Transcript Lecture_High speed DAC

Digital to Analog Converter
(DAC)
Prepared by:
Amr Hatem
Kirolos Shokry
Ibrahim Emad
Mina Ashraf
Mina Samy
Mourad Ghorab
Supervised by:
Dr. Mohamed Abd El Ghany
Outline







Introductions
Binary Converter
R-2R Circuit
IC DAC
Filters
Specs
Applications
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.
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
DAC
Each binary number sampled by the DAC corresponds to a different output level.
Analog Output Signal
•
0
1
0
1
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011
Digital Input Signal
History Of Data Converters
•
•
•
•
•
The earliest recorded binary DAC known is not electronic at all, but hydraulic.
Turkey, in the early 19th century, they had problems with its public water supply
systems were built to meter water
The metering system used
reservoirs (header tank)
maintained at a constant depth
The water output from the
header tank is controlled by
gated binary-weighted nozzles
The output of the nozzle sizes
corresponded to flows of binary
multiples and sub-multiples
This is functionally an 8-bit DAC
with manual input
History Of Data Converters
•
the single largest driving force behind the
development of electronic data converters
over the years has been the field of
communications. The telegraph led to the
invention of the telephone
•
the rapid demand for more capacity, While
time division multiplexing (TDM) achieved
some measure of popularity, frequency
division multiplexing (FDM) using various
carrier-based systems widely used. It was
pulse code modulation (PCM)
•
All of this invention paved the road for the
first telephone which also start the
revolution conversion between the analog
and digital signals.
Applications of DAC
NOT JUST AUDIO !
Audio
DACs are found in CD players, digital music
players, and PC sound cards.
Video
HDMI
DVI
RAMDAC
Other usages
Mechanical
whiffletree electromechanical digital-to-analog
converter linkage in the IBM Selectric typewriter
the main purpose of the DAC
 To convert digital values to analog voltages
is a function that converts digital data (usually binary) into an analog
signal (current, voltage, or electric charge)
 Performs inverse operation of the Analog-to-Digital Converter
(ADC)
Unlike analog signals, digital data can be transmitted, manipulated,
and stored without degradation

Reference Voltage
Digital Value
DAC
Analog Voltage
•
Connecting digital circuitry to sensor devices is simple if the
sensor devices are inherently digital themselves.
•
An ADC inputs an analog electrical
signal such as voltage or current and
outputs a binary number. In block
diagram form, it can be represented as
such:
However, when analog devices are involved, interfacing
becomes much more complex. An analog-to-digital
converter, performs the former task while a digital-to-analog
converter, or DAC, performs the latter.
Together, they are often used in digital systems to
provide complete interface with analog sensors and
output devices for control systems such as those used in• A DAC, on the other hand, inputs a
binary number and outputs an analog
automotive engine controls:
voltage or current signal. In block
diagram form, it looks like this:
•
Types Of DACs
 Types
There are several DAC architectures; the suitability of a DAC for a
particular application is determined by six main parameters:
physical size, power consumption, resolution, speed, accuracy,
cost. Due to the complexity and the need for precisely matched
components, all but the most specialist DACs are implemented as
integrated circuits (ICs).


Binary Weighted Resistor
R-2R Ladder
 Characteristics


Comprised of switches, op-amps, and resistors
Provides resistance inversely proportion to significance of bit
Binary Weighted Resistor
Rf = R
R
2R
4R
Vo
8R
MSB
LSB
-VREF
Binary Weighted Resistor
Rf = R
Inverting summer circuit used in
Binary Weighted Resistor DAC
Vo
R
2R
4R
8R
Vo is 180° out of
phase from Vin
MSB
LSB
-VREF
11
Binary Weighted Resistor
Rf = R
Transistors are used
to switch between
Vref and ground (bit
high or low)
R
2R
Most
Significant Bit
Vo
8R
4R
CLEARED
SET
Least
Significant Bit
-VREF
(1
1
1
1)2 =(15)10
12
Binary Weighted Resistor
 “Weighted
Resistors” based
on bit
 Reduces current
by a factor of 2
for each bit
Rf = R
R
2R
4R
Vo
8R
MSB
LSB
-VREF
(1
1
1
1)2 =(15)10
13
Binary Weighted Resistor
 Result:

Bi = Value of Bit i
14
Binary Weighted Resistor
 More Generally:


Bi = Value of Bit i
n = Number of Bits
15
Advantages and Disadvantages
16
N-bit binary weighted Example
• Find
output voltage, current, and resolution for a binary weighted
resistor DAC of 4 bits for given condition :
-R = 10 kΩ
- Rf = 5 kΩ
-VRef = -10V
Applied binary word is 1001
17
Example Solutions
18
Example Solutions (Cont.)
VLSB
19
R-2R Ladder
R-2R Ladder
R-2R Ladder
R-2R Ladder
R-2R Ladder
Pros & Cons
Binary Weighted
R-2R
Pros
Easily understood
Only 2 resistor values
Easier implementation
Easier to manufacture
Faster response time
Cons
Limited to ~ 8 bits
Large # of resistors
Susceptible to noise
Expensive
Greater Error
More confusing analysis
25
• D/A converters are available
commercially as integrated circuits
which Can be classified in three
categories :
Current output DAC provides the current IO as
output signal
Voltage output D/A converts IO into voltage
internally by using an op amp and provides the
voltage as output signal
In multiplying DAC, the output is product of the input
voltage and the reference source VREF.
• Digital-to-Analog Converters:
A D/A converter takes an input signal in binary form and produces an output voltage or
current in an analog (or continuous) form. A block diagram of an n-bit D/A converter
consisting of binary digits (b1b2 ... bn) . It is assumed that the converter generates the
binary fraction, which is multiplied by the full-scale voltage VFS to give the output voltage,
expressed by
where the ith binary digit is either bi 0 or bi 1 and b1 is the most significant bit (MSB). For
example, for VFS 5 V, n 3, and a binary word b1b2b3 110, Eq. (1.2) gives VO
What will be the analog equivalent of 1001
0001?
Integrated Circuit D/A Converters
• Switches in IC D/A converters are made either of BJTs or
of MOSFETs. They are generally one of two types:
 voltage driven
 current driven
• Voltage-driven converters, which use BJTs or MOSFETs as on or off
switches, are generally used for relatively low-speed low-resolution
applications
• current-driven converter, switching is accomplished using emittercoupled logic (ECL) current switches, which do not saturate but are
driven from the active region to cutoff
The MC1408 is an example of a D/A converter with current output. It is a low-cost, high-speed
converter designed for use in applications where the output current is a linear product of an 8bit digital word and an analog reference voltage. Its internal block diagram, shown in Fig.
16.75(a), consists of four parts: current switches, an R-2R ladder, a biasing current network, and
a reference current amplifier. The connection diagram is shown in Fig. 16.75(b)
The NE/SE-5018 is an example of a D/A converter with voltage output. It gives an output voltage
that is a linear product of an 8-bit digital word and an analog reference voltage. Its internal
block diagram is shown in Fig. 16.76(a). A typical configuration of the 5018 is shown in Fig.
16.76(b)
Reconstruction Filtering


Used when a continuous analog signal is required.
Signal from DAC can be smoothed by a Low pass filter
Piece-wise Continuous
Output
Analog
0 bit
011010010101010100101
101010101011111100101
000010101010111110011
010101010101010101010
111010101011110011000
100101010101010001111
n bit DAC
Continuous
Output
Filter
nth bit
33
Reconstruction Filtering
34
Reconstruction Filtering



In (a) original analog signal is represented in the time
domain
In (b) original analog signal is represented in frequency
domain, where it expends from frequencies 0 to <0.5 of fs
(sampling frequency)
In (c) the signal is sampled by converting it to impulse
train (ideal case). This corresponds to duplication of
spectrum into an infinite number of upper and lower
35
sidebands in (d).
Reconstruction Filtering


Since original frequencies in (b) remain undistorted in (d),
this means that proper sampling took place.
In (e) the sampling rate is less than fs, violating Nyquist
theorem. This results in overlapping spectra in the
frequency domain causing aliasing as shown in (f).
36
Reconstruction Filtering
37
Reconstruction Filtering



In the real world, it’s difficult to generate the previously
shown impulse train. All DAC (digital to analog
conversion) operate by holding last value until another
sample is received. This produces staircase as shown in
figure (c). This is called “zeroth-order hold”.
The “zeroth-order hold” could be understood as the
convolution in the time domain of the previously shown
impulse train and a rectangular pulse of width equal to the
sampling period.
This convolution is equivalent to the multiplication in the
frequency domain between the correct spectrum and the
Fourier transform of the rectangular pulse (the sinc
function) as shown in figure (d).
38
Reconstruction Filtering
39
Reconstruction Filtering

a)
b)
Therefore, the filter needs to:
Remove all frequencies above one half of fs.
Boost frequencies by the reciprocal of zeroth order hold
effect 1/sinc(x), as shown in figure (e).
40
Performance Specifications
•
•
•
•
•
Resolution
Settling time
Linearity
Speed
Errors
41
Resolution
• Resolution: is the amount of variance in output voltage for
every change of the LSB in the digital input.
• As no. of bits available for digital representation increases, as
resolution becomes better.
• For exact reconstruction of analog signals, there must be
infinite number of bit.
• A common DAC has a 8 - 12 bit Resolution
42
N = Number of bits
Resolution
Better Resolution(3 bit)
Poor Resolution(1 bit)
Vout
Vout
Desired Analog signal
Desired Analog signal
111
110
0
Approximate
output
8 Volt. Levels
2 Volt. Levels
1
0
Digital Input
101
100
011
010
001
110
101
100
011
010
001
43
000
000
Approximate
output
Digital Input
Settling Time
• Settling Time: The time required for the input signal voltage to
settle to the expected output voltage.
• Any change in the input state will not be reflected in the
output state immediately. There is a time lag, between the two
events.
44
Linearity
• Linearity: is the difference between the desired analog output
and the actual output over the full range of expected values.
• Ideally, a DAC should produce a linear relationship between a
digital input and the analog output, this is not always the case.
45
Linearity
NON-Linearity(Real World)
Desired/Approximate Output
Desired Output
Analog Output Voltage
Analog Output Voltage
Linearity(Ideal Case)
Approximate
output
Digital Input
Perfect Agreement
Digital Input
Miss-alignment
46
Speed
• Speed: Rate of conversion of a single digital input to its analog
equivalent
• Conversion Rate
a)
b)
Depends on clock speed of input signal
Depends on settling time of converter
47
Errors
• Non-linearity
a) Differential
b) Integral
• Gain
• Offset
48
Differential Non-Linearity
Analog Output Voltage
 Differential Non-Linearity: Difference in voltage step size
from the previous DAC output (Ideally All DLN’s = 1
VLSB)
Ideal Output
2VLSB
Diff. Non-Linearity = 2VLSB
VLSB
Digital Input
49
Integral Non-Linearity
• Integral Non-Linearity: Deviation of the actual DAC output
from the ideal (Ideally all INL’s = 0)
Analog Output Voltage
Ideal Output
Int. Non-Linearity = 1VLSB
1VLSB
50
Digital Input
Gain
• Gain Error: Difference in slope of the ideal curve and the
actual DAC output
High Gain
Desired/Ideal Output
slope greater than ideal
Low Gain Error: Actual
slope less than ideal
Analog Output Voltage
High Gain Error: Actual
Low Gain
51
Digital Input
Offset
• Offset Error: A constant voltage difference between the ideal
DAC output and the actual.
• DAC=0, but Vout ≠ 0
Output Voltage
Desired/Ideal Output
Positive Offset
Negative Offset
Digital Input
52
Applications – Audio
Many audio signals are stored as binary numbers (on media such as CDs and in co
Applications – Video
Video signals from digital sources, such as a computer or DVD must be converted
Other Applications
References








Cogdell, J.R. Foundations of Electrical Engineering. 2nd ed. Upper Saddle River, NJ: Prentice
Hall, 1996.
“Simplified DAC/ADC Lecture Notes,” http://www-personal.engin.umd.umich.edu/
~fmeral/ELECTRONICS II/ElectronicII.html
“Digital-Analog Conversion,” http://www.allaboutcircuits.com.
Barton, Kim, and Neel. “Digital to Analog Converters.” Lecture, March 21, 2001.
http://www.me.gatech.edu/charles.ume/me4447Spring01/ClassNotes/dac.ppt.
Chacko, Deliou, Holst, “ME6465 DAC Lecture” Lecture, 10/ 23/2003,
http://www.me.gatech.edu/mechatronics_course/
Lee, Jeelani, Beckwith, “Digital to Analog Converter” Lecture, Spring 2004,
http://www.me.gatech.edu/mechatronics_course/
http://www.analog.com/media/en/training-seminars/tutorials/MT-015.pdf
http://www.analog.com/library/analogDialogue/archives/3906/Chapter%201%20Data%20Converter%20History%20F.pdf