1
Student Lecture
Fall 2011
ME 4447/6405 Introduction to Mechatronics
Georgia Institute of Technology
Date: Nov 22, 2011
DAC, Diodes and TRIACS
Paragkumar Thadesar
James “Ryan” Cole
Prithiviraj Jothikumar
Mike Weiler
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Outline:
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Paragkumar: What is digital to analog converter (DAC)?
Paragkumar: Types of DAC
Binary Weighted Resistor
R-2R Ladder
Ryan: Discuss Specifications:
Reference Voltages
Resolution
Speed
Settling Time
Linearity
Errors
Ryan: Applications
Prithviraj: Diodes: Theory and applications
Ideal vs. real
Types: Junction and Zener
Mike: Triacs: Theory and applications
3
What is Digital-to-Analog Converter (DAC) ?
• DAC is a device that converts digital numbers
(binary) into an analog voltage or current output.
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
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DAC V/s ADC
• ADCs are used in systems to capture “real world”
signals and convert them to “digital” signals.
• DACs are used in systems to capture “digital”
signals and convert them to “real world” signals
that humans can interpret.
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Significance of Reference Voltage in DACs
• DACs use input reference voltage to generate
analog output from digital signals.
DAC
DAC (using Vref and bits as input) inside an SAR ADC
As explained in earlier student lecture on ADC
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Analog Levels For Sampled Digital Values
• Each binary number sampled by a DAC corresponds
to a different output analog level between “0 and
Vref” for Unipolar and “Vref and –Vref” for Bipolar.
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3 Stages in a DAC
• There are 3 stages in a DAC:
1. Binary to level conversion
2. Zero-order hold
3. Recovery filter
V(n)
Binary to
Level
Conversion
Zero-Order
Hold
Digital-to-Analog Converter
(DAC)
Recovery
Filter
V(t)
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Reconstruction of Sine Wave by Bipolar DAC
Group of binary data
(E.g. Group of 4 bits)
V(n)
Levels gerenated by
sampling groups of
binary data
Binary to
Level
Conversion
Staircase signal
generated using “latch
circuits” to latch a particular
level after sampling until
next level is sampled
Zero-Order
Hold
Digital-to-Analog Converter
(DAC)
Analog signal generated after
removing harmonics from
staircase signal using “low pass
recovery filter”
Recovery
Filter
V(t)
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Types of DAC Implementations
• There can be several types of DAC
implementations. Some of them are:
Covered in this
1. Binary-weighted resistor
presentation
2. R-2R ladder
3. Pulse-width modulation
4. Oversampling DAC (in EVB used in lab)
5. Thermometer-coded DAC
6. Hybrid DAC
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1. Binary-weighted resistor DAC
Concept #1 from past lecture
• Inverting summer consists of 3 parts:
1. An inverting Op-Amp
2. Input voltages either high or ground
3. Adjustment of resistor weights to obtain desired output.
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1. Binary-weighted resistor DAC
Concept #2 from past lecture
Gain of Inverting Op-Amp
Vout = - Vin * (Rf / Rfin) = - I * Rf
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1. Binary-weighted resistor DAC
• Details
– Use Vref as input voltage
– Use transistors to switch between
high and ground
– Use resistors scaled by two to
divide voltage on each branch by a
power of two
– V1 is MSB, V4 LSB in this circuit
• Assumptions:
– Virtual Ground at Inverting
Input
– Vout = -IRf
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1. Binary-weighted resistor DAC
V out   IR f   R f V ref
V out   V ref
Rf
R
n 1
2
i0
B0 
B1
 B n 1 B n  2

 ... n  2  n-1 

2R
2 R 2 R
 R
Bi
( n  1)  i
1
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1. Binary-weighted resistor DAC
• Example: take a 4-bit converter,
• Rf /R= a; a = gain.
• Here ‘a’ should not be ~1000 as in strain gage lab because here
inputs for DAC are Vref and they are in terms of volts where as
in strain gage lab input was in terms of millivolts for ADC.
V out   aV ref
• Input parameters:
 B 3 B 2 B1 B 0 





1
2
4
8


▫ Input voltage Vref = -2V
▫ Binary input = 1011
▫ Coefficient a = ½
V out
 1 0 1 1  11
   2       
 1.375V
2
8
1 2 4 8 
1
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1. Binary-weighted resistor DAC
• Resolution: Making LSB as 1 and all other inputs as
0,
R f V ref
V m in 
n-1
R2
• If Rf = R/2 then resolution is
V ref
2
n
• Max Vout can be obtained making all input bits equal
to 1 and it can be obtained solving geometric series in
equation (1) as
V m ax  V ref
1 

1  n 
2 

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1. Binary-weighted resistor DAC
• Advantages:
▫ Simple
▫ Fast
• Disadvantages
▫ Need large range of resistor values (2048:1 for
12-bit) with high precision in low resistor
values.
▫ Need very small switch resistances.
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2. R-2R Ladder DAC
B2
B1
B0
Ladder of 2 Resistor Values
R and 2R at Input of Inverting Op-Amp
• All the inputs are Vref followed by switches. Output of switches is B2, B1 and B0 in
above circuit.
• Similar to binary weighted DAC, status of switches would define if input bits to
DAC are Vref or 0.
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2. R-2R Ladder DAC
B2
B1
Ladder of 2 Resistor Values
R and 2R at Input of Inverting Op-Amp
B0
• Circuit may be analyzed using Thevenin’s theorem (replace network with
equivalent voltage source and resistance).
• Final result is:
V out   V ref
Rf
R
n 1

i0
Bi
2
ni
2
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2. R-2R Ladder DAC
• Resolution: Making LSB as 1 and all other inputs as 0,
V m in 
R f V ref
• If Rf = R then resolution is
R2
n
V ref
2
n
• Max Vout can be obtained making all input bits equal to 1
and it can be obtained solving geometric series in equation
(1) as
1 

V m ax  V ref  1  n 
2 

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2. R-2R Ladder DAC
• Advantages:
▫ Only 2 resistor values
▫ Lower precision resistors acceptable
• Disadvantages
▫ Slower conversion rate
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Outline:
•
•
•
•
•
•
▫
▫
▫
▫
▫
▫
▫
▫
▫
▫
Paragkumar: What is digital to analog converter (DAC)?
Paragkumar: Types of DAC
Binary Weighted Resistor
R-2R Ladder
Ryan: Discuss Specifications:
Reference Voltages
Resolution
Speed
Settling Time
Linearity
Errors
Ryan: Applications
Prithviraj: Diodes: Theory and applications
Ideal vs. real
Types: Junction and Zener
Mike: Triacs: Theory and applications
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Reference Voltage (𝑉𝑟𝑒𝑓 )
• The reference voltage determines the range of
outputs from the DAC
• For Non-Multiplying DAC
▫ Vref is internally set by the manufacturer and is a
constant value
• For Multiplying DAC
▫ Vref is externally set and can be varied during
operation
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Full Scale Voltage and Resolution
• Full Scale Voltage (Vfs) is the output voltage when all bits
are set high
𝑉𝑓𝑠 =
2𝑁 −1
𝑉𝑟𝑒𝑓 𝑁
2
= 𝑉𝑟𝑒𝑓 − 𝑉𝐿𝑆𝐵
• The DAC resolution is the change in voltage due to an
increment by the least significant bit (LSB)
▫ Data sheets list the resolution in bits
▫ Typical resolution is 8 – 16 bits
∗
𝑉𝑟𝑒𝑓
𝑉𝐿𝑆𝐵 = 𝑁
2
N = # of Bits
*Resolution depends on ratio of Rf and R as explained in previous section. This case is similar to R-2R
ladder resolution with Rf=R
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Sampling Rate (𝑓𝑠 )
• The sampling rate is the rate at which the DAC can
convert the digital input into an output voltage
• The Nyquist Criterion is used to ensure the output
correctly represents the digital input
𝑓𝑠 ≥ 2𝑓𝑚𝑎𝑥
• fmax is the max frequency of the analog signal to be
reconstructed
• fs is limited by the input signal clock speed and DAC
settling time
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Settling Time
• The settling time is the interval between a command to
update (change) its output value and the instant it is
within a specified percentage of its final value
• DAC Limiters
▫ Slew Rate of output amplifier– the maximum rate of change of a
signal
▫ Amplifier Overshoot and Ringing
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Linearity
• The linearity is the relationship between the
output voltage and the input signal
Analog Output Signal
• Ideally the DAC would produce a linear slope
0000
0001
0010
0011
Digital Input Signal
0100
0101
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Errors
Common DAC Errors:
• Offset Error
• Gain Error
• Full Scale Error
• Resolution Errors
• Non Linearity
• Non-Monotonic
• Settling Time and Overshoot
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Offset Error
• An offset error will cause all the output voltages
to be different from the ideal output by the error
▫ It can be determined by measuring the output
voltage for a digital input of zero.
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Gain Error
• The gain error is how well the slope of the actual
transfer function matches the slope of the ideal
transfer function
▫ It can be determined by measuring the output
voltage for a digital input of all 1’s
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Full Scale Error
• Full Scale error is the combination of the Gain
Error and the Offset Error
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Resolution Error
• The resolution will determine how close your output will match the
desired signal
1 Bit Resolution
3 Bit Resolution
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Differential Nonlinearity Error (DNL)
• The difference between two successive digital
output codes is ideally 1 VLSB
• The deviation from a step of 1 VLSB is the DNL error
▫ Manufacturers will specify the maximum DNL error
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Integral Linearity Error (INL)
• The INL is the difference in the ideal linear
voltage and the actual output voltage for a given
digital code
▫ Manufactures will specify the max INL error
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Non-Monotonic
• Monotonic Function
▫ A monotonically increasing function will always increase or
remain constant (non-decreasing)
▫ A monotonically decreasing function will always decrease
or remain constant (non-increasing)
• If an increase in the digital input results in a decrease in
the output voltage the DAC is considered non-monotonic
▫ If the DNL error is less than
± 1 LSB the DAC is
guaranteed to be monotonic
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Applications
• Audio/Video
▫
▫
▫
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▫
MP3 Players
CD Players
Cellphones
USB Speakers
Analog Monitors
• Signal Generators
▫ Sine Wave generation
▫ Square Wave generation
▫ Random Noise generation
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Outline:
•
•
•
•
•
•
▫
▫
▫
▫
▫
▫
▫
▫
▫
▫
Paragkumar: What is digital to analog converter (DAC)?
Paragkumar: Types of DAC
Binary Weighted Resistor
R-2R Ladder
Ryan: Discuss Specifications:
Reference Voltages
Resolution
Speed
Settling Time
Linearity
Errors
Ryan: Applications
Prithviraj: Diodes: Theory and applications
Ideal vs. real
Types: Junction and Zener
Mike: Triacs: Theory and applications
37
Diodes
•
•
•
•
Brief review of semiconductors
Junction Diodes
Zener Diodes
Other type of Junction Diodes
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Review
• The conduction band
allows the electrons to
move within the atomic
lattice of the material
• The valence band is an
energy region where
the states are generally
filled
• Electrons in the valence
band can be moved
to the conductionband
with the application
of energy, usually
thermal energy
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Semiconductors
• A material can be classified as:
1. Insulator – has valence and
conduction bands well
separated
2. Semiconductor – has
valence
band close to
conduction
band (the energy gap is about
1eV).
3. Conductor – has the
conduction and valence bands
overlapping
• Semiconductors two unusual
properties:
1. Conductivity increases
exponentially with
temperature
2. Conductivity can be increased
and precisely controlled by
adding small impurities in a
process called doping.
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Diode
• A diode is created when a p-type semiconductor is
joined with and n-type semiconductor by the addition
of thermal energy.
• When both materials are joined, the thermal energy
causes positive carriers in the p-type material to
diffuse into the n-type region and negative carriers in
the n-type material to diffuse into the p-type region.
• This creates the depletion region within the diode
Majority carriers
p
n
Depletion Region
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Forward and Reverse biased
• A diode is forward biased if the positive terminal of the battery is
connected to the p-type material.
• Current is sustained by the majority carriers.
• A diode is reverse biased if the positive terminal of the battery
is connected to the n-type material.
• There is a small reverse current or leakage current sustained by
the minority carriers
• If reverse bias is sufficiently increased, a sudden increase in
reverse current is observed. This is known as the Zener or Avalanche
effect
Depletion Region
Original Size
Depletion Region
Original Size
if
p
n
V
Forward Biased
p
n
V
Reverse Biased
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Diode Characteristic Curve
I
conduction
region
non-conduction
region
V
Ideal Curve
Ideal Diode – no resistance to current flow
in the forward direction and infinite resistance
in the reverse direction.
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Zener Diode
• Zener diodes operate in the breakdown region.
• Zener diodes have a specified voltage drop when they
are used in reverse bias.
• Every p-n junction (i.e. diode) will break down in
reverse bias if enough voltage is applied.
• Able to maintain a nearly constant voltage under
conditions of widely varying current.
• Zener diodes are operated in reverse bias for normal
voltage regulation.
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Other Types of Diodes
• Light Emitting Diodes (LEDs) - A diode formed from a
semiconductor such as gallium arsenide, carriers that cross
the junction emit photons when they recombine with the
majority carrier on the other side.
• Photodiode – Exploits the fact that all semiconductors are
subject to charged carrier generation when they are exposed
to light. Photodiodes are often used to sense light such as in
an Opto-isolator.
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Outline:
•
•
•
•
•
•
▫
▫
▫
▫
▫
▫
▫
▫
▫
▫
Paragkumar: What is digital to analog converter (DAC)?
Paragkumar: Types of DAC
Binary Weighted Resistor
R-2R Ladder
Ryan: Discuss Specifications:
Reference Voltages
Resolution
Speed
Settling Time
Linearity
Errors
Ryan: Applications
Prithviraj: Diodes: Theory and applications
Ideal vs. real
Types: Junction and Zener
Mike: Triacs: Theory and applications
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What are TRIACS?
Dr. Ume
Dr. Ume, what are
TRIACS?
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What are TRIACS?
• Triode for Alternating Current
• Electronic component that can conduct current in
either direction (bidirectional) when triggered
• Bidirectionality makes TRIACs excellent switches
for AC currents -> can handle large power flows
• Used in high power switching applications i.e.
hundreds of amps / thousands of watts
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How do TRIACs work?
How do TRIACs work?
• To understand operation of TRIACs, we first
need to explain Thyristors…
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What are Thyristors?
• Class of semiconductor components that can
only go in 1 direction.
• Wide range of devices, SCR (silicon controlled
rectifier), SCS (silicon controlled switch),
Diacs, Triacs, and Shockley diodes
• Used in high power switching applications
•
i.e. hundreds of amps / thousands of watts
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How do Thyristors work?
• Unidirectional semiconductor
• PNPN (4-layer) device:
•
PNP and NPN transistor back-to-back.
• With forward voltage, small gate current pulse
turns on device.
•
Once on, each transistor supplies gate current for
the other, so no need for gate input
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…now then, what are TRIACS?
•
•
•
•
A TRIAC is a 3-terminal switch
composed of 2 thyristors facing opposite
directions
It can conduct current bidirectionally
MT1 and MT2 are current carrying
terminals while the Gate terminal is
used for triggering by applying a small
voltage signal.
Once triggered, it continues to conduct
current until the current falls below a
threshold – known as holding current
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Triac Operation
•5 layer device
•Region between MT1 and MT2 are parallel switches (PNPN and NPNP)
•Allows for positive or negative gate triggering
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Triac Triggering Modes
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Triac Operation
• TRIACs start conducting when a minimum
current (gate threshold current) flows into or out
of its gate sufficient to turn on relevant junctions
in that quadrant of operation
• Device remains in “on” state even after gate
current is removed so long as current through the
device remains above holding current
• Once current falls below holding current for an
appropriate time period, device switches “off”
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Triacs Pros/Cons
• Pros:
•
•
Better than a transistor as it has much better
current surge rating – can handle more current
because it simply turns on more
Inexpensive compared to relays
• Cons:
•
Can’t manually control turn-off with the gate, must
turn off by stopping current through device via
terminals
• Specs to consider when purchasing a TRIAC:
•
•
•
Gate signal requirements
Voltage drop
Steady-state/holding/peak current specifications
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Triac Applications
High Power TRIACS
• Switching for AC circuits, allowing the control of
very large power flows with milliampere-scale
control currents
• Can eliminate mechanical wear in a relay
Low Power TRIACS
• Light bulb dimmers (done by applying power later in
the AC cycle aka PWM of AC wave)
• Motor speed controls for electric fans and other AC
motors, and heaters
• Modern computerized control circuits in household
appliances
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Triac Applications
Simple Triac Switch
•Small control
current/voltage
•Eliminates
Mechanical wear in a
Relay
•Much Cheaper
Real World Triacs
• Come in various
shapes and sizes
• Essentially all the
same operationally
• Different mounting
schemes
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References
• Previous student presentations.
• http://en.wikipedia.org/wiki/Digital_to_analog
• http://www.allaboutcircuits.com/vol_4/chpt_13/index.html
• Alicatore, David G. and Michael B Histand. Introduction to
Mechatronics and Measurement Systems, 2nd ed. McGraw-Hill,
2003.
• Walt Kester, “What the Nyquist Criterion Means to Your Sampled
Data System Design”, MT 002 Tutorial, Analog Devices.
• http://www.maxim-ic.com/app-notes/index.mvp/id/641
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QUESTIONS?