DAC, Diodes and TRIACS

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DAC, Diodes and TRIACSParagkumar ThadesarJames “Ryan” ColePrithiviraj JothikumarMike Weiler

Student LectureFall 2011ME 4447/6405 Introduction to MechatronicsGeorgia Institute of Technology

Date: Nov 22, 2011

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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 is Digital-to-Analog Converter (DAC) ?

•DAC is a device that converts digital numbers (binary) into an analog voltage or current output.

0101

0011

0111

1001

1001

1010

1011 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 ADCAs explained in earlier student lecture on ADC

http://en.wikipedia.org/wiki/File:SA_ADC_block_diagram.png

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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 conversion2. Zero-order hold3. Recovery filter

Binary to Level

Conversion

V(n) Zero-OrderHold

RecoveryFilter V(t)

Digital-to-Analog Converter(DAC)

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Reconstruction of Sine Wave by Bipolar DAC

Binary to Level

Conversion

V(n) Zero-OrderHold

RecoveryFilter V(t)

Digital-to-Analog Converter(DAC)

Group of binary data(E.g. Group of 4 bits)

Levels gerenated by sampling

groups of binary data

Staircase signalgenerated using “latch

circuits” to latch a particular level after

sampling until next level is sampled

Analog signal generated after removing harmonics from staircase signal using “low pass recovery filter”

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Types of DAC Implementations

• There can be several types of DAC implementations. Some of them are:

1. Binary-weighted resistor2. R-2R ladder3. Pulse-width modulation4. Oversampling DAC (in EVB used in lab)5. Thermometer-coded DAC6. Hybrid DAC

Covered in this presentation

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1. Binary-weighted resistor DAC

• 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.

Concept #1 from past lecture

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Vout = - Vin * (Rf / Rfin) = - I * Rf

Gain of Inverting Op-Amp

Concept #2 from past lecture

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• Details • Assumptions:– Virtual Ground at Inverting

Input– Vout = -IRf

– Use transistors to switch between high and ground

– Use Vref as input voltage

– Use resistors scaled by two to divide voltage on each branch by a power of two

– V1 is MSB, V4 LSB in this circuit

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1 2 01out f f 2 n-1

...2 2 2

n nref n

B B BBV IR R V

R R R R

1

out ref ( 1)0 2

nf i

n ii

R BV V

R

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.

• Input parameters:▫ Input voltage Vref = -2V▫ Binary input = 1011▫ Coefficient a = ½

3 02 1out 1 2 4 8ref

B BB BV aV

out

1 1 0 1 1 112 1.375

2 1 2 4 8 8V V

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1. Binary-weighted resistor DAC• Resolution: Making LSB as 1 and all other

inputs as 0,

• If Rf = R/2 then resolution is

• Max Vout can be obtained making all input bits equal to 1 and it can be obtained solving geometric series in equation (1) as

f

min n-12refR V

VR

n2refV

max

112ref n

V V

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• 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

• 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.

B2

B1

B0

Ladder of 2 Resistor Values R and 2R at Input of Inverting Op-Amp

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2. R-2R Ladder DAC

• Circuit may be analyzed using Thevenin’s theorem (replace network with equivalent voltage source and resistance).

• Final result is:

B2

B1

B0

Ladder of 2 Resistor Values R and 2R at Input of Inverting Op-Amp

1

out ref0 2

nf i

n ii

R BV V

R

2

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2. R-2R Ladder DAC

f

min n2refR V

VR

• Resolution: Making LSB as 1 and all other inputs as 0,

• If Rf = R then resolution is

• Max Vout can be obtained making all input bits equal to 1 and it can be obtained solving geometric series in equation (1) as

n2refV

max

112ref n

V V

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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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Reference Voltage (

•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

• 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

∗𝑉 𝐿𝑆𝐵=𝑉 𝑟𝑒𝑓

2𝑁 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 (

• 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

• 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

𝑓 𝑠≥2 𝑓 𝑚𝑎𝑥

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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

•Ideally the DAC would produce a linear slope

010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

010101000011001000010000 010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

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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

1 Bit Resolution 3 Bit Resolution

• The resolution will determine how close your output will match the desired signal

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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▫ MP3 Players▫ CD Players▫ Cellphones▫ USB Speakers▫ Analog Monitors

• Signal Generators▫ Sine Wave generation▫ Square Wave generation▫ Random Noise generation

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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 wherethe states are generally filled

• Electrons in the valence band can be moved to the conduction band with the applicationof 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 bandsoverlapping

• 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

np

Depletion Region

Majority carriers

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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 batteryis 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

np

Reverse Biased

Depletion RegionOriginal Size

Forward Biased

npif

Depletion RegionOriginal Size

V V

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V

I

conductionregion

non-conductionregion

Ideal Curve

Ideal Diode – no resistance to current flowin the forward direction and infinite resistancein the reverse direction.

Diode Characteristic Curve

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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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Dr. Ume, what are TRIACS?

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?

DAC, Diodes and TRIACS

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