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Introduction to Mechatronics Student Lecture – Digital to Analog Converters Andrew Gardner Muhammad Salman David Fernandes Jevawn Roberts

Digital to Analog Converters

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Digital to Analog Converters. Andrew Gardner Muhammad Salman David Fernandes Jevawn Roberts. Outline. What is a DAC? Different Types of DACs Binary Weighted Resistor R-2R Ladder Specifications Commonly used DACs Application. Introduction - PowerPoint PPT Presentation

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Page 1: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Digital to Analog Converters

Andrew Gardner

Muhammad Salman

David Fernandes

Jevawn Roberts

Page 2: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Outline

What is a DAC?Different Types of DACs

Binary Weighted ResistorR-2R Ladder

SpecificationsCommonly used DACsApplication

Page 3: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Introduction

A DAC is a Digital to Analog converter. It converts a binary digital number into an analog representation, most commonly voltage though current is also used sometimes.

0101

0011

0111

1001

1001

1010

1011 DAC

Page 4: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

IntroductionEach binary number sampled by the DAC

corresponds to a different output level.

10111001 10100111 10000110010101000011001000010000Digital Input Signal

Ana

log

Out

put

Sig

nal

Page 5: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

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

Page 6: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Binary Weighted Resistor DAC

• Utilizes a summing op-amp circuit

• Weighted resistors are used to distinguish each bit from the most significant to the least significant

• Transistors are used to switch between Vref

and ground (bit high or low)

Page 7: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Summing OP-Amps

• Inverting summer circuit used in Binary Weighted Resistor DAC.

• V(out) is 180° out of phase from V(in)

Page 8: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Binary Weighted Input DAC

• Ideal Op-amp

• No current into

op-amp

• Virtual ground at

inverting input

• Vout= -IRf

R

V

R

V

R

V

R

VRIRV

1-nn321

ffout 242

MSB

LSB

I

-+

R

2R

4R

2n-1R

Rf

Vout

Vref

V1

V2

V3

Vn

Page 9: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Calculation

R

b

R

b

R

bRVV

nnn

refOUT 2...

42( 021

0122

11 2...22(

2bbbb

VV n

nn

nn

refOUT

Page 10: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Cont’d

)2...22(2 012

21

1 bbbbV

V nn

nn

n

refout

refref

out VV

V16

3))1(1)1(2)0(4)0(8(

16

)248(16 0123 bbbbV

V refout

refreffs

nES

ESreffs

VVV

R

RVV

9375.02

12

2/1

4

4

4n

Example:Example:

n = totalbits

Page 11: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Advantages and Disadvantages

Advantage– Easy principle/construction – Fast conversion

Disadvantages– Requirement of several different precise input

resistor values: Requires large range of resistors (2048:1 for 12-bit DAC) with necessary high precision for low resistors one unique value per binary input bit. (High bit DACs)

– Larger resistors ~ more error.– Precise large resistors – expensive.

Page 12: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

R-2R Resistor Ladder DAC

Bit: 0 0 0 0

4-Bit Converter Vout

Vref

MSB LSB

Page 13: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

V0V1V2Vref

R-2R DAC Example

• Convert 0001 to analog

Page 14: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

R-2R DAC Example (cont.)

=V0V1 V0V1

R

RRReq

11 22

1

R

V

R

VV 001

01 2 VV

1 2 21

2

RV V V

R R

2 3 31

2

RV V V

R R

Likewise,

Voltage Divider

Nodal Analysis

Page 15: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Conversion Equation

16

1

8

1

4

1

2

10123refout bbbbVV

For a 4-Bit R-2R Ladder

For general n-Bit R-2R Ladder Binary Weighted Resister DAC

i

n

iinbVV

2

1

1refout

Page 16: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

• Advantages– Only two resistor values– Does not need as precision resistors as Binary weighted

DACs– Cheap and Easy to manufacture

• Disadvantages– Slower conversion rate

R-2R DAC Summary

Page 17: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

DAC Specification

• Resolution

• Reference Voltage

• Speed

• Settling Time

• Linearity

Page 18: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Resolution

• The change in output voltage for a change of the LSB.• Related to the size of the binary representation of the

voltage. (8-bit)• Higher resolution results in smaller steps between

voltage values

n

refV

2 Resolution

Page 19: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Reference Voltage

• Multiplier DAC– Reference voltage is a constant set by the

manufacturer

• Non-Multiplier DAC– Reference voltage is variable

• Full scale Voltage

– Slightly less than the reference voltage (Vref-VLSB)

Page 20: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Speed

• Also called the conversion rate or sampling rate– rate at which the register value is updated

• For sampling rates of over 1 MHz a DAC is designated as high speed.

• Speed is limited by the clock speed of the microcontroller and the settling time of the DAC

Page 21: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Settling Time

• Time in which the DAC output settles at the desired value ± ½ VLSB.

• Faster DACs decrease the settling time

Page 22: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Linearity

• Represents the relationship between digital values and analog outputs.

• Should be related by a single proportionality constant. (constant slope)

Page 23: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

DAC Error

• Non-Linearity– Differential– Integral

• Gain Error • Offset Error • Monotonicity• Resolution

Page 24: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Non-linearity

• Deviation from a linear relationship between digital input and analog output.

Ana

log

Out

put V

olta

ge

Digital Input

Desired Output

Page 25: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Non-Linearity

• Differential

– Worst case deviation from the ideal VLSB step for an increment of LSB

• Integral– Worst case deviation from the line between the

endpoint (zero and full scale) voltages

Digital Input

Ana

log

Out

put V

olta

ge

VLSB

2VLSB

Digital Input

Ana

log

Out

put V

olta

ge

Integral Non-linearity

Page 26: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Gain Error

• Also called Full-Scale Error• Deviation from the ideal full scale voltage due to a higher

or lower gain than expected.

Digital Input

Desired/Ideal Output

Ana

log

Out

put V

olta

ge

Low Gain

High Gain

Page 27: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Offset Error• Also called Zero Error

• Difference between ideal voltage output and actual voltage output for a digital input of zero.

Digital Input

Ideal Output

Output Voltage

Page 28: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Monotonicity

• Increases or decreases of the digital value must correspond to increases or decreases of the voltage output.

Ana

log

Out

put V

olta

ge

Digital Input

Desired Output

Non-monotonic behavior

Page 29: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Resolution Error

• For matching curves over time or simply outputting accurate values a proper resolution must be selected

• Resolution must be high enough for the desired precision (½ VLSB)

Vout Desired Analog signal

Time

00

01

10

11

Page 30: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Applications – AudioMany audio signals are stored as binary numbers (on media such as CDs and in computer files such as MP3s). Therefore computer sound cards, stereo systems, digital cell phones, and portable music players contain DAC to convert the digital representation to an analog signal.

Page 31: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Example DAC

• AD 7224 – – Manufactured by Analog Devices– Type: R-2R Voltage Output– Reference voltage: Non-Multiplier– 2 – 12.5 Volts– 8-bit Input– Settling Time: 7 μs– Cost: about $4.00

Page 32: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Example DAC

18 Pin integrated circuit including output amplifier

Page 33: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Applications – VideoVideo 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.

Page 34: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

ReferencesPrevious Student Lectures

http://en.wikipedia.org/

http://allaboutcircuits.com

Page 35: Digital to Analog Converters

Introduction to Mechatronics

Student Lecture – 10/23/06

Questions