DAC, Diodes, Triacs
ME 6405 – Intro to Mechatronics
Student Lecture
Kevin Johnson
Minh Vo
Lam Duong
Wye-Chi Chok
Kevin Johnson
Outline
• DAC
– What is a DAC?
– Types of DAC
– Specifications
• Diodes
–
–
–
–
What are diodes?
P-N Junction Diode
Real vs. Ideal
Types of Diodes & Applications
• Triacs
– What are thyristors?
– What are triacs?
– Applications
Kevin Johnson
Principal components of DAC
Kevin Johnson
What is a DAC?
• Convert digital signal (number) to analog
signal (voltage or current)
• Either multiplying or non-multiplying
– Non-multiplying contains its own reference
– Multiplying takes external reference.
• Two main types: ladder and delta-sigma
Kevin Johnson
DAC ideal output.
Analog Output Signal
• Each binary number sampled by the DAC
corresponds to a different output level.
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011
Digital Input Signal
Kevin Johnson
DAC real output.
DACs capture a number 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
DAC due to sample & hold
Kevin Johnson
Smoothing
• Used when a continuous analog signal is
required.
• Signal from DAC can be smoothed by a Low
pass filter
Piece-wise
Continuous Output
Digital Input
Analog
Continuous Output
0 bit
011010010101010100101
101010101011111100101
000010101010111110011
010101010101010101010
111010101011110011000
100101010101010001111
n bit DAC
nth bit
Filter
Kevin Johnson
Applications.
• Audio/Video
– MP3 players
– Cellphones
– Television
• (well, old ones)

Motor, valve, actuator
 Rarely; usually PWM.
• Signal Generators
–
–
–
–
Sine wave generation
Square wave generation
Triangle wave generation
Random noise generation
Kevin Johnson
Types of DAC implementations
•
•
•
•
Binary Weighted Resistor
R-2R Ladder
Pulse Width Modulator (not covered)
Oversampling DAC, aka Delta Sigma (used
internally in HCS12)
Kevin Johnson
Binary Weighted Resistor
B5
B4
B3
B2
• Assume binary
inputs B0 (LSB)
to Bn-1 (MSB)
• Each Bi is 1 or 0
and is
multiplied by
Vref to get input
voltage
B1
B0
Vout
B0 
B1
 Bn1 Bn2
  IRf   Rf Vref 

 ... n2  n-1 
2R
2 R 2 R
 R
Kevin Johnson
Binary weight theory


Need to fill jars
to a specific
level using set
of measuring
cups.
Cups are ½, ¼,
1/8, 1/16, etc.
http://www.msbtech.com/support/How_DACs_Work.php
Kevin Johnson
BWR Pros and Cons
 Advantages
 Simple
 Fast
 Disadvantages
 Need large range of resistor values (2048:1 for 12bit) with high precision in low resistor values
 Need very small switch resistances
 Op-amp may have trouble producing low currents
at the low range of a high precision DAC
Kevin Johnson
R-2R ladder basic circuit



Equivalent resistance to ground at each top node is R.
At each node, current gets split in two.
Since nodes are cascaded, currents are ½, ¼, 1/8, etc.
Kevin Johnson
R-2R Ladder results
• Final result is:
Vout  Vref
Rf
n 1
Bi

R i  0 2n  i
• Assuming Rf = R (and ignoring negative)
• Resolution is smallest step: i.e. B=1 in above equation.
Kevin Johnson
R-2R Ladder
• Advantages:
– Only 2 resistor values
– Lower precision resistors acceptable
• Disadvantages
– Slightly slower conversion rate
– Op-amp must still handle very small currents
at high bit numbers.
Kevin Johnson
Delta-sigma DAC



Now all cups are
the same size (or
more precisely, he
uses the same cup
over and over).
Cup size is
1/(2^n).
He must add this
amount the proper
number of times
(pulse-count
modulation).
http://www.msbtech.com/support/How_DACs_Work.php
Kevin Johnson
Delta-sigma Pros and Cons
• Pros:
– Very accurate
– High bit-depth possible
– Reduced aliasing
• Cons:
– Requires very fast oversampling clock.
• At least 2^n times faster than sampling rate
– Complicated
– Sensitive to clock jitter
Kevin Johnson
General comments
• Circuits as shown produce only unipolar
output
• Replacing ground with –Vref will allow Vout
to be positive or negative
Minh Vo
Specifications of a DAC






Reference Voltage
Resolution
Sampling Rate
Settling Time
Linearity
Errors
Minh Vo
Reference Voltage Vref
Determines the output voltage range
Non-multiplying DAC
– Fixed Vref set internally by manufacturer
Multiplying DAC
– Vref is set externally and can be vary during operation
• Full-scale voltage Vfs
– Voltage when all digital inputs are 1’s
Vref (2 N  1)
Vfs 
N
2
Minh Vo
Resolution
The resolution is the amount of output voltage
change in response to a least significant bit (LSB)
transition.
Vref
Resolution  N  VLSB
2
Smaller resolution results in a smoother output
A common DAC has a 8 - 16 bit resolution
Minh Vo
Sampling Rate fsampling
Rate of conversion of a single digital input to
its analog equivalent
When the input changes rapidly, fmax, the DAC
conversion speed must be high
– Nyquist Criterion: fsampling  2 f max
Limited by the clock speed of the input signal
and the settling time of the DAC
Minh Vo
Settling Time
• DAC needs time to reach the actual expected
analog output voltage
• The time required for the output voltage to
settle within +/- ½ of VLSB of the expected
voltage
Minh Vo
Linearity
• The difference between the desired analog
output and the actual output over the full
range of expected values
0000
Analog Output Signal
Non-Linear
Analog Output Signal
Linear (Ideal)
0001
0010
0011
Digital Input Signal
0100
0101
0000
0001
0010
0011
Digital Input Signal
0100
0101
Minh Vo
Errors
•
•
•
•
•
•
•
Gain Error
Offset Error
Full Scale Error
Non Linearity
Non-Monotonic
Resolution Errors
Settling Time and Overshoot
Minh Vo
Gain Error
• Deviation in the slope of the ideal curve and
with respect to the actual DAC output
Gain Error is adjustable
to zero using an
external potentiometer
High Gain
Analog Output Voltage
High Gain Error: Step
amplitude is higher than
the desired output
Low Gain Error: Step
amplitude is lower than
the desired output
Desired/Ideal Output
Low Gain
Digital Input
Minh Vo
Offset Error
• Occurs when there is an offset in the output
voltage in reference to the ideal output
This error may be
detected when all
input bits are low
(i.e. 0).
Output Voltage
Desired/Ideal Output
Positive Offset
Negative Offset
Digital Input
Minh Vo
Full Scale Error
• Combination of gain and offset error
Minh Vo
Differential Non-Linearity
Analog Output Voltage
• Voltage step size changes vary with as digital
input increases. Ideally each step should be
equivalent.
Ideal Output
2VLSB
Diff. Non-Linearity = 2VLSB
VLSB
Digital Input
Minh Vo
Integral Non-Linearity
Analog Output Voltage
• Occurs when the output voltage is non linear.
Basically an inability to adhere to the ideal
slope.
Ideal Output
1VLSB
Int. Non-Linearity = 1VLSB
Digital Input
Minh Vo
Non-Monotonic
Analog Output Voltage
• Occurs when the an increase in digital input
results in a lower output voltage.
Desired Output
Non-Monotonic
Monotonic
Digital Input
Minh Vo
Resolution Errors
• Does not accurately approximate the desired
output due large voltage divisions.
Poor Resolution(1 bit)
Vout
2 Volt. Levels
Desired Analog
signal
1
0
Approximate
output
0
Digital Input
Minh Vo
Settling Time and Overshoot
• Any change in the input time will not be
reflected immediately due to the lag time.
• Overshoot occurs when the output voltage
overshoots the desired analog output voltage.
Lam Duong
What is a Diode?
• A diode is a two terminal electric component which conducts
current more easily in one direction than in the opposite
direction.
• The most common usage of a diode is as an electronic valve
which allows current to flow in one direction but not the
opposite direction.
Lam Duong
A bit of history
• Diodes were known as rectifiers until 1919,
when a physicist by the name of William
Eccles coined the term diode, which from
its Greek roots means “through-path.”
• In 1873 Fredrick Guthrie discovered
thermionic diodes (vacuum tube diodes) .
Heating the cathode in forward bias
permitted electrons to be transmitted into
the vacuum, but in reverse bias the
electrons were not easily release from the
unheated anode.
35
Lam Duong
A bit of history
• In 1874 Karl Braun discovered the first
solid state diode (crystal diode). It
consists of using Galena crystals as the
semiconducting material.
• In 1939 Russell Ohl discovered the first
P-N junction at Bell Labs.
• Today, the majority of diodes are made
of semiconductor silicon P-N junctions.
36
Lam Duong
P-N Junction Diode
• A P-N junction diode consists of a p-type
semiconductor (silicon) joined with an ntype semiconductor.
• P-type – A semiconductor doped with
impurities to create positive charge
carriers (holes).
• N-type – A semiconductor doped with
impurities to create negative charged
carriers.
• A depletion region is created when
negative charge carriers from the N-type
region diffuse into the P-type region, and
vice versa.
Majority carriers
p
n
Depletion Region
37
Lam Duong
P-N Junction Diode
• The behavior of a diode depends upon the
polarity of the supply voltage.
• Under forward bias the depletion region is i
f
reduced in size and less energy is required
for the charged majority carriers to cross
the depletion region.
• This decrease in energy requirement
results in more charged majority carriers to
cross the depletion region which induces a
current.
Depletion Region
p
n
Forward Biased
Lam Duong
P-N Junction Diode
• Under reverse bias the depletion
region is greatly increased in size and
requires significantly more energy
from the majority carriers in order to
cross.
• Most majority carriers won’t be able
to cross the depletion region and
thus are unable to induce a current.
Depletion Region
p
n
V
Reverse Biased
ir
Real vs. Ideal
• Ideal P-N Diode – no resistance to current in
forward bias and infinite resistance in reverse
bias. (Similar to a switch)
• In reality there is resistance to current flow in
forward bias. It requires a certain voltage to be
reached before the depletion region is
eliminated and full current flow is permitted.
• Likewise, in reverse bias there is a small reverse
(leakage) current induced by the flow of
minority carriers. At a certain voltage (break
down voltage) the reverse current will increase
significantly. This is called the Avalanche current.
Lam Duong
I
non-conduction
region
conduction
region
V
Ideal Curve
Lam Duong
Schottky Diode
• Unlike P-N junction diodes, Schottky diodes are
based on a metal and semiconductor junction.
• An advantage of Schottky diodes over P-N
junction diodes is that Schottky diodes have no
recovery time when switching from conducting
to non-conducting state and vice versa.
• The main disadvantage of Schottky diodes are
that they operate in low voltage compare to P-N
junction diodes (up to 50V).
• Another significant difference is that the “onvoltage” for a Schottky diode is around .3V
while it is .7V for a P-N junction diode.
Metal
N-Type
Lam Duong
Flyback Diode
• Schottky diodes are often used as Flyback diodes
due to their quick recovery and low forward voltage
drop.
• A Flyback diode is a diode used to eliminate the
sudden voltage spike that occurs across an
indicutive load when voltage is abruptly reduced or
removed.
• Lenz’s law - if the current through an inductance
changes, this inductance induces a voltage so the
current will go on flowing as long as there is energy
in the magnetic field.
• Flyback diodes are important in mechatronics
applications where one may want to vary the
voltage of an inductive load to control its operation.
Lam Duong
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.
• Zener Diode – Allows current in forward bias like a
regular diode, but also in reverse bias if the voltage
is larger than designed voltage, called the
Breakdown voltage.
What are TRIACS?
Wye-Chi Chok
In order to know, we must first look at
thyristors…
44
What are Thyristors?
Wye-Chi Chok
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
45
How do Thyristors work?
Wye-Chi Chok
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
 only way to turn it off is to stop current (i.e. bring
voltage to zero)
Wye-Chi Chok
Thyristors cont’d.
47
Wye-Chi Chok
…now then, what are TRIACS?
 A TRIAC (TRIode for Alternating Current) is a
3-terminal AC semiconductor switch.
 Composed of 2 thyristors facing opposite
directions such that it can conduct current in
either direction.
 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 value.
Wye-Chi Chok
Triac Operation
•5 layer device
•Region between MT1 and MT2 are parallel switches (PNPN and NPNP)
•Allows for positive or negative gate triggering
Wye-Chi Chok
Triac Characteristic Curve
Wye-Chi Chok
Triac Characteristic Curve
o 1st quadrant - MT2 is (+) with respect to MT1
o VDRM is the break-over voltage of the Triac
and the highest voltage that can be blocked
o IRDM is the leakage current of the Triac when
VDRM is applied to MT1 and MT2
o IRDM is several orders of magnitude smaller
than the “on” rating
Wye-Chi Chok
Triacs
 Pros:
 Better than a transistor as it has much better current
surge rating – it can handle more current as 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 the device via the
terminals.
 Specs to buy one:
 Gate signal requirements
 Voltage drop
 Steady-state/holding current (continuously handle)
 Peak current (maximum amount to handle surge)
Wye-Chi Chok
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
53
Wye-Chi Chok
Triac Applications
Simple Triac Switch
•Small control
current/voltage
•Eliminates Mechanical
wear in a Relay
•Much Cheaper
Wye-Chi Chok
Real World Triacs
• Come in various
shapes and sizes
• Essentially all the
same operationally
• Different mounting
schemes
QUESTIONS?
56