Digital to Analog Conversion ME4447: Introduction to Mechatronics

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Digital to Analog ConversionME4447
Introduction to Mechatronics

• March 25, 2002

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DAC Lecturers

• Yusuf Rashada
• Julien Pennecot
• Nurudeen Olayiwola

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DAC Lecture Outline

• What is DAC?
• Types of DAC
• Explain/Discuss
• Binary Weighted Resistor
• R-2R Ladder
• Discuss DAC Specifications
• Resolution
• Speed

• Linearity
• Settling Time
• Reference Voltages
• Errors
• Applications
• Conclusion

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What is DAC?

• Circuit that produces analog current or voltage
• Output proportional to analog reference (Vref or
  Iref) and an N-bit Binary Word
• Vout k x Vref x (Binary Word)

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What is DAC? (continued)

• Generate piecewise continuous Analog signals from
  digital input or coding
• Receives a Binary Word from the microprocessor
• Converts it to a scaled analog voltage or current

N-Bit Binary Word
Analog Reference Voltage (Vref)
Digital to Analog Converter
Analog Output (Vout)
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Types of DAC

• Multiplying DAC
• reference source external to DAC package
• Nonmultiplying DAC
• reference source inside DAC package
• Multiplying DAC is advantageous considering the
  external reference.

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Advantages of Multiplying DAC

• External Ref Time Varying Analog Voltage
• multiplies binary function
• scales CONTINUOUS output

• External Ref Fixed Reference Voltage
• less error due to drifting than internal
  reference sources

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Two Types of DAC Circuits

• N-Bit Binary Weighted Resistor
• R-2R Ladder

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N-Bit Binary Weighted Resistor
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Weighted Resistor Principles
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Weighted Resistor Principles

• V0 RfI0
• V0 voltage output from amplifier
• Rf feedback resistance
• Resolution VR/2N
• For a gain of 1, Rf .5R

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Example Problem

• Find output voltage and current for a binary
  weighted resistor DAC of 4 bits where
• R 10 kOhms, Rf 5 kOhms and VR -10 Volts.
  Applied binary word is 1001

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Example Solutions
Rf (R/2)
Vo
R
2R
4R
8R
1-bit MSB
2-bit
3-bit
4-bit
VR
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Solutions (Continued)
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Solutions (Continued)
Binary Word input 10012 910 From example, V0
5.625V Vout k x Vref x (Binary Word) V0/VR
5.625V/10V 9/16
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Weighted Resistor Limitations

• Has problems if bit length is longer than 8 bits
• For example, if R 10 kOhms
• R8 28-1(10 k Ohms) 1280 kOhms
• If VR 10 Volts,
• I8 10V/1280 k Ohms 7.8 ?A
• Op-amps that handle these currents are expensive
  because these currents are below the
  current-noise threshold.

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Weighted Resistor Limitations (Contd)

• Has problems if R is too small
• For example, If R 100 Ohms and Vref 10 V
• I VR/R 10V/100 Ohms 100 mA
• This current is more than a typical op-amp
• can handle.

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Solution R-2R Ladder

• Only two resistor values
• Resolves BWL problems
• Most popular single package DAC

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Equations governing R/2R
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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

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problems

• HC11 do not have any DAC built in
• For the R-2R or the BWL, the electronic switches
  are hard to implement

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Solution

• Get a signal using output compares
• Averaging the output compare signal

• Output voltage proportional to duty cycle
• Easily programmable using output compares
• RC must be chosen adequately

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DAC Specifications

• RESOLUTION
• -LINEAR RELATIONSHIP, BETWEEN RESOLUTION AND
  NUMBER OF BITS
• -COMMONLY USED NUMBER OF BITS IS 8 BIT
• -12 BIT DAC IS USED IN HIGH END APPLICATIONS
• LINEARITY
• MAX. DEVIATION OVER FULL RANGE OF OUTPUT.
• SETTLING TIME
• TYPICAL CONVERSION TIMES (10NS TO 1 MICROSEC)
• REFERENCE VOLTAGE
• THIS COULD BE EITHER INTERNAL OR EXTERNAL,
  EXTERNAL IS PREFERRED BECAUSE INTERNAL CAUSES
  HIGH UNDESIRABLE TEMPERATURE.

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Errors of the DAC

• 10 different errors will be discussed

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Resolution error

• It will will give a more precise reading with
  larger number of bits.

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Settling time and overshoot

• Any change in the input state will not be
  reflected in the output state immediately. There
  is some sort of lag, between the two events.

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Absolute accuracy error

• Difference between theoretical and actual output.
  A percentage of the full scale output value.

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Conversion speed

• Inputs that fluctuate rapidly require high
  conversion speed, to obtain an accurate
  conversion, most digital sources are fast

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Non Monotonicity

• When there is an increased input, it sometimes
  decreases the Vo. A monotonic DAC yields an
  increase in output as input increases. It should
  basically be linear.

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Differential Non-Linearity

• Deviation of actual converter step size from the
  ideal (theoretical) predicted wave step.
• It is a measure of the worst variation in analog
  step size from the ideal step over the full range
  of the DAC.

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Gain error

• Gain too low same analog ouput
• Gain too high output is too large.
• It is an error in the slope of the DA transfer
  function.

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Offset error

• There is a default error in the DAC

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Resistance error

• Due to many resistors, they tend to affect the
  performance of the DAC

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Saturation error

• Due to the use of Op-Amps the voltage scaling has
  to be bounded by the spec. of the op-amp.

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DAC Applications

• Control Systems
• Ex. Motor Speed Control
• Digital Audio
• Digital Telephones
• Cruise Control
• Waveform Generation
• Ex. Oscilloscope

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Conclusion

• General Equation
• Vout k x Vref x (Binary Word)
• Types of DAC
• Binary Weighted Resistor
• R-2R Ladder
• Limitations and Errors