Digital to Analog Converters DAC

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Digital to Analog Converters (DAC)

• Jesse Barton
• Hyun Gyu Kim
• Christopher Neel

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What is a DAC?

• A digital-to-analog converter (DAC) is a
  circuit that produces an analog current or
  voltage that is proportional to an analog
  reference (voltage or current) and an N-bit
  binary word.
• Vout k x Vref x (Binary Word)

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In English

• DACs generate piecewise continuous signals from
  digital code.
• OR
• DAC converters are devices that receive a binary
  word from the microprocessor and convert it to a
  scaled analog voltage (or current).

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DAC Configuration
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DAC Types

• Multiplying DAC
• - reference source is external to the DAC
  package
• Nonmultiplying DAC
• - reference source is inside the DAC package

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Multiplying DAC advantages

• External ref. can be time-varying analog voltage
  that multiplies binary function ?
• fixed programmable byte scales continuous
  output instead of using time-varying bytes w/
  fixed VR to produce discrete output
• External reference can be fixed ?
• less likely to produce error from reference
  voltage
• drift with temperature than internal reference

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DAC Circuit Types

• Two types of DAC Circuits
• 1. Binary weighted
• 2. R-2R ladder

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N-Bit Binary Weighted DAC
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Binary Weighted Principles
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Principles Contd

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

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Example

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

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Solution
Rf (R/2)
Vo
R
2R
4R
8R
1-bit MSB
2-bit
3-bit
4-bit
VR
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Solution Contd
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Solution Contd

• Binary input 1001 9
• From example, V0 5.625V
• V0/VR 5.625V/10V 9/16

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Limitations of the Binary Weighted DAC

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

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Limitations Contd

• If R 10 Ohms and Vref 10 V
• I VR/R 10V/10 Ohms 1 A
• This current is more than a typical op-amp
• can handle.

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Limitations Contd

• Intuitively, the resistance values must be
  accurate to less than one part in 2N for the RN
  input to be meaningful. This is difficult to do,
  especially in ICs.

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R/2R ladder DAC

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

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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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Specifications of DACs

• Resolution
• Increases (improves) as number of bits increases
• Most microcontrollers use 8 bit DAC
• Some 12 bit DAC used in high end applications
• Linearity
• Max deviation over full range of output _at_ room
  temp.
• Settling Time
• Time for DAC to come w/in 0.5 LSB Vo 0.5(VR
  /2N) of new voltage after binary change
• Typ. current output DACs conversion times (10 ns
  to 1 µs)
• Reference Voltage
• Internal / external

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DAC Errors

• Resolution
• more bits more precise
• Overshoot Settling Time
• String of amplifiers w/ feedback loops very
  rapid response or very slow response depending on
  system properties
• Absolute Accuracy Error
• Difference between theoretical and actual output
• Conversion Speed
• Rapidly fluctuating inputs require high
  conversion speed to be interpreted accurately

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DAC Errors Contd

• Non-Monotonicity
• Certain conditions where increased input results
  in decrease Vo
• Differential Non-Linearity
• Deviation of actual converter step size from the
  ideal predicted wave step
• Gain Error
• Gain too low same analog output gain too high
  too large an output
• Offset Error
• Constant error of DAC

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DAC Errors Contd

• Resistance Error
• Pertains mainly to BWR DAC since large variety of
  resistors used ? error varies greatly disturbing
  DAC performance
• Saturation
• Use of op-amps requires that input voltage and
  scaling voltages be bounded to the specifications
  of the op-amp.

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Applications of DAC

• Control Systems
• Digital Audio
• Digital Telephones
• Cruise Control
• Waveform Generation

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Discussion