Heather Humphreys

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Digital to Analog Conversion

• Heather Humphreys
• Cheng Shu Ngoo
• Woongsik Ham
• Ken Marek

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Topics Discussed
Woongsik Ham

• What is a DAC?
• Applications
• Types of DAC circuit
• Binary weighted DAC
• R-2R Ladder DAC
• Specifications of DAC
• Resolution
• Reference Voltage
• Speed
• Settling Time
• Linearity
• DAC associated errors

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What is a DAC?
Woongsik Ham

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

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Principal components of DAC
Woongsik Ham
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What is a DAC?
Woongsik Ham

• Digital ? Analog
• Each binary number sampled by the DAC corresponds
  to a different output level.

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Woongsik Ham
Typical Output DACs capture and hold a number,
convert it to a physical signal, and hold that
value for a given sample interval. This is known
as a zero-order hold and results in a piecewise
constant output.
DAC
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Types of DAC
Woongsik Ham

• 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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Common Applications
Woongsik Ham

• Used when a continuous analog signal is required.
• Signal from DAC can be smoothed by a Low pass
  filter

Piece-wise Continuous Output
Analog Continuous Output
Digital Input
n bit DAC
0 bit
011010010101010100101 101010101011111100101 000010
101010111110011 010101010101010101010 111010101011
110011000 100101010101010001111
Filter
nth bit
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Common ApplicationsFunction Generators
Woongsik Ham

• Digital Oscilloscopes
• Digital Input
• Analog Ouput

• Signal Generators
• Sine wave generation
• Square wave generation
• Triangle wave generation
• Random noise generation

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Woongsik Ham
Applications Video Video signals from digital
sources, such as a computer or DVD must be
converted to analog signals before being
displayed on an analog monitor. Beginning on
February 18th, 2009 all television broadcasts in
the United States will be in a digital format,
requiring ATSC tuners (either internal or set-top
box) to convert the signal to analog.
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Common ApplicationsMotor Controllers
Woongsik Ham

• Cruise Control
• Valve Control
• Motor Control

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Types of DAC
Woongsik Ham

• 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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Types of DAC implementations
Ken Marek

• Binary Weighted Resistor
• R-2R Ladder
• Pulse Width Modulator (not covered)
• Oversampling DAC (used internally in HCS12)

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Binary Weighted Resistor
Ken Marek

• Start with summing op-amp circuit
• Input voltage either high or ground
• Adjust resistor weighting to achieve desired Vout

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Binary Weighted Resistor
Ken Marek

• Details
• Use transistors to switch between high and ground
• Use resistors scaled by two to divide voltage on
  each branch by a power of two
• V1 is MSB, V4 LSB in this circuit
• Assumptions
• Ideal Op-Amp
• No Current into Op-Amp
• Virtual Ground at Inverting Input
• Vout -IRf

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Binary Weighted Resistor
Ken Marek

• Assume binary inputs B0 (LSB) to Bn-1 (MSB)
• Each Bi 1 or 0 and is multiplied by Vref to get
  input voltage

B5
B4
B3
B2
B1
B0
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Binary Weighted Resistor
Ken Marek

• Example take a 4-bit converter, Rf aR
• Input parameters
• Input voltage Vref -2V
• Binary input 1011
• Coefficient a ½

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Binary Weighted Resistor
Ken Marek

• Resolution find minimum nonzero output
• If Rf R/2 then resolution isand max Vout is

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Binary Weighted Resistor
Ken Marek

• Advantages
• Simple
• Fast
• Disadvantages
• Need large range of resistor values (20481 for
  12-bit) with high precision in low resistor
  values
• Need very small switch resistances
• Op-amp may have trouble producing low currents at
  the low range of a high precision DAC

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R-2R Ladder
Ken Marek

• Each bit corresponds to a switch
• If the bit is high, the corresponding switch is
  connected to the inverting input of the op-amp.
• If the bit is low, the corresponding switch is
  connected to ground.

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R-2R Ladder
Ken Marek
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R-2R Ladder
Ken Marek

• Circuit may be analyzed using Thevenins theorem
  (replace network with equivalent voltage source
  and resistance)
• Final result is

Rf
Compare to binary weighted circuit
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R-2R Ladder
Ken Marek

• Resolution
• If Rf R then resolution isand max Vout is

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R-2R Ladder
Ken Marek

• Advantages
• Only 2 resistor values
• Lower precision resistors acceptable
• Disadvantages
• Slower conversion rate

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General comments
Ken Marek

• Circuits as shown produce only unipolar output
• Replacing ground with Vref will allow Vout to be
  positive or negative

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DAC Specifications
Cheng Shu Ngoo

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

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Reference Voltage
Cheng Shu Ngoo

• Determines Characteristic of DACs
• Set externally or Generated inside DAC
• Vref sets maximum DAC output voltage (if not
  amplified)
• Full scale output voltage
• Vref determines analog output voltage changes to
  steps taken by 1 LSB of digital input signal
  (resolution)

X analog output k Constant A Vref analog B
Binary (digital) input
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Reference Voltage
Cheng Shu Ngoo

• Internal vs. External Vref?

Internal External
Non-Multiplier DAC Vref fixed by manufacturer Qualified for specified temperature range Multiplying DAC Vary Vref Consider current required Consider Voltage range Consider dynamic effects of inner structure
Multiplying DAC is advantageous considering the
external reference.
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Resolution
Cheng Shu Ngoo

• 1 LSB (digital)1 step size for DAC output
  (analog)
• Increasing the number of bits results in a finer
  resolution
• Most DAC - 8 to 16-bits (256 to 65,536 steps)
• e.g. 5Vref DAC
• 1LSB5/28 0.0195V resolution (8-bit)
• 1LSB5/23 0.625V resolution (3-bit)

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Speed (Max. Sampling Frequency)
Cheng Shu Ngoo

• The maximum rate at which DAC is reproducing
  usable analog output from digital input register
• Digital input signal that fluctuates at/ has high
  frequency require high conversion speed
• Speed is limited by the clock speed of the
  microcontroller (input clock speed) and the
  settling time of the DAC
• Shannon-Nyquist sampling theorem ? fsampling
  2fmax
• Eg. To reproduce audio signal up to 20kHz,
  standard CD samples audio at 44.1kHz with DAC
  40kHz
• Typical computer sound cards 48kHz sampling freq
• gt1MHz for High Speed DACs

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Settling Time
Cheng Shu Ngoo

• The interval between a command to update (change)
  its output value and the instant it reaches its
  final value, within a specified percentage ( ½
  LSB)
• Ideal DAC output would be sequence of impulses ?
  Instantaneous update
• Causes
• Slew rate of output amplifier
• Amount of amplifier ringing and signal overshoot
• Faster DACs have shorter settling time
• Electronic switching ? fast
• Amplifier settling time ? dominant effect

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Settling Time
Cheng Shu Ngoo
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DAC Linearity
Cheng Shu Ngoo

• The difference between the desired analog output
  and the actual output over the full range of
  expected values
• Does the DAC analog output vary linearly with
  digital input signal?
• Can the DAC behavior follow a constant Transfer
  Function relationship?
• Ideally, proportionality constant linear slope
• Increase in input ? increase in output ?
  monotonic
• Integral non-linearity (INL) Differential
  non-linearity (DNL)

Linear
Non-Linear
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Types of DAC Errors
Heather Humphreys

• Gain Error
• Offset Error
• Full Scale Error
• Non-Monotonic Output Error
• Differential Nonlinearity Error
• Integral Nonlinearity Error
• Settling Time and Overshoot Error
• Resolution Error
• Sources of Errors

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Gain Error
Heather Humphreys

• Slope deviation from ideal gain
• Low Gain Step Amplitude Less than Ideal
• High Gain Step Amplitude Higher than Ideal

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Offset Error
Heather Humphreys

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

This error may be detected when all input bits
are low (i.e. 0).
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Full-Scale Error
Heather Humphreys

• Includes gain error and offset error
• Occurs when there is an offset in voltage form
  the ideal output and a deviation in slope from
  the ideal gain.
• Error at full scale contrast with offset error
  at zero

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Non-Monotonic Output Error
Heather Humphreys

• A form of non-linearity, due to errors in
  individual bits of the input
• Refers to output that is not monotonic

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Differential Nonlinearity Error
Heather Humphreys

• The largest difference between the actual and
  theoretical output as a percentage of full-scale
  output voltage.
• Voltage step size differences vary as digital
  input increases. Ideally each step should be
  equivalent.
• In other words, DNL error is the difference
  between the ideal and the measured output
  responses for successive steps.
• An ideal DAC response would have analog output
  values exactly one code (LSB) apart (DNL 0).

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Integral Nonlinearity Error
Heather Humphreys

• Occurs when the output voltage is non linear an
  inability to adhere to the ideal slope.
• INL is the deviation of an actual transfer
  function from a straight line. After nullifying
  offset and gain errors, the straight line is
  either a best-fit straight line or a line drawn
  between the end points of the transfer function.
• INL is often called 'relative accuracy.'

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Settling Time and Overshoot Error
Heather Humphreys

• Settling Time The time required for the voltage
  to settle within /- the voltage associated with
  the VLSB. Any change in the input time will not
  be reflected immediately due to the lag time.
• Settling time generally determines maximum
  operating frequency of the DAC
• One of the principal limiting factors of any
  commercial DAC is the settling time of the op-amp

• Overshoot occurs when the output voltage
  overshoots the desired analog output voltage.

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Resolution Errors
Heather Humphreys

• Inherent errors associated with resolution
• More Bits gt Less Error Greater Resolution
• Less Bits gt More Error Less Resolution
• Q How does very high resolution affect
  measurements?
• A LSB may be in noise range and not produce an
  output it may be difficult to find an op-amp to
  amplify such small current

Poor Resolution (1 Bit)
Better Resolution (3 Bit)
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Sources of Errors
Heather Humphreys

• Deviation of voltage sources from nominal values
• Variations and tolerances on resistance values
• Non-ideal operational amplifiers
• Other non-ideal circuit components, temperature
  dependence, etc.

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Project Applications
Woongsik Ham

• Motor speed controller
• Solenoid valves (pneumatics)
• Digital Motor Control
• Computer Printers
• Sound Equipment (e.g. CD/MP3 Players, etc.)
• Electronic Cruise Control
• Digital Thermostat

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References

• Previous student presentations and
• http//en.wikipedia.org/wiki/Digital_to_analog
• http//www.allaboutcircuits.com/vol_4/chpt_13/inde
  x.html
• Alicatore, David G. and Michael B Histand.
  Introduction to Mechatronics and Measurement
  Systems, 2nd ed. McGraw-Hill, 2003.
• http//www.emersonprocess.com/fisher/products/fiel
  dvue/dvc/
• http//auto.howstuffworks.com/cruise-control.htm
• http//www.thermionics.com/smc.htm
• Maxim AN641 Glossary
• http//www.electrorent.com/products/search/General
  _Purpose_Oscilloscopes.html
• http//www.bkprecision.com/power_supplies_supply_g
  enerators.htm
• http//hyperphysics.phy-astr.gsu.edu/hbase/electro
  nic/dac.htmlc4