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Digital to Analog Converter

Nov. 1, 2005

Fabian Goericke, Keunhan Park, Geoffrey Williams

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Outline What is a DAC? Types of DAC Circuits

Resistor-string DAC Binary weighted DAC

R-2R Ladder DAC

Specifications of DAC

Errors Applications

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A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output.

0101

0011

0111

1001

1001

1010

1011 DAC

What is a DAC?

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What is a DAC?

10111001 10100111 10000110010101000011001000010000Digital Input Signal

Ana

log

Out

put

Sig

nal

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Types of DAC Circuits

1. Resistor String2. Binary Weighted Resistor3. R-2R Ladder

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Components of a String DAC

• Resistor String supply discrete voltage levels

• Selection Switches connect the right voltage level to op-amp according to input bits

• Op-amp amplifies the discrete voltage levels to desired range, keeps the current low

Resistor String DAC

7

8

/ /(8 )

8 8

total

REF total REF

n n

nn REF

REF

R R

I V R V R

V R I n R I

V n R I nV V

V R I

Resistor String

3

8

38 3

8

REFV V

V V V

Example

Resistor String DAC

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1 1 0 6V 1 1 1 7V

1 0 0 4V 0 0 0 0V

Selection Switches

Resistor String DAC

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Advantages:• simple• fast for < 8 bits

Disadvantages:• high element count for higher resolutions, reason:

number of resistors:

number of switches: • slow for > 10 bits

2n

2 1n

Resistor String DAC

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Basic Idea:

•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

-

+

R

2R

4R

2nR

Rf

Vout

refV

Binary Weighted Resistor DAC

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• non-inverting input on ground virtual ground at inverting input

• KIRCHHOFF’s current law and no input current into op-amp I1 + I2 = 0

•I1 = V1 / R + V2 / (2R) + V3 / (4R) + …

31 2 42 1( ) ...

2 4 8out f f f

VV V VV R I R I R

R R R R

Binary Weighted Resistor DAC

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Binary Weighted Resistor DAC

31 2 42 1( ) ...

2 4 8out f f f

VV V VV R I R I R

R R R R

Terms have less influence

Most significant

bit

Least significant

bit

Vn = Vref, if bit is set

Vn = 0, if bit is clear

Rf = R / 2

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Advantages Simple Fast

Disadvantages Needs large range of resistor values (2000:1 for 12-

bit) with high precision in low resistor values Needs very small switch resistances

Binary Weighted Resistor DAC

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R-2R Resistor Ladder DAC

Simplest type of DAC

Requires only two precision resistance valuce (R and 2R)

Each bit controls a switch betweenground and the inverting input of theop amp.

The switch is connected to ground ifthe corresponding bit is zero.

0 0 0 0

4 bit converter

Vref

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R-2R DAC Example Convert 0001 to analog

V0V1V2V3

1

1/ 2 1/ 2eqR RR R

0 1 11

2

RV V V

R R

V0V1V0V1

=

1 2 21

2

RV V V

R R

2 3 31

2

RV V V

R R

Vref

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R-2R DAC Example

Convert 0001 to analog

01

8 refV V

2R

R

V0

out 0R 1

V2R 16 refV V

Vref

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R-2R DAC Summary Conversion results for each bit

Conversion equation for N-bit DAC

Digital bit Analog Conversion

0001

0010

0100

1000

,0 /16out refV V

,1 / 8out refV V

,2 / 4out refV V

,3 / 2out refV V

3 ,3 2 ,2

1 ,1 0 ,0

out out out

out out

V b V b V

bV b V

for

3 2 1 0 ( 0 or 1)ib b b b b

( )1 2

Nref

out N i ii

VV b

Resolution

2

refN

V

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Advantages Only two resistor values Does not need the kind of precision as Binary

weighted DACs Easy to manufacture Faster response time

Disadvantages More confusing analysis

R-2R DAC Summary

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Specification of DAC

Resolution Speed Settling time Linearity Reference voltage

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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 - 16 bit Resolution

NLSB

VV

2Resolution Ref N = Number of bits

Specification - Resolution

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

Conversion Rate depends on clock speed of input signal settling time of converter

When the input changes rapidly, the DAC conversion speed must be high.

Specification - Speed

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The time required for the input signal voltage to settle to the

expected output voltage (within +/- ½ of VLSB).

Ideally, an instantaneous change in analog voltage would occur

when a new binary word enters into DAC

Fast converters reduce slew time, but usually result in longer ring

time.

Specification – Settling Time

tdelay

tslew tring

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The difference between the desired analog output and the actual output over the full range of expected values.

Specification – Linearity

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Specification – Linearity

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

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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A specified voltage used to determine how each digital input will be assigned to each voltage division.

Types: Non-multiplier DAC: Vref is fixed (specified by the

manufacturer)

Multiplier DAC: Vref is provided via an external source

Specification – Reference Voltage

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Full Scale Voltage Defined as the output when digital input is all 1’s.

Specification – Reference Voltage

1

10

2 11

2 2

N Nref

fs refi Ni

VV V

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Errors

Common DAC Errors: Gain Error Offset Error Full Scale Error Non Linearity Non-Monotonic Resolution Errors Settling Time and Overshoot

There are a multiple sources of error associated with DAC

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Gain Error: Deviation in the slope of the ideal curve and with respect to the actual DAC output.

Gain ErrorGain Error

High Gain Error: Step amplitude is higher than the desired output

Low Gain Error: Step amplitude is lower than the desired output

Digital Input

Desired/Ideal OutputA

nalo

g O

utpu

t Vol

tage

Low Gain

High Gain

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

voltage in reference to the ideal output.

Offset ErrorOffset Error

Digital Input

Desired/Ideal OutputOutput Voltage

Positive Offset

Negative Offset

This error may be detected when all input bits are low (i.e. 0).

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Full Scale ErrorFull Scale Error: occurs when there is an offset in

voltage form the ideal output and a deviation in slope from the ideal gain.

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Differential Non-Linearity: Voltage step size changes vary with as digital input increases. Ideally each step

should be equivalent.

Differential Non-Linearity

Digital Input

Ideal Output

Ana

log

Out

put V

olta

ge

VLSB

2VLSB Diff. Non-Linearity = 2VLSB

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Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope.

Integral Non-Linearity

Digital Input

Ideal Output

1VLSB Int. Non-Linearity = 1VLSB

Ana

log

Out

put V

olta

ge

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Non-Monotonic Output Error: Occurs when the an increase in digital input results in a lower output

voltage.

Non-Monotonic Output Error

Ana

log

Out

put V

olta

ge

Digital Input

Desired Output

Monotonic

Non-Monotonic

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Resolution Errors

Poor Resolution(1 bit)

Vout

Desired Analog signal

Approximate output

2 V

olt.

Lev

els

Digital Input0 0

1Does not accurately approximate the desired output due large voltage divisions.

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Resolution ErrorsBetter Resolution(3 bit)

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

Better approximation of the of the desired output signal due to the smaller voltage divisions.

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Settling Time and Overshoot

Analog Output Voltage

Expected Voltage

+VLSB

-VLSB

Settling time Time

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.

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Common Applications

Audio: Most modern audio signals are stored in digital form (for example MP3s and CDs) and in order to be heard through speakers they must be converted into an analog signal

Video:Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor.

http://en.wikipedia.org/wiki/Digital-to-analog_converter

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References

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.asp?product=AD7224 http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp-0

2.pdf

http://www.eecg.toronto.edu/~kphang/ece1371/chap11_slides.pdf

Previous students’ lectures on DAC

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Questions?