DIGITAL TO ANALOG CONVERTOR

A quick presentation to introduce our peers on the techniques, specifications and applications of the DAC

03/16/2007

Compiled by Rafael, Ravikanth and Hrishi

Table Of Contents
Introduction Types

Of DAC Specifications Applications Conclusion

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

INTRODUCTION
The

DAC fundamentally converts finiteprecision numbers (usually fixed-point binary numbers) into a physical quantity, usually an electrical voltage. Normally the output voltage is a linear function of the input number. Usually these numbers are updated at uniform sampling intervals and can be thought of as numbers obtained from a sampling process
03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Analog Output Signal

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 Digital Input Signal
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Output is a sequence of piecewise constant values or rectangular pulses, means that there is an inherent effect of the zero-order hold on the effective frequency response of the DAC resulting in a mild roll-off of gain at the higher frequencies

Ideally Sampled Signal

Output typical of a real, practical DAC due to sample & hold

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Types of DACs
Many

types of DACs available. Usually switches, resistors, and op-amps used to implement conversion Three Types:

Resistor String Binary Weighted Resistor R-2R Ladder PWM (Pulse Width Modulation)
03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Resistor String DAC

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

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Resistor String DAC

Resistor String

Example

VREF = 8V

Rtotal = 8R I = REF R total V REF /(8 ) V / = R Vn =Rn I= n R I Vn n R I n = =V n VREF 8R I 8 VREF

3 V3 = 8V = 3V 8

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Compiled by Rafael, Ravikanth and Hrish

SELECTION SWITCHES

1 0 0 4V

1 1 0 6V

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0 0 0 0V 1 1 1 7V

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Resistor String DAC

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 2n 1

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Compiled by Rafael, Ravikanth and Hrish

Binary Weighted Resistor DAC

Utilizes

a summing op-amp circuit Weighted resistors are used to distinguish each bit from the most significant to the least significant Transistors are used to switch between Vref and ground (bit high or low)

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Summing OP-Amps
Inverting

summer circuit used in Binary Weighted Resistor DAC. V(out) is 180 out of phase from V(in)

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Binary Weighted Resistor

Vref

Assume Ideal OpAmp No Current into OP-Amp Virtual ground at inverting input

R 2R 4R + 2nR

Rf

Vou t

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Calculation

bn 1 bn 2 b0 VOUT = Vref R( + + ... + n 2R 4R 2 R

VOUT =

Vref 2
n

(2 n 1 bn 1 + 2 n 2 bn 2 + ... + 2 b1 + b0
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Compiled by Rafael, Ravikanth and Hrish

Example:

n=4
Vout = Vref (2 n 1 bn 1 + 2 n 2 bn 2 + ... + 2b1 + b0 )

Contd

Vout =

Vref 16

(8b3 + 4b2 + 2b1 + b0 )

Vout =
V fs

Vref

16 = ref RE V S

(8(0) + 4(0) + 2(1) +1(1)) =

3 Vref 16

RE = / 2 n 1 S V fs = ref V 2 4 1 35 2 4 =0.9 7
03/16/2007

n = totalbits

Vref

Compiled by Rafael, Ravikanth and Hrish

Advantages and Disadvantages

Advantages

Easy principle/construction Fast conversion Requirement of several different precise input resistor values: Requires large range of resistors (2048:1 for 12-bit DAC) with necessary high precision for low resistors one unique value per binary input bit. (High bit DACs) Larger resistors ~ more error. Precise large resistors expensive.

Disadvantages

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

R-2R ladder DAC Example

Vref V2 V1 V0

MSB

LSB

Convert 0001 to analog

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R-2R DAC Example (cont.)

V1 V0 V1 V0

=
1 Req = =R 1 1 ( 2R ) + ( 2R)

V1 V0 V0 = R R

V1 = 2 V0

Nodal Analysis Likewise,

V1 = R 1 R 1 V2 = V2 V2 = V3 = V3 R+R 2 R+R 2

Voltage Divider

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Conversion Equation
For a 4-Bit R-2R Ladder

Vout

1 1 1 1 = Vref b3 + b2 + b1 + b0 4 8 16 2

For general n-Bit R-2R Ladder Binary Weighted Resister DAC

1 Vout = Vref bn i i 2 i =1

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Compiled by Rafael, Ravikanth and Hrish

R-2R DAC Summary

Advantages

Only two resistor values Does not need as precision resistors as Binary weighted DACs Cheap and Easy to manufacture

Disadvantages

Slower conversion rate

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

Pulse Width Modulation

Approximate analog signal by switching on/off at high frequency Integral of output voltage from PWM ideally is the same as integral of desired output voltage Example: Desired output = 7V, supply voltage = 10V Operate 10V at 70% duty cycle to approximate 7V In practice: use counter, comparator, clock, integrator
03/16/2007

Compiled by Rafael, Ravikanth and Hrish

SPECIFICATIONS
Resolution Speed Linearity Settling

Time Reference Voltage Errors

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RESOLUTION

Defined by the change in output voltage for a change of the LSB. Related to the size of the binary representation of the voltage. (8-bit) Higher resolution results in smaller steps between voltage values

Resolution=

Vref 2
n

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Compiled by Rafael, Ravikanth and Hrish

SPEED
Defined

by the rate at which the register value is updated. Also called the conversion rate or sampling rate Speed is limited by the clock speed of the microcontroller and the settling time of the DAC
03/16/2007

Compiled by Rafael, Ravikanth and Hrish

LINEARITY

Analog Output Voltage

Represents the relationship between digital values and analog outputs Should be related by a single proportionality constant. (constant slope)

Desired Output

Digital Input
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Compiled by Rafael, Ravikanth and Hrish

SETTLING TIME

Time in which the DAC output settles at the desired value VLSB . Ideally, an instantaneous change in analog volatage would occur when a new binary word enters into the DAC

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

REFERENCE VOLTAGE
Used

to determine how each digital input will be assigned to each voltage division Types:

Non Multiplier DAC: Vref is fixed Multiplier DAC: Vref provided by external source

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Compiled by Rafael, Ravikanth and Hrish

ERRORS
Gain Offset Full

scale Non-Monocity

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GAIN ERROR

Analog Output .

Occurs when the slope of the actual output deviates from the ideal output

D ig it a l In p u t
I d e a l O u tp u tP o s itiv e O f f s e t E r rNo e rg a tiv e O f f s e t E r r o r

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

OFFSET ERROR

Analog Output .

Occurs when there is a constant offset between the actual output and the ideal output

D ig it a l In p u t

I d e a l O u tp u tP o s itiv e O f f s e t E r rN rerg a tiv e O f f s e t E r r o r o

03/16/2007

Compiled by Rafael, Ravikanth and Hrish

FULL SCALE ERROR

Analog Output

Occurs when the actual signal has both gain and offset errors

D ig ita l In p u t
Ideal O utput F ull S cale E rror E rror

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Compiled by Rafael, Ravikanth and Hrish

Non-Monotonic Error

Occurs when an increase in digital input results in a decrease in the analog output

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Common Applications

Electronic Cruise Control Computer Printers Sound Equipment (e.g. CD/MP3 Players)

Project applications Motor speed controller Solenoid valves (pneumatics)

03/16/2007

Compiled by Rafael, Ravikanth and Hrishi