# Digital to Analog Conversion

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```					Digital to Analog Conversion

Presenters:
Yasmine Umbdenstock
Sylvain Vitry
Matt Boyd
2002
Outline
 What is DAC ?
 DAC specifications
   Resolution
   Speed / Settling Time
   Errors
   Linearity / Monotonicity
   Glitching noise
 Types of DAC
 Reference Voltages
 Binary Weighted Resistor
 Applications

DAC   Yasmine Umbdenstock           Sylvain Vitry   Matt Boyd
What is DAC ?
Reference Voltage   Digital-to-Analog      Output voltage     A Digital-to-Analog Converter
(Vref)                 Converter                    (Vout)    uses an analog reference
(DAC)
voltage to convert a N-bit
digital input word into an
Digital input data                        analog output signal.
(b1,b2,…,bN)

Vout = K·Vref·(b1·2-1+b2·2-2+…+bN·2-N)               K : gain of the converter

The analog output voltage can only change in discrete steps.
Practically, it is filtered to obtain a continuous signal.

DAC Output Signal       Filtered Signal

DAC                Yasmine Umbdenstock                   Sylvain Vitry              Matt Boyd
DAC Specifications

Transfer characteristic of
an ideal linear 3-bit DAC

Resolution: 1 LSB = 1V
Operating range: ΔVmax = 0–7 V
Vref = 8 V

Operating range (ΔVmax): Bounded range of possible output voltage values

ΔVm ax Vref
Resolution : Unitary step size for DAC output:      1 LSB             N
2N 1   2

DAC                Yasmine Umbdenstock               Sylvain Vitry            Matt Boyd
DAC Specifications (Cont’d)

Transfer characteristic of
an ideal linear 3-bit DAC

Dynamic range:
r = 20·log10(23-1) = 20·log10(7) ≈ 17db

Accuracy : Difference between ideal and actual output, expressed as a
percentage of the full scale output value
Ex: 10-bit DAC, resolution = 0.1%, accuracy = ±0.5 LSB = ±0.005%

Dynamic range : Range of signal amplitudes the DAC can resolve, typically
expressed in decibels
Ex: 4-bit DAC  2N -1 = 15 usable values  20·log10(15) ≈ 24db

DAC                Yasmine Umbdenstock               Sylvain Vitry             Matt Boyd
DAC specifications (Cont’d)
Output Voltage

Final output value

+½ LSB
-½ LSB

Settling Time              Time

Settling time : actual amount of time it takes a DAC output to reach its final
value (within a certain percentage) once the input state has
changed

DAC               Yasmine Umbdenstock                     Sylvain Vitry   Matt Boyd
DAC Errors
Ideal DAC DAC
Ideal         Actual DAC
Actual DAC

9

Analog output voltage (V)
8

Offset error                                                                     7
6
5
Offset Error = +1.5 LSB
Difference between the actual                                                             4

and the ideal output voltage                                                              3
2
for digital input code 0                                                                  1
0

000

001

010

011

100

101

110

111
Digital input code

Ideal DAC DAC
Ideal         Actual DAC
Actual DAC

9
Gain error = -2LSB
Analog output voltage (V)

8
7
6
Gain error
5
4
Difference between the actual
3                                                                                                               and the ideal full scale output
2
1
(with offset error removed)
0
000

001

010

011

100

101

110

111

Digital input code

DAC                                   Yasmine Umbdenstock                                                               Sylvain Vitry                              Matt Boyd
DAC Linearity Errors
Ideal DAC DAC
Ideal           Actual DAC
ActualDAC

9

Analog output voltage (V)
8                                   DNL error = -0.5 LSB
Differential Non-Linearity error                                                                           7          DNL error = +1 LSB
6

Error in step size from ideal between                                                                                       5
4

DNL i [Vout(i 1)Vout(i)]1LSB                                                           2
1
DNL error = -0.5 LSB
0

000

001

010

011

100

101

110

111
Digital input code
Ideal DAC DAC
Ideal       Actual DAC
ActualDAC

9
Analog output voltage (V)

8
7           INL error = +0.5 LSB
Integral Non-Linearity error
6
5                                                                                              Deviation of the actual                                             transfer
4
function from the ideal one
INL i  [Vout(i 1)Vout(i)]
3
2
INL error = -0.5 LSB                                                                  i
1
0
for i=0 up to the given input
000

001

010

011

100

101

110

111

Digital input code

DAC                               Yasmine Umbdenstock                                                          Sylvain Vitry                                   Matt Boyd
Monotonicity

Non Monotonicity
An increase in the digital code results in a decrease in the output voltage
 The same output voltage can have different digital inputs

DAC                  Yasmine Umbdenstock             Sylvain Vitry           Matt Boyd
Glitching noise
Glitch Impulse Energy
160

Glitch Impulse is a measure of this
140                    Transient. Approx. of area under "Impulse"
across Delta T                               Delta T
120
Picavolt Output Voltage

100

80

60

40

20

0
Time(microsec)             4                  8               12             16

Voltage(pV)
Microseconds

Asynchronous switching of DACs
 Transient parasitic impulses in the output signal

DAC                                                Yasmine Umbdenstock                       Sylvain Vitry        Matt Boyd
Typical DAC configuration
MSB

Digital Input Buffer
Voltage
Reference

Binary                    Analog
-
Switch        +
Output
Voltage
Weighting
Summing Op Amp
Network
LSB

• Internal reference voltage
 Qualified only for a limited temperature range

• External reference voltage
 Multiplying mode possible: digital potentiometer

DAC                             Yasmine Umbdenstock                  Sylvain Vitry         Matt Boyd
Binary weighted DACs

 Binary Weighted resistor

Resistive network vs Capacitive network

DAC    Yasmine Umbdenstock        Sylvain Vitry   Matt Boyd
Digital Input Buffer (N bits)           Binary Weighted Resistor DAC
MSB           LSB
MSB
1                     I1                           Digital input : (b1, b2, …, bN)
R                                                      Vref
0                     I2                           • Ohm’s law : I i            (branch i)
2i 1  R
2R               Rf =½R                                                Vref N b i
1                     IN-1 ITot                    • Kirchhoff’s current law : I tot        
-         Vout                                         R i 1 2 i 1
2N-2R       0
1                     IN          +                                               where bi = 0 or 1
LSB             2N-1R
• Ideal Inverting Op Amp : Vout   R f  I tot
VRef
with Rf = R/2
N
bi
Vout      Vref   i   Vref  (b 1 2 1  .b 2 2  2  ..  b N 2  N )
i 1 2

Vref N               V
Vout     N   b i 2 N i   ref  (b 1 2 N 1  b 2 2 N  2  ..  b N 20 )
2    i 1             2N
Decimal equivalent of
1 LSB       the binary input word
DAC                                   Yasmine Umbdenstock                   Sylvain Vitry            Matt Boyd
Binary Weighted Resistor DAC (Cont’d)
Digital Input Buffer (N bits)

• Resolution :
MSB
1                   I1                                      V
1LSB  ref         (bi=0 for every i except i=N)
R                                            2N
0                   I2
2R               Rf =½R           • Operating range :
1                   IN-1 ITot
2N  1
-         Vout      ΔVmax          Vref  Vref  1LSB
2N-2R
+                             2N
1                   IN
LSB        2N-1R
VRef                                                     The output voltage of a DAC
can never reach Vref

Example problem :
Find Itot and Vout for a 4-bit binary weighted resistor DAC where the digital input code
is 1001, Vref = -10V and Rf = 10kΩ.
Solution :
1LSB = 10/(24) = 0.625 V                         Vout = 0.625*9 = 5.625 V
Thus
10012 = 910                                      Itot = -Vout/Rf = -2*5.625/10000 = -1.125 mA
DAC                                 Yasmine Umbdenstock                  Sylvain Vitry               Matt Boyd
Binary Weighted Resistor DAC (Cont’d)

Digital Input Buffer (N bits)
MSB
1            I1
R
0            I2
2R               Rf =½R
1            IN-1 ITot
-            Vout
2N-2R
1            IN          +
LSB    2N-1R
VRef

• Need of an accurate voltage reference and feedback resistor

• Need of an Op Amp with good characteristics

• Need of accurate resistor ratios over wide range of resistor values
 Not suitable for moderate and high-bit converters

DAC               Yasmine Umbdenstock                                              Sylvain Vitry   Matt Boyd
MSB               LSB
R                 R         2R
I1        I2        IN-1        IN                          Digital input : (b1, b2, …, bN)
VRef   2R         2R        2R          2R                                                    R                R            2R
Rf =R                           I1        I2        IN-1         IN
ITot                    VRef     2R         2R        2R          2R
-        Vout
0
MSB                                     LSB              +
1      1             0      1                                                               Vref
Ii                   (branch i)
Digital Input Buffer (N bits)                                                                      2i  R
Vref N b i
Vout  R f  I tot  R f                   i              where bi = 0 or 1
R i 1 2
N
bi
Vout      Vref   i  Vref  (b 1 2 1  .b 2 2  2  ..  b N 2  N )
i 1 2

Vref N               V
Vout     N   b i 2 N i   ref  (b 1 2 N 1  b 2 2 N  2  ..  b N 20 )
2    i 1             2N
Decimal equivalent of
1 LSB       the binary input word

DAC                             Yasmine Umbdenstock                           Sylvain Vitry                              Matt Boyd
R                R          2R
• Resolution :
I1        I2        IN-1        IN
VRef                                                                               V
2R         2R        2R          2R
1LSB  ref
Rf =R                      2N
ITot
-       Vout
0                         • Operating range :
MSB                                     LSB              +
2N  1
1      1             0      1                                       ΔVmax      N
 Vref  Vref  1LSB
Digital Input Buffer (N bits)                                                        2

The output voltage of a DAC
can never reach Vref

• Need of switches with low on-resistance and zero offset voltage
• Only two resistor values, exact value not critical
 Well-suited to integrated circuit realization

DAC                             Yasmine Umbdenstock                         Sylvain Vitry            Matt Boyd
FUNCTIONAL BLOCK DIAGRAM                              PIN CONFIGURATIONS

Resistor String      • Single 8-bit DAC                                          D
Vout  VDD 
R

R
• Guaranteed monotonic by design                           256
R
• Reference derived from power supply (2.7 V to 5.5 V)
To OUTPUT
AMPLIFIER

• Serial data input
R
Resolution= 8      Settling time= 4-6 µs  Glitch impulse= 20 nV*s
R                           Offset error= 0.5-3.5 LSB          DNL= ±0.25 LSB;
Gain error= ±1.25 LSB              INL= ±1 LSB
DAC                    Yasmine Umbdenstock             Sylvain Vitry               Matt Boyd
DAC Applications

• There are many, many systems that use digital-analog
conversion

   Oscilloscopes
   Digital Telephones
   Data Acquisition/Control Systems
   CD Players (Delta-Sigma Modulation)

DAC               Yasmine Umbdenstock       Sylvain Vitry   Matt Boyd
DAC Applications: Oscilloscopes

• This digital oscilloscope takes two analog signals and
converts them into digital form. Then they are converted
back so they can be represented as x and y amplitudes
on the screen.

DAC          Yasmine Umbdenstock    Sylvain Vitry   Matt Boyd
DAC Applications: Digital Telephones

• Digital phones take an analog voice, convert it to
digital, and then back to analog.
• Before digital technology, the signal was analog
the whole way.
• With digital technology, several signals can be
transmitted together.

DAC        Yasmine Umbdenstock   Sylvain Vitry   Matt Boyd
DAC Applications: Data Acquisition

a sensor and converts is to digital form used by the PC.
The PC user can then use the digital data or send it to
the DAC to get an analog output.

DAC          Yasmine Umbdenstock    Sylvain Vitry    Matt Boyd
DAC Applications: Control Systems

• This actuator control circuit uses a microcontroller to
open and close a valve. The DAC is used to convert the
digital signal from the microcontroller to an analog signal
used to actuate the valve.

DAC          Yasmine Umbdenstock      Sylvain Vitry    Matt Boyd
CD Players and Delta-Sigma Modulation

• The larger the number of bits, the more resistors are
required. For most CD players, a 16-bit DAC would be
required which would consist of at least 16 matched resistors.

• Instead a CD player uses a delta-sigma modulator and a 1-bit
DAC.

DAC           Yasmine Umbdenstock       Sylvain Vitry     Matt Boyd
CD Players and Delta-Sigma Modulation

• The delta-sigma modulator circuit translates a binary number into a
pulse train with a duty cycle proportional to that number. The pulse
train is then converted into an analog signal by averaging it over
time with a low-pass filter.

DAC            Yasmine Umbdenstock         Sylvain Vitry       Matt Boyd
CD Players and Delta-Sigma Modulation

Delta – this part of the circuit creates an error signal based on the difference
between the incoming binary signal and the outgoing pulse train.

Sigma – this part of the circuit adds up the results of the error signal
created by delta and supplies it to the low-pass filter

DAC                 Yasmine Umbdenstock                 Sylvain Vitry                Matt Boyd
CD Players and Delta-Sigma Modulation

• Cheap – only comprised of two summing chips, a clock, a comparator,
and a low-pass filter.
• All-digital circuit that produces an analog output.

• Large clock speed required. For an n-bit number, the clock must be 2n
times as fast as the sample rate.
• The output is very sensitive to the accuracy of the clock pulses.

DAC                Yasmine Umbdenstock           Sylvain Vitry         Matt Boyd
DAC and the HC11

• There is no on-board DAC included in the HC11

• Most DACs can be interfaced with the HC11, but
some require more complex hardware and
software than others.

• Since the HC11 is an 8-bit microprocessor, an
8-bit DAC is the easiest to interface with.
 Connect the DAC to the parallel I/O port (Port C).
 Simply write something to port C and signal the DAC to begin.

DAC              Yasmine Umbdenstock         Sylvain Vitry       Matt Boyd
References
DAC
•http://www.analog.com
•http://www.hcc.hawaii.edu/~richardi/113/c113_4e/4e_1/4e1.htm

Delta-sigma Modulation
•http://www.ee.washington.edu/conselec/CE/kuhn/onebit/primer.htm

Application CD-Player
•http://www.tc.umn.edu/~erick205/Papers/paper.html#dacs

DAC              Yasmine Umbdenstock           Sylvain Vitry          Matt Boyd
Questions?

DAC   Yasmine Umbdenstock   Sylvain Vitry   Matt Boyd

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