Dac

ME 4447: Introduction to Mechatronics

1

Digital to Analog Converters (DAC)

Jesse BartonHyun Gyu Kim

Christopher Neel


2

What is a DAC?

A digital-to-analog converter (DAC) is a circuit that produces an analog current or voltage that is proportional to an analog reference (voltage or current) and an N-bit binary word.

Vout = k x Vref x (Binary Word)


3

In English

• DACs generate piecewise continuous signals from digital code.

OR• DAC converters are devices that receive a

binary word from the microprocessor and convert it to a scaled analog voltage (or current).


4

DAC Configuration


5

DAC Types

Multiplying DAC - reference source is external to the DAC

package

Nonmultiplying DAC - reference source is inside the DAC package


6

Multiplying DAC advantages• External ref. can be time-varying analog voltage that multiplies

binary function fixed programmable byte scales continuous output

instead of using time-varying bytes w/ fixed VR to produce discrete output

• External reference can be fixed less likely to produce error from reference voltagedrift with temperature than internal reference


7

DAC Circuit Types

Two types of DAC Circuits:

1. Binary weighted

2. R-2R ladder


8

N-Bit Binary Weighted DAC


9

Binary Weighted Principles

MSB b

bitsinput ofnumber N

MSB toingcorrespond resistance R

junction leaving currents of sumI

2

1

0

110

N

iii

R R

bVI


10

Principles Cont’d

V0 = -RfI0

V0 = voltage output from amplifier

Rf = feedback resistance

Resolution= VR/2N

Note: For a gain of 1, R = 2Rf


11

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.


12

SolutionRf = (R/2)

R2R4R8R Vo

VR

1-bit

MSB

2-bit3-bit4-bit

iI


13

Solution Cont’d

V625.5)A001125.0)(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


14

Solution Cont’d

Binary input = 1001 = 9

From example, V0 = 5.625V

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


15

Limitations of the Binary Weighted DAC

Has problems if bit length is longer than 8 bitsFor example, if R = 10 k OhmsR8 = 28-1(10 k Ohms) = 1280 k OhmsIf 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.


16

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-amp

can handle.


17

Limitations Cont’d

Intuitively, the resistance values must be accurate to less than one part in 2N for the RN input to be meaningful. This is difficult to do, especially in IC’s.


18

R/2R ladder DAC

• Most popular single package DAC

• Resolves BWL problems• Only two resistor values


19

Equations governing R/2R

bitsofnumberisNwhere;2

ResolutionNRV

MSBisbwhere;2 1

1

N

iii

Ro

bVV

bitsofnumberisNwhere;2

11

NRfso VV

MSBisbwhere;22 1

11

N

iiiR

i

b

R

VI


20

Principles of Operation

• Binary Switch true ground w/ LOW input

• Binary Switch op-amp virtual ground w/ HI input

• Splits current at each bit• After multiplication of

binary word Io

• Inverting Op-amp used to generate analog output voltage

• Performed many times per second semi-continuous DAC


21

Specifications of DAC’s• Resolution

– Increases (improves) as number of bits increases– Most microcontrollers use 8 bit DAC– Some 12 bit DAC used in high end applications

• Linearity– Max deviation over full range of output @ room temp.

• Settling Time– Time for DAC to come w/in 0.5 LSB {Vo ± 0.5*(VR /2N)} of new voltage after binary change– Typ. current output DAC’s conversion times (10 ns to 1 μs)

• Reference Voltage– Internal / external


22

DAC Errors

• Resolution: more bits = more precise

• Overshoot & Settling Time: String of amplifiers w/ feedback loops = very rapid response or

very slow response depending on system properties

• Absolute Accuracy Error: Difference between theoretical and actual output

• Conversion Speed: Rapidly fluctuating inputs require high conversion speed to be

interpreted accurately


23

DAC Errors Cont’d

• Non-Monotonicity: Certain conditions where increased input results in decrease Vo

• Differential Non-Linearity: Deviation of actual converter step size from the ideal predicted wave

step

• Gain Error: Gain too low = same analog output; gain too high = too large an

output

• Offset Error: Constant error of DAC


24

DAC Errors Cont’d

• Resistance Error: Pertains mainly to BWR DAC since large variety of resistors used

error varies greatly disturbing DAC performance

• Saturation: Use of op-amps requires that input voltage and scaling voltages be

bounded to the specifications of the op-amp.


25


26


27


28


29


30


31

Applications of DAC

• Control Systems• Digital Audio• Digital Telephones• Cruise Control• Waveform Generation


32

Discussion

Business

Dac