Digital to Analog Converters

Tyler Smith

Brent Nelson

Jerry Jackson

10/14/04

Topics Discussed

What is a DAC? Choosing a DAC Resistor String DAC

Weighted Resistor DAC R-2R DAC PWM

DAC associated errors Applications Conclusion

What is a DAC

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

Choosing a DAC

There are six main parameters that should be considered when choosing a DAC for a particular project.

Reference Voltage Resolution Linearity Speed Settling time Error

Choosing a DAC

Reference VoltageTo a large extent the output properties of a DAC are determined by the reference voltage.

Multiplier DAC – The reference voltage is constant and is set by the manufacturer.

Non-Multiplier DAC – The reference voltage can be changed during operation.

Choosing a DAC

ResolutionThe resolution is the amount of voltage rise created by increasing the LSB of the input by 1. This voltage value is a function of the number of input bits and the reference voltage value.

- Increasing the number of bits results in a finer resolution

- Most DACs in the 12-18 bit range

nbits2

VoltageReference_Resolution

Choosing a DAC

LinearityThe linearity is the relationship between the output voltage and the digital signal input.

Choosing a DAC

SpeedUsually specified as the conversion rate or sampling rate. It is the rate at which the input register is cycled through in the DAC.

High speed DACs are defined as operating at greater than 1 millisecond per sample (1MHz).

Some state of the art 12-16 bit DAC can reach speeds of 1GHz The conversion of the digital input signal is limited by the clock

speed of the input signal and the settling time of the DAC.

Choosing a DAC

Settling TimeIdeally a DAC would instantaneously change its output value when

the digital input would change. However, in a real DAC it takes time for the DAC to reach the actual expected output value.

Choosing a DAC

ErrorThere are multiple sources of error in computing the analog output.

Example of a DAC - AD7224

An example of a DAC would be the Analog Devices AD 7224 D/A Converter. The AD7224 is a precision 8-bit, voltage-output, digital-to-analog converter with an output amplifier.

Specifications:

DAC Type – R-2R Voltage Out

Input – Dual 8 Bit

Reference voltage – Non-Multiplier

2v – 12.5v

Settling Time - 7μs

Cost - Under $4.00

Example of a DAC - AD7224

Types of DAC Circuits

1. Resistor String2. N-Bit Binary Weighted Resistor3. R-2R Ladder4. PWM DAC

Resistor String DAC

3 Bit Resistor String DACComponents of a String DAC

•Resistor String

• Selection Switches

• Opamp

Resistor String DAC

How many internal components would be needed to create an 8 bit resistor string DAC?

Number of Resistors =

Number of Switches =

Impractical for a DAC with more than a couple bits input.

255122 81

0

in

i

25622 8 n

Weighted Resistor DAC

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

R/2

Vout

refV

Weighted Resistor Example

...

8424321

R

V

R

V

R

V

R

VRV foutSumming op-Amp:

•Vref = -2V•Digital word = 1010•V1 = -2V•V2 = 0V•V3 = -2V•V4 = 0V•Rf = R/2

VVout 25.18

0

4

2

2

0

1

2

2

1

-

+

R

2R

4R

8R

Rf

Vout

refV

V1

V2

V3

V4

Weighted Resistor Summary Advantages

Simple Fast

Disadvantages Need large range of resistor values (2000:1 for 12-bit)

with high precision in low resistor values Need very small switch resistances

Summary Use in fast, low-precision converter

R-2R DACBasic Idea:

•Use only 2 resistor values•Use equal resistances in parallel to halve the resistance•Creates a series of voltage dividers cutting voltages in half•Another summing op-amp

R-2R Example•Digital word = 001•V0 has two 2R resistances in parallel connected to ground

•Equivalent of R between V0 and ground•V1 now has a resistance R to V0 and R to ground

•V0 = V1/2•V1 has two 2R resistances to ground•Equivalent of R between V1 and ground

•V2 now has a resistance R to V1 and R to ground•V1 = V2/2•V2 = Vref

•V0 = V2/4•V0 = Vref/4•Vout = -V0/2•Vout = -Vref/8

R-2R Summary

Advantages Only 2 resistor values

Summary Better than weighted resistor DAC

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

•N-bit digital words updated at rate f

•DAC clock must run at rate 2n*f

•Example:

•Desired output = 7V, supply voltage = 10V

Operate 10V at 70% duty cycle to approximate 7V

•In practice: use counter, comparator, clock, integrator

PWM Summary

Advantages All digital Cheap

Disadvantages High sampling rate required Sensitive to clock variations

Summary Best when load is a (relatively) slowly

responding system

Errors

Errors

Gain Error Offset Error Full Scale Error Linearity Non-Monotonic Output Error Settling Time and Overshoot Resolution

Gain Error

Slope deviation from ideal gain

Low Gain Error: Step Amplitude is less than ideal

High Gain Error: Step Amplitude is higher than ideal

Offset Error

The voltage is offset from zero when all input bits are low

Full Scale Error

Combination of gain error and offset error

Non-Linearity

The linearity error is due to the fact that the resolution of the converter is not constant.

Non-linearity

The largest difference between the actual and theoretical output as a percentage of full-scale output voltage

Non-linearity

It is the difference of tension obtained during the passage in the next digital code.

Should be 1 LSB in theory.

Non-monotonic Output Error

A form of non-linearity due to errors in individual bits of the input

Settling Time and Overshoot

Changes in input are not reflected immediately in the output

Lag times result

Resolution Errors

Inherent errors associated with the resolution More Bits = Less Error and Greater

Resolution Less Bits = More Error and Less

Resolution

Applications

Programmable gain OpAmps

Voltage controlled Amplifier (digital input, Vref as control)

Digitally operated attenuators (Vref as input, digital control)

Programmable Filters

Integrate DACs in filters

Variable cutoff frequency commanded by a digital signal

DAC Applications

Used at the end of a digital processing chain when analog signals are required

Digital Audio CD Players, digital telephones, etc.

Industrial Control Systems Motor speed, valves, etc.

Waveform Function Generators Cruise Control

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://www.me.gatech.edu/charles.ume/me6405Fall01/ClassNotes/DA_fall_01.ppt

http://products.analog.com/products/info.asp?product=AD7224 Analog Devices AD 7224 DAC General Overview and Specifications

http://courses.washington.edu/jbcallis/lectures/C464_Lec5_Sp-02.pdf D/A Converter  Fundamentals and Definition Of Terms

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