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Digital to Analog Converter(DAC)

- Trayvon Leslie
- Orlando Carreon
- Zack Sosebee

ME 6405 Intro to Mechatronics March 14, 2008

Outline

- Overview
- Choosing a DAC
- Specifications
- Resolution
- Speed
- Linearity
- Settling Time
- Reference Voltages
- Errors
- Errors
- Types of DAC
- Binary Weighted Resistor
- R-2R Ladder
- Multiplier DAC
- Non-Multiplier DAC

Trayvon Leslie

Overview

- Digital to Analog Converter (DAC)
- A digital to analog converter (DAC) is a device

that converts digital numbers (binary) into an

analog voltage, current, or electric charge

output.

Trayvon Leslie

Overview

- Digital to Analog Converter (DAC)
- Generate piecewise continuous signals from

digital code.

Trayvon Leslie

Overview

Each binary number sampled by the DAC corresponds

to a different output level.

Trayvon Leslie

Overview

What a DAC Looks Like

Trayvon Leslie

Overview

Example of DAC

An example of a DAC would be the Analog Devices

AD 7224 D/A Converter. The AD7224 is a precision

8-bit, voltage-output, digital-to-analog

converter with an output amplifier. Specificati

ons DAC Type R-2R Voltage Out Input Dual

8 Bit Reference voltage Non-Multiplier 2v

12.5v Settling Time - 7µs Cost - Under 4.00

Trayvon Leslie

Overview

Examples of DAC AD7224

Trayvon Leslie

Choosing a DAC

- There are six(6) main specifications that should

be considered when choosing a DAC for a

particular project. - Reference Voltage
- Resolution
- Linearity
- Speed
- Settling Time
- Error

Trayvon Leslie

Specifications

- Reference Voltage
- To a large extent the output properties of a DAC

are determined by the reference voltage. - Multiplier DAC The reference voltage is

constant and is set by the manufacturer. - Non-Multiplier DAC The reference voltage can

be changed during operation.

Trayvon Leslie

Specifications

- Resolution
- The resolution is the amount of voltage rise

created by increasing the LSB (Least Significant

Bit) of the input by 1. This voltage value is a

function of the number of input bits and the

reference voltage value. - 1 bit DAC is designed to reproduce 2 (21) levels

while an 8 bit DAC is designed for 256 (28)

levels. - Increasing the number of bits results in a finer

resolution - Most DACs are in the 12-18 bit range

Trayvon Leslie

Specifications

Linearity The linearity is the relationship

between the output voltage and the digital signal

input.

Trayvon Leslie

Specifications

- Speed
- Usually specified as the conversion rate or

sampling rate. - It is the rate at which the input register is

updated. - High speed DACs are defined as operating at

greater than 1 MHz. - Some state of the art 12-16 bit DAC can reach

speeds of 1GHz - The conversion of the digital input signal is

limited by the clock speed of the microprocessor

and the settling time of the DAC.

Trayvon Leslie

Specifications

Settling Time Ideally a DAC would instantaneously

change its output value when the digital input

would change. In a real DAC it takes time for

the DAC to reach the actual expected output

value.

Ideal Sampled Signal

Real DAC Output

Trayvon Leslie

Specifications

- Error
- There are multiple sources of error in computing

the analog output. - Gain Error
- Offset Error
- Full Scale Error
- Linearity
- Non-Monotonic Output Error
- Settling Time and Overshoot
- Resolution

Trayvon Leslie

Errors

- Gain ErrorDeviation in the slope of the ideal

curve and with respect to the actual DAC output

High Gain Error Step amplitude is higher than

the desired output

Low Gain Error Step amplitude is lower than the

desired output

Orlando Carreon

Errors

- Offset Error
- Occurs when there is an offset in the output

voltage in reference to the ideal output.

This error may be detected when all input bits

are low (i.e. 0).

Orlando Carreon

Errors

- Full Scale Error

- Occurs when there is an offset in voltage form

the ideal output and a deviation in slope from

the ideal gain.

Orlando Carreon

Errors

- Non-LinearityDifferential Non-Linearity Voltage

step size differences vary as digital input

increases. Ideally each step should be

equivalent.

Orlando Carreon

Errors

- Non-LinearityIntegral Non-Linearity Occurs when

the output voltage is non linear. Basically an

inability to adhere to the ideal slope.

Orlando Carreon

Errors

- Non-Monotonic Output Error
- Occurs when the an increase in digital input

results in a lower output voltage.

Orlando Carreon

Errors

- Settling Time and Overshoot

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. Overshoot occurs when the output voltage

overshoots the desired analog output voltage.

Orlando Carreon

Errors

- Settling Time and Overshoot

Orlando Carreon

Errors

- Resolution
- Inherent errors associated with the resolution
- More Bits Less Error and Greater Resolution
- Less Bits More Error and Less Resolution

Orlando Carreon

Errors

- Resolution Poor Resolution (1 Bit)

Does not accurately approximate the desired

output due large voltage divisions.

Orlando Carreon

Errors

- Resolution Better Resolution (3 Bit)

Better approximation of the of the desired output

signal due to the smaller voltage divisions.

Orlando Carreon

Types of DAC

Binary Weighted Resistor

- Basic Ideas
- Use a summing op-amp circuit
- Use transistors to switch between high and

ground - Use resistors scaled by two to divide voltage on

each branch by a power of two

- Assumptions
- Ideal Op-Amp
- No Current into Op-Amp
- Virtual Ground at Inverting Input
- Vout -IRf

Zack Sosebee

Types of DAC

Binary Weighted Resistor

Voltages V1 through Vn are either Vref if

corresponding bit is high or ground if

corresponding bit is low V1 is most significant

bit Vn is least significant bit

MSB

LSB

Zack Sosebee

Types of DAC

Binary Weighted Resistor

If RfR/2

For example, a 4-Bit converter yields

Where b3 corresponds to Bit-3, b2 to Bit-2, etc.

Zack Sosebee

Types of DAC

Binary Weighted Resistor

- Example
- Vref -2V
- Digital Word 1010
- V1 -2V
- V2 0V
- V3 -2V
- V4 0V
- Rf R/2

Zack Sosebee

Types of DAC

Limitations of Binary Weighted Resistor

1. If R 10 kO, 8 bits DAC, and VRef 10 V R8

2(8-1)(10 kO) 1280 kO I8 VRef/R8 10V/1280

kO 7.8 µA

Op-amps that can handle those currents are rare

and expensive.

2. If R 10 O and VRef 10 V R1 2(1-1)(10 O)

10 O I1 VRef/R1 10V/10 O 1 A

This current is more than a typical op-amp can

handle.

Zack Sosebee

Types of DAC

Binary Weighted Resistor Summary

- Advantages
- Simple
- Fast
- Disadvantages
- Need large range of resistor values (20001 for

12-bit) with high precision in low resistor

values - Need very small switch resistances
- Summary
- Use in fast, low-precision converter

Zack Sosebee

Types of DAC

R-2R Ladder

Each 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.

Zack Sosebee

Types of DAC

R-2R Ladder

Ideal Op-amp

Zack Sosebee

Types of DAC

R-2R Ladder

I

Likewise,

Zack Sosebee

Types of DAC

R-2R Ladder

Results

Where b3 corresponds to bit 3, b2 to bit 2,

etc. If bit n is set, bn1 If bit n is clear,

bn0

Zack Sosebee

Types of DAC

R-2R Ladder

For a 4-Bit R-2R Ladder

For general n-Bit R-2R Ladder or Binary Weighted

Resister DAC

Zack Sosebee

Types of DAC

R-2R Ladder Summary

- Advantages
- Only 2 resistor values
- Summary
- Better than weighted resistor DAC

Zack Sosebee

Types of DAC

Binary Weighted Resistor vs. R-2R Ladder

Zack Sosebee

Applications

- Generic Use
- Circuit Components
- Audio and Video
- Oscilloscopes/Generators
- Motor Controllers

Orlando Carreon

Applications

- Generic Use
- Used when a continuous analog signal is required.
- Signal from DAC can be smoothed by a Low pass

filter

Orlando Carreon

Applications

- Circuit Components
- 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

Orlando Carreon

Applications

- Audio
- Most modern audio signals are stored in digital

form and in order to be heard through speakers

they must be converted into an analog signal. - CD Players - Digital Telephones
- MP3 Player - Hi-Fi Systems
- Video
- Video signals from a digital source must be

converted to analog form if they are to be

displayed on an analog monitor - - Computers - Digital Video Player

Orlando Carreon

Applications

Oscilloscopes/Generators

- Digital Oscilloscopes
- Digital Input
- Analog Output

- Signal Generators
- Sine wave generation
- Square wave generation
- Triangle wave generation
- Random noise generation

Orlando Carreon

Applications

- Motor Controllers
- Cruise Control
- Valve Control
- Motor Control

Orlando Carreon

References

- http//en.wikipedia.org/wiki/Digital-to-analog_con

verter - Alciatore, Introduction to Mechatronics and

Measurement Systems, McGraw-Hill, 2003 - Horowitz and Hill, The Art of Electronics,

Cambridge University Press, 2nd Ed. 1995 - http//products.analog.com/products/info.aspprodu

ctAD7224 - http//courses.washington.edu/jbcallis/lectures/C4

64_Lec5_Sp-02.pdf - http//www.eecg.toronto.edu/kphang/ece1371/chap11

_s.pdf - Past student lectures

Questions

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