1. DAC, Diodes and TRIACS Paragkumar Thadesar James “Ryan” Cole
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

2. 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

3. What is Digital-to-Analog Converter (DAC) ?
DAC is a device that converts digital numbers (binary) into an analog voltage or current output.
1001
0101
0011
0111
1001
1010
1011
DAC

4. 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.

5. 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

6. 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.

7. Digital-to-Analog Converter
3 Stages in a DAC
There are 3 stages in a DAC:
1. Binary to level conversion
2. Zero-order hold
3. Recovery filter
Binary to
Level
Conversion
Zero-Order
Hold
Recovery
Filter
V(n)
V(t)
Digital-to-Analog Converter
(DAC)

8. Reconstruction of Sine Wave by Bipolar DAC
Staircase signal
generated 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”
Levels gerenated by sampling groups of binary data
Group of binary data
(E.g. Group of 4 bits)
Binary to
Level
Conversion
Zero-Order
Hold
Recovery
Filter
V(n)
V(t)
Digital-to-Analog Converter
(DAC)

9. Types of DAC Implementations
There can be several types of DAC implementations. Some of them are:
1. Binary-weighted resistor
2. R-2R ladder
3. Pulse-width modulation
4. Oversampling DAC (in EVB used in lab)
5. Thermometer-coded DAC
6. Hybrid DAC
Covered in this presentation

10. 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.

11. 1. Binary-weighted resistor DAC
Concept #2 from past lecture
Gain of Inverting Op-Amp
Vout = - Vin * (Rf / Rfin) = - I * Rf

12. 1. Binary-weighted resistor DAC
Details
Assumptions:
Virtual Ground at Inverting Input
Vout = -IRf
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

13. 1. Binary-weighted resistor DAC

14. 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

15. 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

16. 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.

17. 2. R-2R Ladder DAC B2 B1 Ladder of 2 Resistor Values
R and 2R at Input of Inverting Op-Amp B0
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.

18. 2. R-2R Ladder DAC 2 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: 2

19. 2. R-2R Ladder DAC
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

20. 2. R-2R Ladder DAC Advantages: Disadvantages Only 2 resistor values
Lower precision resistors acceptable
Disadvantages
Slower conversion rate

21. 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

22. Reference Voltage ( 𝑉 𝑟𝑒𝑓 )
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

23. 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 𝑓𝑠 = 𝑉 𝑟𝑒𝑓 2 𝑁 −1 2 𝑁 = 𝑉 𝑟𝑒𝑓 − 𝑉 𝐿𝑆𝐵
∗𝑉 𝐿𝑆𝐵 = 𝑉 𝑟𝑒𝑓 2 𝑁
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

24. Sampling Rate ( 𝑓 𝑠 ) 𝑓 𝑠 ≥2 𝑓 𝑚𝑎𝑥
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

25. 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

26. Linearity
The linearity is the relationship between the output voltage and the input signal
Ideally the DAC would produce a linear slope

27. Errors Common DAC Errors: Offset Error Gain Error Full Scale Error
Resolution Errors
Non Linearity
Non-Monotonic
Settling Time and Overshoot

28. 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.

29. 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

30. Full Scale Error
Full Scale error is the combination of the Gain Error and the Offset Error

31. Resolution Error
The resolution will determine how close your output will match the desired signal
1 Bit Resolution
3 Bit Resolution

32. 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

33. 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

34. 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

35. Applications Audio/Video Signal Generators MP3 Players CD Players
Cellphones
USB Speakers
Analog Monitors
Signal Generators
Sine Wave generation
Square Wave generation
Random Noise generation

36. 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

38. 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 conduction band with the application of energy, usually thermal energy
存在于价带和导带之间的部分称之为能隙。

39. Semiconductors
A material can be classified as: 1. Insulator – has valence and conduction bands well separated Semiconductor – has valence band close to conduction band (the energy gap is about 1eV) 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.

40. 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 n p
Depletion Region
Majority carriers

41. 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
Forward Biased n p if
Depletion Region
Original Size n p
Reverse Biased V V

42. Diode Characteristic Curve
conduction
region
non-conduction
Ideal Curve
Ideal Diode – no resistance to current flow in the forward direction and infinite resistance in the reverse direction.

43. 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.

44. 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.

45. 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

46. What are TRIACS?
Dr. Ume
Dr. Ume, what are TRIACS?

47. 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

48. How do TRIACs work? How do TRIACs work?
To understand operation of TRIACs, we first need to explain Thyristors…

49. 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

50. 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

51. …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

52. Triac Operation 5 layer device
Region between MT1 and MT2 are parallel switches (PNPN and NPNP)
Allows for positive or negative gate triggering

53. Triac Triggering Modes

54. 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”

55. Triacs Pros/Cons Pros: Cons:
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

56. 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

57. Triac Applications Simple Triac Switch Small control current/voltage
Eliminates Mechanical wear in a Relay
Much Cheaper

58. Real World Triacs Come in various shapes and sizes
Essentially all the same operationally
Different mounting schemes

59. References Previous student presentations.
Alicatore, David G. and Michael B Histand. Introduction to Mechatronics and Measurement Systems, 2nd ed. McGraw-Hill,
Walt Kester, “What the Nyquist Criterion Means to Your Sampled Data System Design”, MT 002 Tutorial, Analog Devices.

60. QUESTIONS?