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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.

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digital to analog converters

Digital to Analog Converters

Tyler Smith

Brent Nelson

Jerry Jackson


topics discussed
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
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
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 dac5
Choosing a DAC

Reference Voltage

To 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 dac6
Choosing a DAC


The 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

choosing a dac7
Choosing a DAC


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

choosing a dac8
Choosing a DAC


Usually 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 dac9
Choosing a DAC

Settling Time

Ideally 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 dac10
Choosing a DAC


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

example of a dac ad7224
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.


DAC Type – R-2R Voltage Out

Input – Dual 8 Bit

Reference voltage – Non-Multiplier

2v – 12.5v

Settling Time - 7μs

Cost - Under $4.00

types of dac circuits
Types of DAC Circuits

1. Resistor String

2. N-Bit Binary Weighted Resistor

3. R-2R Ladder


resistor string dac
Resistor String DAC
  • 3 Bit Resistor String DAC
  • Components of a String DAC
  • Resistor String
  • Selection Switches
  • Opamp
resistor string dac15
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.
weighted resistor dac
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
weighted resistor example
Weighted Resistor Example

Summing op-Amp:

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













weighted resistor summary
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 dac
  • Basic 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
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
R-2R Summary
  • Advantages
    • Only 2 resistor values
  • Summary
    • Better than weighted resistor DAC
pulse width modulation
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
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
  • Gain Error
  • Offset Error
  • Full Scale Error
  • Linearity
  • Non-Monotonic Output Error
  • Settling Time and Overshoot
  • Resolution
gain error
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
Offset Error
  • The voltage is offset from zero when all input bits are low
full scale error
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.


  • The largest difference between the actual and theoretical output as a percentage of full-scale output voltage
non linearity31
It is the difference of tension obtained during the passage in the next digital code.Non-linearity
  • Should be 1 LSB in theory.
non monotonic output error
Non-monotonic Output Error
  • A form of non-linearity due to errors in individual bits of the input
settling time and overshoot
Settling Time and Overshoot
  • Changes in input are not reflected immediately in the output
  • Lag times result
resolution errors
Resolution Errors
  • Inherent errors associated with the resolution
    • More Bits = Less Error and Greater Resolution
    • Less Bits = More Error and Less Resolution
programmable gain opamps
Programmable gain OpAmps
  • Voltage controlled Amplifier (digital input, Vref as control)
  • Digitally operated attenuators (Vref as input, digital control)
programmable filters
Programmable Filters
  • Integrate DACs in filters
  • Variable cutoff frequency commanded by a digital signal
dac applications
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
  • Alciatore, “Introduction to Mechatronics and Measurement Systems,” McGraw-Hill, 2003
  • Horowitz and Hill, “The Art of Electronics,” Cambridge University Press, 2nd Ed. 1995
  • Analog Devices AD 7224 DAC General Overview and Specifications
  • D/A Converter  Fundamentals and Definition Of Terms
  • Data Converter  Fundamentals