ME6405 DAC Lecture

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ME6405 DAC Lecture

• Sunij Chacko
• Pierre Emmanuel Deliou
• Thomas Holst

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Overview

• What is a DAC?
• General Characteristics of DACs
• Types of DACs
• Binary Weighted Resistor
• R/2R Ladder
• Common Errors in DACs
• Applications

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Digital to Analog Converter

• What is a digital to analog converter (DAC)?
• Converts digital input signal to an analog output
  signal

0101
0011
0111
1001
1001
1010
1011
DAC
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Digital to Analog Converter
Analog Output Signal
Digital Input Signal
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What a DAC Looks Like
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General DAC Characteristics

• Resolution
• Linearity
• Speed
• Settling Time
• Reference Voltages

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Resolution

• The variation of the output voltage corresponding
  to the variation of the least significant binary
  bit (LSB)
• Inversely proportional to the number of bits
• Commonly 12-bit because of tradeoff between cost
  and resolution

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Linearity

• Consistency of step sizes

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Speed

• Rate of conversion of a single digital signal to
  its analog equivalent
• Depends on
• Clock speed of input signal
• Settling time of DAC

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Settling Time
-
½ LSB
tsettling
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Reference Voltages

• Non multiplier DAC Vref is fixedgiven by the
  Manufacturer
• Multiplier DAC Vref can be variable
• Multiplies digital word by analog Vref input

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Full Scale Voltage

• Full scale voltage is determined using the
  reference voltage

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Types of DAC

• 2. Two types of DAC
• Binary Weighted Resistor DAC
• R-2R Ladder DAC

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Binary Weighted Resistor DAC

• R/2nR DAC
• Variation on the
• inverting summer
• op-amp circuit

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Binary Weighted Resistor DACAnalysis

• Recall inverting summer Op-Amp
• Set the input resistor values at
• multiple powers of two.
• Using KCL and Op-Amp properties
• V(-) V() 0 V

Inverting summer Op-Amp
Starting from V1 and going through V3, this would
give each input voltage exactly half the effect
on the output as the voltage before it.
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Binary Weighted Resistor DAC Analysis
Binary inputs so that each input is either 0
volts or full supply voltage, the output
voltage will be an analog representation of the
binary value of these bits.
A reference voltage defines the full scale of the
converter
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Binary Weighted Resistor DAC

• The output will be

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Binary Weighted Resistor DAC

• Example

Full scale voltage
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Binary Weighted Resistor DAC

• Advantage
• Easy principle (low bit DACs)
• Disadvantages
• Requirement of several different precise input
  resistor values one unique value per binary
  input bit. (High bit DACs)
• Larger resistors more error.
• Precise large resistors expensive.
• High number of bits lead to current changes in
  the magnitude of noise amplitudes.

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R-2R Ladder DAC

• Network of R and 2R
• resistances
• Most commonly used

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R-2R Ladder DAC Analysis

• Weighting factors using Thevenin Analysis
• Summing Op-Amp Properties

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R-2R Ladder DAC Analysis
Thevenin Analysis
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R-2R Ladder DAC Analysis
Thevenin Analysis Example
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R-2R Ladder DAC Analysis
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R-2R Ladder DAC Analysis

• The output will be

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R-2R Ladder DAC

• Only two resistor values- R and 2R
• Does not need the kind of precision as Binary
  weighted DACs
• Easy to manufacture
• More popular
• Less errors

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Common DAC Errors

• 3. DAC Errors
• Gain Error
• Offset Error
• Non-Linearities
• Monotony

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Gain Error

• Distance between the theoretical value and the
  real value measured on the last transition of the
  converter and expressed in LSB.
• Assumes the adjustment of the zero is completed.

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Offset Error

• Distance between the theoretical value and the
  real value measured on the first transition of
  the converter and expressed in LSB

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Linearity

• The linearity error of is due to the fact that
  the resolution of the converter is not constant
• Two types
• Integral non linearity
• Differential non linearity

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Integral non-linearity

• It is the maximum difference noticed on all the
  range of conversion between the theoretical
  values and the real values

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Differential non linearity

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

• Should be 1 LSB in theory.

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Monotony

• Inflection in the transfer function
• For one Output value, two binary input are
  possible.

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Overall Precision

• Its the sum of all previous errors.
• Its given in a percentage of the full scale.

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Applications

• Conventional use
• Programmable gain OpAmps
• Programmable Filters
• Multiplier

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Conventional use

• Used at the end of a digital processing chain
  when an analog signal is required.
• It will be followed by a filter in order to
  abolish the steps inherent to the
  digitalization.

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Programmable gain OpAmps

• Voltage controlled Amplifier(digital input, Vref
  as control)
• Digitally operated attenuators(Vref as input,
  digital control)

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Programmable Filters

• Integrate DACs in filters
• Variable cutoff frequency commended by a digital
  signal

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References

• http//www.allaboutcircuits.com
• http//www.dwelle.de/rtc/infotheque/digital_signal
  /conversion.pdf
• http//hyperphysics.phy-astr.gsu.edu
• http//www.fujitsu.com

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Acknowledgements

• Dr. I. Charles Ume
• Teaching Assistants
• Students from previous years.

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Questions?
Questions?
Questions?
Questions?