Gain

High Gain Error: Actualslope greater than ideal

Low Gain Error: Actualslope less than ideal

Digital Input

Desired/Ideal Output

AnalogOutputVoltage

Low Gain

High Gain

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Offset Error: A constant voltage differencebetween the ideal DAC output and the actual. The voltage axis intercept of the DAC output curve is

different than the ideal.



-Errors: Offset

Digital Input

Desired/Ideal OutputOutput Voltage

Positive Offset

NegativeOffset

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Non-Monotonic: A decrease in outputvoltage with an increase in the digital input



-Errors: Non-Monotonicity

Analog

OutputVoltage

Digital Input

Desired Output

Monotonic

Non-Monotonic

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Generic use

Circuit Components

Digital Audio

Function Generators/Oscilloscopes

Motor Controllers


-Common Applications

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Used when a continuous analog signal isrequired.

Signal from DAC can be smoothed by aLow pass filter



-Generic

0 bit

nth bit

n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111

Digital Input

Filter

Piece-wiseContinuous Output

AnalogContinuous Output

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Voltage controlled Amplifier

digital input, External Reference Voltage as control

Digitally operated attenuator

External Reference Voltage as input, digital control

Programmable Filters

Digitally controlled cutoff frequencies



-Circuit Components

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CD Players

MP3 Players

Digital Telephone/Answering Machines



-Digital Audio

1. http://electronics.howstuffworks.com/cd.htm2. http://accessories.us.dell.com/sna/sna.aspx?c=us&cs=19&l=en&s=dhs&~topic=odg_dj

1 23

3. http://www.toshiba.com/taistsd/pages/prd_dtc_digphones.html
http://configure.us.dell.com/dellstore/config.aspx?c=us&cs=19&l=en&oc=DDJ20M&s=dhshttp://configure.us.dell.com/dellstore/config.aspx?c=us&cs=19&l=en&oc=DDJ20M&s=dhs

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-Function Generators

Digital Oscilloscopes

Digital Input

Analog Ouput

Signal Generators Sine wave generation

Square wave generation

Triangle wave generation

Random noise generation

1

1. http://www.electrorent.com/products/search/General_Purpose_Oscilloscopes.html

2

2. http://www.bkprecision.com/power_supplies_supply_generators.htm
http://www.electrorent.com/products/search/detail.aspx?Mfr=Lecroy+Corporation&MfrMod=LEC-LC584AL&Desc=1GHz+4CH+Digital+Scope

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Cruise Control

Valve Control

Motor Control



-Motor Controllers

1

1. http://auto.howstuffworks.com/cruise-control.htm

2

2. http://www.emersonprocess.com/fisher/products/fieldvue/dvc/

3

3. http://www.thermionics.com/smc.htm

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References

Cogdell, J.R. Foundations of Electrical Engineering. 2nd ed. Upper Saddle River,NJ: Prentice Hall, 1996.

Simplified DAC/ADC Lecture Notes, http://www-personal.engin.umd.umich.edu/~fmeral/ELECTRONICS II/ElectronicII.html

Digital-Analog Conversion, http://www.allaboutcircuits.com. Barton, Kim, and Neel. Digital to Analog Converters. Lecture, March 21, 2001.

http://www.me.gatech.edu/charles.ume/me4447Spring01/ClassNotes/dac.ppt.

Chacko, Deliou, Holst, ME6465 DAC Lecture Lecture, 10/ 23/2003,

http://www.me.gatech.edu/mechatronics_course/

Lee, Jeelani, Beckwith, Digital to Analog Converter Lecture, Spring 2004,http://www.me.gatech.edu/mechatronics_course/

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