Transcript Errors - Georgia Institute of Technology

Digital to Analog Converters
Tyler Smith
Brent Nelson
Jerry Jackson
10/14/04
Topics Discussed
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What is a DAC?
Choosing a DAC
Resistor String DAC
Weighted Resistor DAC
R-2R DAC
PWM
DAC associated errors
Applications
Conclusion
What is a DAC
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A digital to analog
converter (DAC) is a
device that converts
digital numbers (binary)
into an analog voltage or
current output.
Choosing a DAC
There are six main parameters that should be considered when
choosing a DAC for a particular project.
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Reference Voltage
Resolution
Linearity
Speed
Settling time
Error
Choosing a DAC
Reference Voltage
To a large extent the output properties of a DAC are
determined by the reference voltage.
Multiplier DAC – The reference voltage is constant and is set by
the manufacturer.
Non-Multiplier DAC – The reference voltage can be changed
during operation.
Choosing a DAC
Resolution
The resolution is the amount of voltage rise created by increasing
the LSB of the input by 1. This voltage value is a function of the
number of input bits and the reference voltage value.
- Increasing the number of bits results in a finer resolution
- Most DACs in the 12-18 bit range
Resolution 
Reference_ Voltage
2 nbits
Choosing a DAC
Linearity
The linearity is the relationship between the output voltage and the
digital signal input.
Choosing a DAC
Speed
Usually specified as the conversion rate or sampling rate. It is the
rate at which the input register is cycled through in the DAC.
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High speed DACs are defined as operating at greater than 1
millisecond per sample (1MHz).
Some state of the art 12-16 bit DAC can reach speeds of 1GHz
The conversion of the digital input signal is limited by the clock
speed of the input signal and the settling time of the DAC.
Choosing a DAC
Settling Time
Ideally a DAC would instantaneously change its output value when
the digital input would change. However, in a real DAC it takes
time for the DAC to reach the actual expected output value.
Choosing a DAC
Error
There are multiple sources of error in computing the analog
output.
Example of a DAC - AD7224
An example of a DAC would be the Analog
Devices AD 7224 D/A Converter. The AD7224
is a precision 8-bit, voltage-output, digital-toanalog converter with an output amplifier.
Specifications:
DAC Type – R-2R Voltage Out
Input – Dual 8 Bit
Reference voltage – Non-Multiplier
2v – 12.5v
Settling Time - 7μs
Cost - Under $4.00
Example of a DAC - AD7224
Types of DAC Circuits
1. Resistor String
2. N-Bit Binary Weighted Resistor
3. R-2R Ladder
4. PWM DAC
Resistor String DAC
3 Bit Resistor String
DAC
Components of a String DAC
•Resistor String
• Selection Switches
• Opamp
Resistor String DAC
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How many internal components would be needed to
create an 8 bit resistor string DAC?
Number of Resistors =
2n  28  256
n 1
Number of Switches =
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 2i  28 1  255
i 0
Impractical for a DAC with more than a couple bits
input.
Weighted Resistor DAC
Basic Idea:
•Use a summing
op-amp circuit
•Use transistors to
switch between
high and ground
•Use resistors
scaled by two to
divide voltage on
each branch by a
power of two
Vref
R
R/2
2R
4R
+
2nR
Vout
Weighted Resistor Example
V
V
V V

Summing op-Amp: Vout   R f  1  2  3  4  ...
 R 2 R 4 R 8R

•Vref = -2V
•Digital word = 1010
•V1 = -2V
•V2 = 0V
•V3 = -2V
•V4 = 0V
•Rf = R/2
Vout 
Vref
V1
R
V2
2R
V3
4R
Rf
-
1   2 0  2 0 
 
   1.25V

2  1 2 4 8
+
V4
8R
Vout
Weighted Resistor Summary
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Advantages
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Disadvantages
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Simple
Fast
Need large range of resistor values (2000:1 for 12bit) with high precision in low resistor values
Need very small switch resistances
Summary
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Use in fast, low-precision converter
R-2R DAC
Basic Idea:
•Use only 2 resistor values
•Use equal resistances in parallel to halve the resistance
•Creates a series of voltage dividers cutting voltages in half
•Another summing op-amp
R-2R Example
•Digital word = 001
•V0 has two 2R resistances in parallel connected to ground
•Equivalent of R between V0 and ground
•V1 now has a resistance R to V0 and R to ground
•V0 = V1/2
•V1 has two 2R resistances to ground
•Equivalent of R between V1 and ground
•V2 now has a resistance R to V1 and R to ground
•V1 = V2/2
•V2 = Vref
•V0 = V2/4
•V0 = Vref/4
•Vout = -V0/2
•Vout = -Vref/8
R-2R Summary
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Advantages
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Only 2 resistor values
Summary
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Better than weighted resistor DAC
Pulse Width Modulation
•Approximate analog signal by switching on/off at high
frequency
•Integral of output voltage from PWM ideally is the same
as integral of desired output voltage
•N-bit digital words updated at rate f
•DAC clock must run at rate 2n*f
•Example:
•Desired output = 7V, supply voltage = 10V
Operate 10V at 70% duty cycle to approximate 7V
•In practice: use counter, comparator, clock, integrator
PWM Summary
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Advantages
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Disadvantages
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All digital
Cheap
High sampling rate required
Sensitive to clock variations
Summary
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Best when load is a (relatively) slowly
responding system
Errors
Errors
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Gain Error
Offset Error
Full Scale Error
Linearity
Non-Monotonic Output Error
Settling Time and Overshoot
Resolution
Gain Error
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Slope deviation
from ideal gain
Low Gain Error:
Step Amplitude is
less than ideal
High Gain Error:
Step Amplitude is
higher than ideal
Offset Error
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The voltage is offset from zero when all input
bits are low
Full Scale Error
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Combination of gain error and offset
error
Non-Linearity
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The linearity error is due to the fact
that the resolution of the converter
is not constant.
Non-linearity
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The largest
difference between
the actual and
theoretical output
as a percentage of
full-scale output
voltage
Non-linearity
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It is the difference
of tension
obtained during
the passage in the
next digital code.
Should be 1 LSB in theory.
Non-monotonic Output Error
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A form of nonlinearity due to
errors in individual
bits of the input
Settling Time and Overshoot
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Changes in input are not reflected
immediately in the output
Lag times result
Resolution Errors
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Inherent errors associated with the
resolution
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More Bits = Less Error and Greater
Resolution
Less Bits = More Error and Less
Resolution
Applications
Programmable gain OpAmps
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Voltage controlled Amplifier (digital
input, Vref as control)
Digitally operated attenuators (Vref
as input, digital control)
Programmable Filters
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Integrate DACs in filters
Variable cutoff frequency
commanded by a digital signal
DAC Applications
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Used at the end of a digital
processing chain when analog
signals are required
Digital Audio
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Industrial Control Systems
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CD Players, digital telephones, etc.
Motor speed, valves, etc.
Waveform Function Generators
Cruise Control
References
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Alciatore, “Introduction to Mechatronics and Measurement
Systems,” McGraw-Hill, 2003
Horowitz and Hill, “The Art of Electronics,” Cambridge
University Press, 2nd Ed. 1995
http://www.me.gatech.edu/charles.ume/me6405Fall01/Cl
assNotes/DA_fall_01.ppt
http://products.analog.com/products/info.asp?product=A
D7224 Analog Devices AD 7224 DAC General Overview
and Specifications
http://courses.washington.edu/jbcallis/lectures/C464_Lec
5_Sp-02.pdf D/A Converter Fundamentals and Definition
Of Terms
http://www.eecg.toronto.edu/~kphang/ece1371/chap11_
slides.pdf Data Converter Fundamentals