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

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Digital to analog converters

Digital to Analog Converters

Andrew Gardner

Muhammad Salman

David Fernandes

Jevawn Roberts

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

Outline

What is a DAC?

Different Types of DACs

Binary Weighted Resistor

R-2R Ladder

Specifications

Commonly used DACs

Application

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

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.

1001

0101

0011

0111

1001

1010

1011

DAC

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

Analog Output Signal

Digital Input Signal

Introduction

Each binary number sampled by the DAC corresponds to a different output level.

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

Ideally Sampled Signal

Output typical of a real, practical DAC due to sample & hold

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.

DAC

Introduction to Mechatronics

Student Lecture – 10/23/06


Binary weighted resistor dac

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)

Introduction to Mechatronics

Student Lecture – 10/23/06


Summing op amps

Summing OP-Amps

  • Inverting summer circuit used in Binary Weighted Resistor DAC.

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Binary weighted input dac

Vout

Rf

2n-1R

R

-

+

2R

I

4R

Vn

Vref

V1

V2

V3

Rf

2n-1R

2R

R

4R

Vref

V1

I

V2

V3

-

Vout

Vn

+

Binary Weighted Input DAC

  • Ideal Op-amp

  • No current into

    op-amp

  • Virtual ground at

    inverting input

  • Vout= -IRf

MSB

LSB

Introduction to Mechatronics

Student Lecture – 10/23/06


Calculation

Calculation

Introduction to Mechatronics

Student Lecture – 10/23/06


Cont d

Cont’d

  • Example:

n = totalbits

Introduction to Mechatronics

Student Lecture – 10/23/06


Advantages and disadvantages

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.

Introduction to Mechatronics

Student Lecture – 10/23/06


R 2r resistor ladder dac

R-2R Resistor Ladder DAC

Vref

MSB

LSB

Bit: 0 0 0 0

Vout

4-Bit Converter

Introduction to Mechatronics

Student Lecture – 10/23/06


R 2r dac example

R-2R DAC Example

  • Convert 0001 to analog

V2

V1

V0

Vref

Introduction to Mechatronics

Student Lecture – 10/23/06


R 2r dac example cont

R-2R DAC Example (cont.)

V0

V1

V1

V0

=

Nodal Analysis

Likewise,

Voltage Divider

Introduction to Mechatronics

Student Lecture – 10/23/06


Conversion equation

Conversion Equation

For a 4-Bit R-2R Ladder

For general n-Bit R-2R Ladder

Binary Weighted Resister DAC

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

R-2R DAC Summary

  • Advantages

    • Only two resistor values

    • Does not need as precision resistors as Binary weighted DACs

    • Cheap and Easy to manufacture

  • Disadvantages

    • Slower conversion rate

Introduction to Mechatronics

Student Lecture – 10/23/06


Dac specification

DAC Specification

  • Resolution

  • Reference Voltage

  • Speed

  • Settling Time

  • Linearity

Introduction to Mechatronics

Student Lecture – 10/23/06


Resolution

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Reference voltage

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)

Introduction to Mechatronics

Student Lecture – 10/23/06


Speed

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Settling time

Settling Time

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

  • Faster DACs decrease the settling time

Introduction to Mechatronics

Student Lecture – 10/23/06


Linearity

Linearity

  • Represents the relationship between digital values and analog outputs.

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Dac error

DAC Error

  • Non-Linearity

    • Differential

    • Integral

  • Gain Error

  • Offset Error

  • Monotonicity

  • Resolution

Introduction to Mechatronics

Student Lecture – 10/23/06


Non linearity

Desired Output

Analog Output Voltage

Digital Input

Non-linearity

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Non linearity1

Integral

Non-linearity

Analog Output Voltage

Analog Output Voltage

2VLSB

VLSB

Digital Input

Digital Input

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Gain error

Gain Error

  • Also called Full-Scale Error

  • Deviation from the ideal full scale voltage due to a higher or lower gain than expected.

High Gain

Desired/Ideal Output

Analog Output Voltage

Low Gain

Introduction to Mechatronics

Student Lecture – 10/23/06

Digital Input


Offset error

Output Voltage

Ideal Output

Digital Input

Offset Error

  • Also called Zero Error

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Monotonicity

Desired Output

Analog Output Voltage

Digital Input

Monotonicity

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

Non-monotonic behavior

Introduction to Mechatronics

Student Lecture – 10/23/06


Resolution error

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

11

10

01

00

Introduction to Mechatronics

Student Lecture – 10/23/06

Time


Digital to analog converters

Applications – Audio

Many 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.

Introduction to Mechatronics

Student Lecture – 10/23/06


Example dac

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

Introduction to Mechatronics

Student Lecture – 10/23/06


Example dac1

Example DAC

18 Pin integrated circuit including output amplifier

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

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.

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

References

Previous Student Lectures

http://en.wikipedia.org/

http://allaboutcircuits.com

Introduction to Mechatronics

Student Lecture – 10/23/06


Digital to analog converters

Questions

Introduction to Mechatronics

Student Lecture – 10/23/06


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