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UNIVERSITY OF HORMUUD

Analog to digital converter

And

Digital to analog converter

By: Ahmed Salad Osman

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Part one

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Part two2

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analog to digital converter

Part one

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Outline

DefinitionWhy we need ADCTypes ADC and each basic operationApplications of analog to digital converter

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Definition

An electronic integrated circuit which transforms a signal from analog(continues) to digital(discrete) form

Analog signals are directly measurable quantities

Digital signals only have two states for digital computer we refer to binary states, 0 and 1

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The heart of computer-based data acquisition is usually the analog to digital converter

Basically this device is digital volt meterDigital Systems require discrète digital data

Digital System?Analog Digital

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Digital computers require signals to be in digital form whereas most instrumentation transducers have an output signal in analogue form.

ADC conversion is therefore required at the interface between analogue transducers and the digital computer

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• Voltmeter

Examples of use

• Cell phone (microphone)

ΔV 7.77 V

Wave

Voice

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Why we need ADC

Microprocessors can only perform complex processing on digitized signals

When signals are in digital form they are less susceptible to the deleterious effects of additive noise

ADC Provides a link between the analog world of transducers and the digital world of signal processing and data handling.

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Types of analog to digital converter

There are many different types of analog to digital converters

Each offers something in the way ofSpeedCostPower dissipationcomplexity

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Types of analog to digital converter

Counter typeSuccessive approximationThere are many types such as flash

type and sigma-delta but we will cover these two types

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Counter type

One of the simplest types of analog to digital converter is counter type ADC

The input signal of ADC is connected to the signal input of its internal comparator

The ADC then systematically increases the voltage of the reference input of the comparator until the reference becomes larger than the signal

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Continue

And the comparator output goes to 0Ex: consider an input signal is 4.78 volts. The

initial comparator’s input would be 2.5 voltsThe comparator compares the two value then

the result this is less than 4.78 then the next higher voltage (5.00 volts) is applied

The comparator compares the two value and says this is greater than 4.78 and switches 0

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The digital output of the ADC is the number of times the ADC increase the voltage after starting at the initial 2.5 volts

This scheme is relatively simple , but as the number of ADC increases the time it takes to scan through all possible values lower than input will grow quickly

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Components of counter type

This type of converter uses some type of counter as part of its operation

Counter type contains the following elements:Digital to analog converterSome type of counting mechanismComparatorclock

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Features of counter type

Use a clock to index the counterUse DAC to generate analog signal to

compare against inputComparator is used to compare VIN and VDAC

where VIN is the signal to be digitizedThe input to the DAC is from the counter

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Operation of counter type

Control Logic

D A C Counter

START

Vin

Comparator

Digital Output

clock

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Operation of counter type

Control Logic

D A C Counter

START

Vin

Comparator

Digital Output

clock

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Successive approximation

A Successive Approximation Register (SAR) is added to the circuit

Instead of counting up in binary sequence, this register counts by trying all values of bits starting with the MSB and finishing at the LSB.

The register monitors the comparators output to see if the binary count is greater or less than the analog signal input and adjusts the bits accordingly

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The SAR architecture mainly uses the binary search algorithm

The SAR ADC consists of fewer blocks such as one comparator, one DAC (Digital to Analog Converter) and one control logic.

The algorithm is very similar to like searching a number from telephone book

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How Successive Approximation Works

• Example : analog input = 6.428v, reference = 10.000vMSB5.000V

2SB2.500V

3SB1.250V

LSB0.625V

VIN > 5.000V VIN > 6.875VVIN > 6.250VVIN > 7.500V

YES

1

NO

0

YES

1

NO

0

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Applications

Scanner : when you scan a picture with a scanner , what scanner is doing is an analog to digital conversion : it is taking the analog information provided by the picture(light) and converting into digital

Recording a voice : when u=you record your voice or use a VoIP solution on your computer you r using analog to digital converter to convert you voice , which is analog into digital information

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Part two

Digital to analog converter

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Outline

DefinitionTypes of DAC and each operationDAC performance specificationsApplications of ADC

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Definition

To convert digital values to analog voltagePerforms inverse operation of analog to digital

converter

DAC100101…

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What is DAC

10111001 10100111 10000110010101000011001000010000

An

alog

ou

tput

sig

nal

Digital input signal

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ANALOGOUTPUT

DIGITALINPUT

REFERENCEINPUT

RESOLUTION= N BITS

RESOLUTION= N BITS

Digital Input Analog Output = x Reference Input

(2N - 1)

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ADC is function that converts digital data(usually binary) into analog signal(current , voltage, or electric charge)

digital-to-analog converter, a device (usually a single chip) that converts digital data into analog signals.

Modems require a DAC to convert data to analog signals that can be carried by telephone wires.

Video adapters also require DACs, called RAMDACs, to convert digital data to analog signals that the monitor can process.

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Types of DAC

There are two types of ADCWeighted Resistor or Resistive Divider type

And there is an other type of R -2R ladder

Digital to analog converter

01

2

n-2

N bit digital data

Analog data

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Weighted Resistors

• In this type of DAC components used is– Operational amplifier– Switches– Resistors– Voltage source– Ground

Rf = R

8R4R2RR

-VREF

iI

LSB

MSB

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Definition of weighted resistors

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

Binary weighted resistors Reduces current by a factor of 2 for each bit

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Binary Weighted resistors is reliable, and simple to do

The circuit shown is a digital to analog converter 4-bits weighted binary resistance network circuit types.

Resistor values can be calculated using the weight of the binary number.

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Circuit diagram of weighted resistors

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Weighted Binary Resistance Network

20K

RF

18.7K 150K37.5K 75K

R4 R3 R2R1

3V

ABCD

VVVO

UT

-

+Vout

-

+Vout

Weighted Binary Resistance Network Circuit

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For exampleReferring to the circuit as shown, the highest

value resistor (150KΩ) is a digital input resistor. The smallest bit (least significant bit), and the values of other resistor is

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Circuit analysis to find Vout

R1 = 150KΩ, RF = 20KΩ, Vref = 3V

Voltage Gain (AV) = RF = 20KΩ = 0.133

R1 150KΩ

Vout = Vref X AV

= 3V X 0.1333

= 0.4V

If binary input is 0001

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Continue If binary input is 0110

R2 = 75KΩ, R3 = 37.5KΩ, RF = 20KΩ, Vref = 3V

RT = R2//R3 = 25KΩ

Voltage Gain (AV) = RF = 20KΩ = 0.8 RT 25KΩ

Vout = Vref X AV

= 3V X 0.8= 2.4V

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Calculate

If binary input is 1100

R3 = 37.5KΩ, R4=18.75 RF = 20KΩ, Vref = 3V

RT = R3//R4 = 12.5KΩ

Voltage Gain (AV) = RF = 20KΩ = 1.6

RT 12.5KΩ

Vout = Vref X AV

= 3V X 1.6= 4.8

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Simply that we can see the resulting output is shown in the table below

Decimal Digital input Vout (V)D C B A0 0 0 0 0 01 0 0 0 1 0.42 0 0 1 0 0.83 0 0 1 1 1.24 0 1 0 0 1.65 0 1 0 1 2.06 0 1 1 0 2.47 0 1 1 1 2.88 1 0 0 0 3.29 1 0 0 1 3.6

10 1 0 1 0 4.011 1 0 1 1 4.412 1 1 0 0 4.813 1 1 0 1 5.214 1 1 1 0 5.615 1 1 1 1 6.0

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Example

Find output voltage and current for a binary weighted resistor DAC of 4 bits where :

R = 10 k Ohms, Rf = 5 k Ohms and VR = 10 Volts. Applied binary word is 1001.

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Solution

Rf = (R/2)

R2R4R8RVo

VR

1-bit

MSB

2-bit3-bit4-bit

iI

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Solution Cont’d

V625.5)A001125.0)(10*5(

IR- V

A 0.001125-

10*2

1

10*2

0

10*2

0

10*2

1V10

30

0f0

0

43424140

V

I

Io

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Solution Cont’d

Binary input = 1001 = 9

From example, V0 = 5.625V

V0/VR = 5.625V/10V = 9/16

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Binary Weighted Resistor

Advantages Simple Construction/Analysis Fast Conversion

Disadvantages Requires large range of resistors (2000:1 for 12-

bit DAC) with necessary high precision for low resistors

Requires low switch resistances in transistors Can be expensive. Therefore, usually limited to

8-bit resolution.

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Limitations of binary weighted

Has problems if bit length is longer than 8 bitsFor example, if R = 10 k Ohms

R8 = 28-1(10 k Ohms) = 1280 k Ohms

If VR = 10 Volts,

I8 = 10V/1280 k Ohms = 7.8 AOp-amps to handle those currents are expensive

because this is usually below the current noise threshold.

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Limitations Cont’d

If R = 10 Ohms and Vref = 10 V

I = VR/R = 10V/10 Ohms = 1 A

This current is more than a typical op-ampcan handle.Large resistors more error

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DAC performance specification

ResolutionReference VoltagesSettling TimeLinearitySpeedErrors

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Resolution

Resolution: is the amount of variance in output voltage for every change of the LSB in the digital input.

How closely can we approximate the desired output signal(Higher Res. = finer detail=smaller Voltage divisions)

A common DAC has a 8 - 12 bit Resolution

NLSB

VV

2Resolution Ref N = Number of bits

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Resolution continue

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

Vout

Desired Analog signal

Approximate output

2 V

olt.

Lev

els

Digital Input0 0

1

Digital Input

Vout

Desired Analog signal

Approximate output

8 V

olt.

Lev

els

000

001

010

011

100

101

110

111

110

101

100

011

010

001

000

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Reference voltage

Reference Voltage: A specified voltage used 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

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Reference voltage typesNon-Multiplier: (Vref = C)

Digital Input

4

3C

2

C

4

C

0

Voltage

00

01 01

00

10 10

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Multiplier: (Vref = Asin(wt))

0

Voltage

Digital Input

4

3A

2

A

4

A

00 00

01 01

10 10

11

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Settle time

Settling Time: The time required for the input 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 two events.

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Settle time continue

• Analog Output Voltage

• Expected Voltage

• +VLSB

• -VLSB

• Settling time• Time

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Linearity

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.

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Linearity continue

Linearity(Ideal Case)

Digital Input

Perfect Agreement

Desired/Approximate Output

Ana

log

Out

put V

olta

ge

NON-Linearity(Real World)

Ana

log

Out

put V

olta

ge

Digital Input

Desired Output

Miss-alignment

Approximate output

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Speed

Speed: Rate of conversion of a single digital input to its analog equivalent

Conversion Rate Depends on clock speed of input signalDepends on settling time of converter

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Errors

Non-linearityDifferentialIntegral

GainOffset

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Non linearity: differential

Differential Non-Linearity: Difference in voltage step size from the previous DAC output (Ideally All DLN’s = 1 VLSB)

Digital Input

Ideal Output

Ana

log

Out

put V

olta

ge

VLSB

2VLSB Diff. Non-Linearity = 2VLSB

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Non linearity: integral

Integral Non-Linearity: Deviation of the actual DAC output from the ideal (Ideally all INL’s = 0)

Digital Input

Ideal Output

1VLSB Int. Non-Linearity = 1VLSB

Ana

log

Out

put V

olta

ge

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Gain error

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

High Gain Error: Actual slope greater than ideal

Low Gain Error: Actual slope less than ideal

Digital Input

Desired/Ideal OutputA

nalo

g O

utpu

t Vol

tage

Low Gain

High Gain

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Offset

Offset Error: A constant voltage difference between the ideal DAC output and the actual.– The voltage axis intercept of the DAC output curve is different than the

ideal.

Digital Input

Desired/Ideal OutputOutput Voltage

Positive Offset

Negative Offset

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Applications of DAC

Digital Motor ControlComputer PrintersSound Equipment (e.g. CD/MP3 Players, etc.)Function Generators/OscilloscopesDigital Audio

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References

• Callis, J. B. “The Digital to Analog Converter.” 2002. http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp-02.pdf. 14 March 2006

• “DAC.” 2006. http://en.wikipedia.org/wiki/Digital-to-analog_converter#DAC_types. 14 March 2006.

• Johns, David and Ken Martin. “Data Converter Fundamentals.” © 1997. http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pdf. 14 March 2006

• Goericke, Fabian, Keunhan Park and Geoffrey Williams. “Digital to Analog Converter.” © 2005. http://www.me.gatech.edu/mechatronics_course/DAC_F05.ppt. 14 March 2006

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Questions