DAC, Diodes, Triacs

Kevin JohnsonMinh Vo

Lam DuongWye-Chi Chok

ME 6405 – Intro to MechatronicsStudent Lecture

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 DACKevin 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.

• Each binary number sampled by the DAC corresponds to a different output level.

10111001 10100111 10000110010101000011001000010000Digital Input Signal

Ana

log

Out

put

Sig

nal

Kevin Johnson

Ideally Sampled Signal Output typical of a real, practical DAC due to sample & hold

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

DAC real output.Kevin Johnson

Smoothing

• Used when a continuous analog signal is required.

• Signal from DAC can be smoothed by a Low pass filter

0 bit

nth bit

n bit DAC011010010101010100101101010101011111100101000010101010111110011010101010101010101010111010101011110011000100101010101010001111

Digital Input

Filter

Piece-wise Continuous Output

Analog Continuous Output

Kevin Johnson

• Audio/Video– MP3 players– Cellphones– Television

• (well, old ones)

• Signal Generators– Sine wave generation– Square wave generation– Triangle wave generation– Random noise generation

Motor, valve, actuatorRarely; usually PWM.

Applications.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• Assume binary

inputs B0 (LSB) to Bn-1 (MSB)

• Each Bi is 1 or 0 and is multiplied by Vref to get input voltage

1 2 01out f f 2 n-1

...2 2 2

n nref n

B B BBV IR R V

R R R R

B0

B5

B4

B3

B2

B1

Kevin Johnson

Binary weight theory

http://www.msbtech.com/support/How_DACs_Work.php

Need to fill jars to a specific level using set of measuring cups.

Cups are ½, ¼, 1/8, 1/16, etc.

Kevin Johnson

BWR Pros and Cons

AdvantagesSimpleFast

DisadvantagesNeed large range of resistor values (2048:1 for 12-

bit) with high precision in low resistor valuesNeed very small switch resistancesOp-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:

• Assuming Rf = R (and ignoring negative)

• Resolution is smallest step: i.e. B=1 in above equation.

1

out ref0 2

nf i

n ii

R BV V

R

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

http://www.msbtech.com/support/How_DACs_Work.php

Now all cups are the same size (or more precisely, he uses the same cup over and over).

Cup size is1/(2^n).

He must add this amount the proper number of times(pulse-count modulation).

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

Kevin Johnson

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

N

NVV

2

)12(reffs

Minh Vo

Resolution

The resolution is the amount of output voltage change in response to a least significant bit (LSB) transition.

Smaller resolution results in a smoother output A common DAC has a 8 - 16 bit resolution

LSBref

2Resolution V

VN

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:

Limited by the clock speed of the input signal and the settling time of the DAC

maxsampling 2 ff

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

010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

010101000011001000010000 010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

010101000011001000010000 010101000011001000010000Digital Input Signal

Anal

og O

utpu

t Sig

nal

Linear (Ideal) Non-Linear

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

High Gain Error: Step amplitude is higher than the desired outputLow Gain Error: Step amplitude is lower than the desired output

Gain Error is adjustable to zero using an external potentiometer

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).

Minh Vo

Full Scale Error

• Combination of gain and offset error

Minh Vo

Differential Non-Linearity

• Voltage step size changes vary with as digital input increases. Ideally each step should be equivalent.

Minh Vo

Integral Non-Linearity

• Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope.

Minh Vo

Non-Monotonic

• Occurs when the an increase in digital input results in a lower output voltage.

Minh Vo

Resolution Errors

• Does not accurately approximate the desired output due large voltage divisions.

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.

Minh Vo

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.

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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.

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Lam Duong

P-N Junction Diode• A P-N junction diode consists of a p-type

semiconductor (silicon) joined with an n-type 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.

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np

Depletion Region

Majority carriers

Lam Duong

Forward Biased

npif

Depletion Region

P-N Junction Diode• The behavior of a diode depends upon the

polarity of the supply voltage.• Under forward bias the depletion region is

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.

Lam Duong

np

Reverse Biased

Depletion Region

ir

V

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.

Lam Duong

V

I

conductionregion

non-conductionregion

Ideal Curve

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

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 “on-voltage” 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.

Lam Duong

What are TRIACS?

In order to know, we must first look at thyristors…

44

Wye-Chi Chok

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 applicationsi.e. hundreds of amps / thousands of watts

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Wye-Chi Chok

How do Thyristors work?

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.

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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 CurveWye-Chi Chok

Triac Characteristic Curve

o 1st quadrant - MT2 is (+) with respect to MT1o VDRM is the break-over voltage of the Triac and

the highest voltage that can be blockedo 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 ApplicationsHigh 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

appliances53

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

Wye-Chi Chok

QUESTIONS?

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