Andrew Gardner
Muhammad Salman
David Fernandes
Jevawn Roberts
Introduction to Mechatronics
Student Lecture – 10/23/06

What is a DAC?
Different Types of DACs
Binary Weighted Resistor
R-2R Ladder
Specifications
Commonly used DACs
Application
Introduction to Mechatronics
Student Lecture – 10/23/06

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.
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
DAC
Introduction to Mechatronics
Student Lecture – 10/23/06

Each binary number sampled by the DAC corresponds to a different output level.
0000 0001 0010 0011 0100 0101 0110 0111 1000
Digital Input Signal
1001 1010 1011
Introduction to Mechatronics
Student Lecture – 10/23/06

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
Ideally Sampled Signal
Output typical of a real, practical
Introduction to Mechatronics DAC due to sample & hold
Student Lecture – 10/23/06

• 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
V ref and ground (bit high or low)
Introduction to Mechatronics
Student Lecture – 10/23/06

• Inverting summer circuit used in Binary
Weighted Resistor DAC.
• V(out) is 180° out of phase from V(in)
Introduction to Mechatronics
Student Lecture – 10/23/06

• Ideal Op-amp
• No current into
V ref
V
1 R op-amp
• Virtual ground at
V
2
V
3
2R
4R
V out
 
IR f
 
R f
V n 2 n-1 R inverting input
MSB
•
V out
= IR f
V
1

R
V
2
2 R

V
3
4 R
 
V n
2 n 1
R
I
-
+
LSB
Rf
V ou t
Introduction to Mechatronics
Student Lecture – 10/23/06

V
OUT
 
V ref

R ( b n

1
2 R
 b n

2
4 R

...
 b
0
2 n
R
V
OUT


V ref
2 n
( 2 n

1  b n

1

2 n

2  b n

2

...

2
 b
1
 b
0
Introduction to Mechatronics
Student Lecture – 10/23/06

 Example: n

4
V out


V ref
2 n
( 2 n

1 b n

1

2 n

2 b n

2

...

2 b
1
 b
0
)
V out


V ref
16
( 8 b
3

4 b
2

2 b
1
 b
0
)
V out
V fs



V
16
V ref ref
( 8 ( 0 )


4 (
R
ES
0 )

2 ( 1 )

1 ( 1 ))


3
V ref
16
R
ES

1 / 2 n n = totalbits
V fs

V ref


2
4
2

1
4



0 .
9375 V ref
Student Lecture – 10/23/06

Advantage
– Easy principle/construction
– Fast conversion
Disadvantages
– Requirement of several different precise input resistor values: Requires large range of resistors
(2048:1 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.
Introduction to Mechatronics
Student Lecture – 10/23/06

V ref
MSB
Bit: 0 0 0 0
LSB
4-Bit Converter
Introduction to Mechatronics
Student Lecture – 10/23/06
V out

V
2
V
1
V
0 V ref
• Convert 0001 to analog
Introduction to Mechatronics
Student Lecture – 10/23/06

V
1
V
0 V
1
V
0
=
V
1

V
0
R

V
0
R
V
1

2

V
0
Nodal Analysis
R eq


1
1
 

  
1

R
Voltage Divider
Likewise,
V
1

R
R

R
V
2

1
2
V
2
Introduction to Mechatronics
Student Lecture – 10/23/06
V
2

R
R

R
V
3

1
2
V
3

V out
 
V ref b
3
1
2
 b
2
1
4
 b
1
1
8
 b
0
1
16
For a 4-Bit R-2R Ladder
For general n-Bit
R-2R Ladder
Binary Weighted
Resister DAC
V out
 
V ref i
 n

1 b n
 i
2 i
1
Introduction to Mechatronics
Student Lecture – 10/23/06

• Advantages
– Only two resistor values
– Does not need as precision resistors as Binary weighted
DACs
– Cheap and Easy to manufacture
• Disadvantages
– Slower conversion rate
Introduction to Mechatronics
Student Lecture – 10/23/06

• Resolution
• Reference Voltage
• Speed
• Settling Time
• Linearity
Introduction to Mechatronics
Student Lecture – 10/23/06

• 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

V ref
n
Introduction to Mechatronics
Student Lecture – 10/23/06

• 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 (V ref
-V
LSB
)
Introduction to Mechatronics
Student Lecture – 10/23/06

• 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
Introduction to Mechatronics
Student Lecture – 10/23/06

• Time in which the DAC output settles at the desired value ± ½ V
LSB
.
• Faster DACs decrease the settling time
Introduction to Mechatronics
Student Lecture – 10/23/06

• Represents the relationship between digital values and analog outputs.
• Should be related by a single proportionality constant.
(constant slope)
Introduction to Mechatronics
Student Lecture – 10/23/06

• Non-Linearity
– Differential
– Integral
• Gain Error
• Offset Error
• Monotonicity
• Resolution
Introduction to Mechatronics
Student Lecture – 10/23/06

• Deviation from a linear relationship between digital input and analog output.
Desired Output
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06

• Differential
– Worst case deviation from the ideal V
LSB increment of LSB step for an
• Integral
– Worst case deviation from the line between the endpoint (zero and full scale) voltages
Integral
Non-linearity
2V
LSB
V
LSB
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06
Digital Input

• 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
Low Gain
Student Lecture – 10/23/06

• Also called Zero Error
• Difference between ideal voltage output and actual voltage output for a digital input of zero.
Output Voltage
Ideal Output
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06

• Increases or decreases of the digital value must correspond to increases or decreases of the voltage output.
Non-monotonic behavior
Desired Output
Digital Input
Introduction to Mechatronics
Student Lecture – 10/23/06

• 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 V
LSB
)
Vout
Desired Analog signal
11
10
01
00
Introduction to Mechatronics
Time
Student Lecture – 10/23/06

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.
Introduction to Mechatronics
Student Lecture – 10/23/06

• 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
Introduction to Mechatronics
Student Lecture – 10/23/06

18 Pin integrated circuit including output amplifier
Introduction to Mechatronics
Student Lecture – 10/23/06

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 18 th ,
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.
Introduction to Mechatronics
Student Lecture – 10/23/06

Previous Student Lectures http://en.wikipedia.org/ http://allaboutcircuits.com
Introduction to Mechatronics
Student Lecture – 10/23/06

Introduction to Mechatronics
Student Lecture – 10/23/06