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

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

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

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.

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

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.

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)

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)

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

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.

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

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

1. Binary-weighted resistor DAC

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

Diodes Brief review of semiconductors Junction Diodes Zener Diodes Other type of Junction Diodes

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。

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.

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

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

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.

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.

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.

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

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

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

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

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

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

…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

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

Triac Triggering Modes

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”

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

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

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

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

QUESTIONS?