Introduction to Mechatronics

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Digital to Analog Converters
Andrew Gardner Muhammad Salman David
Fernandes Jevawn Roberts
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Outline
What is a DAC? Different Types of DACs Binary
Weighted Resistor R-2R Ladder Specifications Comm
only used DACs Application
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Introduction A DAC is a Digital to Analog
converter. It converts a binary digital number
into an analog representation, most commonly
voltage though current is also used sometimes.
0101
0011
0111
1001
1001
1010
1011
DAC
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Introduction Each binary number sampled by the
DAC corresponds to a different output level.
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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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Binary Weighted Resistor DAC

• Utilizes a summing op-amp circuit
• Weighted resistors are used to distinguish each
  bit from the most significant to the least
  significant
• Transistors are used to switch between Vref and
  ground (bit high or low)

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Summing OP-Amps

• Inverting summer circuit used in Binary Weighted
  Resistor DAC.
• V(out) is 180 out of phase from V(in)

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Binary Weighted Input DAC

• Ideal Op-amp
• No current into
• op-amp
• Virtual ground at
• inverting input
• Vout -IRf

MSB
LSB
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Calculation
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Contd

• Example

n totalbits
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Advantages and Disadvantages

• Advantage
• Easy principle/construction
• Fast conversion
• Disadvantages
• Requirement of several different precise input
  resistor values Requires large range of
  resistors (20481 for 12-bit DAC) with necessary
  high precision for low resistors one unique value
  per binary input bit. (High bit DACs)
• Larger resistors more error.
• Precise large resistors expensive.

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R-2R Resistor Ladder DAC
Vref
MSB
LSB
Bit 0 0 0 0
Vout
4-Bit Converter
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R-2R DAC Example
V0
V1
V2
Vref

• Convert 0001 to analog

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R-2R DAC Example (cont.)
V0
V1
V0
V1

Nodal Analysis
Likewise,
Voltage Divider
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Conversion Equation
For a 4-Bit R-2R Ladder
For general n-Bit R-2R Ladder Binary Weighted
Resister DAC
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R-2R DAC Summary

• Advantages
• Only two resistor values
• Does not need as precision resistors as Binary
  weighted DACs
• Cheap and Easy to manufacture
• Disadvantages
• Slower conversion rate

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DAC Specification

• Resolution
• Reference Voltage
• Speed
• Settling Time
• Linearity

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Resolution

• The change in output voltage for a change of the
  LSB.
• Related to the size of the binary representation
  of the voltage. (8-bit)
• Higher resolution results in smaller steps
  between voltage values

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Reference Voltage

• Multiplier DAC
• Reference voltage is a constant set by the
  manufacturer
• Non-Multiplier DAC
• Reference voltage is variable
• Full scale Voltage
• Slightly less than the reference voltage
  (Vref-VLSB)

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Speed

• Also called the conversion rate or sampling rate
• rate at which the register value is updated
• For sampling rates of over 1 MHz a DAC is
  designated as high speed.
• Speed is limited by the clock speed of the
  microcontroller and the settling time of the DAC

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Settling Time

• Time in which the DAC output settles at the
  desired value ½ VLSB.
• Faster DACs decrease the settling time

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Linearity

• Represents the relationship between digital
  values and analog outputs.
• Should be related by a single proportionality
  constant. (constant slope)

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DAC Error

• Non-Linearity
• Differential
• Integral
• Gain Error
• Offset Error
• Monotonicity
• Resolution

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Non-linearity

• Deviation from a linear relationship between
  digital input and analog output.

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Non-Linearity

• Differential
• Worst case deviation from the ideal VLSB step for
  an increment of LSB
• Integral
• Worst case deviation from the line between the
  endpoint (zero and full scale) voltages

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Gain Error

• Also called Full-Scale Error
• Deviation from the ideal full scale voltage due
  to a higher or lower gain than expected.

High Gain
Desired/Ideal Output
Analog Output Voltage
Low Gain
Digital Input
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Offset Error

• Also called Zero Error
• Difference between ideal voltage output and
  actual voltage output for a digital input of zero.

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Monotonicity

• Increases or decreases of the digital value must
  correspond to increases or decreases of the
  voltage output.

Non-monotonic behavior
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Resolution Error

• For matching curves over time or simply
  outputting accurate values a proper resolution
  must be selected
• Resolution must be high enough for the desired
  precision (½ VLSB)

Vout
Desired Analog signal
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10
01
00
Time
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Applications Audio Many audio signals are
stored as binary numbers (on media such as CDs
and in computer files such as MP3s). Therefore
computer sound cards, stereo systems, digital
cell phones, and portable music players contain
DAC to convert the digital representation to an
analog signal.
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Example DAC

• AD 7224
• Manufactured by Analog Devices
• Type R-2R Voltage Output
• Reference voltage Non-Multiplier
• 2 12.5 Volts
• 8-bit Input
• Settling Time 7 µs
• Cost about 4.00

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Example DAC
18 Pin integrated circuit including output
amplifier
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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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References Previous Student Lectures http//en.wik
ipedia.org/ http//allaboutcircuits.com
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Questions