Digital to Analog Converter

[Pages:20]Digital to Analog Converter

Jungchul Lee Kamran Jeelani Jonathan Beckwith

Topics of Discussion

? What is a DAC? ? Types of DAC Circuits

? Resistor-string DAC ? N-Bit Binary weighted DAC ? R-2R Ladder DAC

? Specifications of DAC ? Applications

What is a DAC?

? Digital-to-Analog Converter: An electronic device, often an integrated circuit, that converts a digital number into a corresponding analog voltage or current.

? Relation between analog signal and digital equivalent

n

Va = bi 2-i ? Vref i=1

? AD conversion ? Va -> bi (encoder) ex) Transducer interface ? DA conversion ? bi -> Va (decoder) ex) motor, heater control

DAC configurations

? Assume the analog signal is a voltage

N-bit digital word Analog voltage signal

... DN-1, DN-2 ...

D1, D0

VRef

=VDrVefAO*DCut /2N VOut

Types of DAC Circuits

1. Resistor-string 2. N-Bit Binary Weighted Resistor 3. R-2R Ladder

V Ref

R

1

R

0

R

1

R

0

R

1

R

0

R

1

R

0

B2

A Resistor-string DAC

1 0

1 0

B1

1 0

B0

Example of 3 bit resistor-string DAC Required component

- a resistor string - a set of switches ? select output to use - opamp ? buffer

Vo

V0

=

VRe f

b N-1 i 2i+1 i=0

Resistor String DAC Example

? How many resistors and switches would be required to implement an 8 bit resistor-string DAC?

Ans)

# of resistors = 2N=28=256

N -1

# of switches = 2i = 28 -1 = 255

i=0

Impractical for converters with more than a few bits of

resolution

N-Bit Binary Weighted Resistor

R

MSB 1

2

I0

2R

1

2

4R

1

2

8R

1

2

... ...

LSB

1

2^(N-1)R 2

V Ref

3

+ -

R/2

1 4

2

V out

I0

=

VR

N i=1

bi 2(i-1) R

5

V0 = -Rf I0

N-bit binary weighted Example

? Find output voltage, current, and resolution for a binary weighted resistor DAC of 4 bits - given condition R = 10 k, Rf = 5 k, VR = -10 V Applied binary word is 1001

Example Solutions

-10 V VR

1 2

3 3

2 1 3

2 1 1

2 3

Rf=R/2 5 k

3

R 1

4 2

? Vout

+ -

5

8R

4R

2R

R

10 k

0 Bit

1 Bit

2 Bit

3 Bit

1 0 0 1 ? binary input

Example Solutions (Cont.)

Ans)

I0

=

-10

V

20

1 ?104

+

0 21 ?104

+

22

0 ?104

+

23

1 ?104

= - 0.001125 A

V0 = - Rf I0 = -(5?103) ? (-0.001125A) = 5.625V

Resolution

=

LSB=

VRef 2n

=

10V 24

=

0.625V

Example Solutions (Cont.)

... DN-1, DN-2 ...

D1, D0

VRef

=VDrVefAO*DuCt /2N

VOut

? Binary Word input = 10012 = 910 ? # of input combination : 24 =16 ? Vout = Vref * D/2N = 10*9/16 =5.625 V

Limitations of the Binary Weighted DAC

1. If R = 10 k, 8 bits DAC, and VRef = 10 V R8 = 28-1*(10 k) = 1280 k I8 = VRef/R8 =10V/1280 k = 7.8 ?A

Op-amps that can handle those currents are rare and expensive.

2. If R = 10 and VRef = 10 V R1 = 21-1*(10 ) = 10 I1 = VRef/R1 = 10V/10 = 1 A

This current is more than a typical op-amp can handle.

R-2R Resistor Ladder DAC

Vs

R

R

R

2R

2R

2R

2R

2R

Bit 3

Bit 2

Bit 1

Bit 0

R

Vout

+ -

?Simplest type of DAC

?Requires only two precision resistance value (R and 2R)

R-2R Resistor Ladder DAC

V3

V2

V1

V0

Vs

R

R

R

2R

2R

2R

2R

2R

Bit 3

Bit 2

Bit 1

Bit 0

Each Bit controls a switch between ground and the inverting input of the op amp

The switch is connected to ground if the corresponding bit = 0

R

Vout

4 Bit Converter

+ -

+ -

R-2R DAC Example

Ex. Convert 0001 to analog

V3

V2

V1

V0

Vs

R

R

R

2R

2R

2R

2R

2R

Bit 3

Bit 2

2R Bit 1

2R Bit 0

Switch for bit 0 is connected to op amp input. All other switches connected to ground

R

Vout

Digital Value: O O O 1

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