Lecture 4 - Motors, Drives, Unsigned Binary, Boolean Logic Gates and Algebra PDF

ECOR1044: Boolean Logic Motors and Drives Unsigned Binary Boolean Logic Gates Algebra 1 Motor/Generator A motor/generator consists of a rotor spinning in a magnetic field produced by permanent magnets or by coils. The process of generat...

ECOR1044: Boolean Logic Motors and Drives Unsigned Binary Boolean Logic Gates Algebra 1 Motor/Generator A motor/generator consists of a rotor spinning in a magnetic field produced by permanent magnets or by coils. The process of generating a magnetic field by means of an electric current is called excitation. 2 3 Motor/Generator 4 DC Motor Principle When a current flows, a torque is generated producing an angular acceleration. When μ and B are aligned, the torque is zero, but the loop has angular velocity and angular momentum. It therefore overshoots the aligned position. A split ring causes the current to reverse direction, just as it passes the aligned position. This accelerates the loop again through another 180 degree turn. https://www.youtube.com/watch?v=LAtPHANEfQo 5 DC Motors › The interaction of the fields produces the movement of the shaft/armature. › The "flipping the electric field" part of an electric motor is accomplished by two parts: the commutator and the brushes. 6 DC Motors › The interaction of the fields produces the movement of the shaft/armature. › When the loop rotates through 180°, the direction of the voltage reverses leading to the following total induced voltage: Armature Fixed Magnet 7 Commutator 8 Motor Windings › To avoid irregular motion and for a smooth operation, several winding loops are used. https://www.youtube.com/watch?v=LAtPHANEfQo 9 Stepper Motor › No need of a feedback loop. › Half stepping operation. 10 Stepper Motor › Control Technique: 11 Stepper Motor › Half stepping operation: https://www.youtube.com/watch?v=eyqwLiowZiU 12 Power Converter Topologies Matrix Chopper Rectifier Inverter Converter › Chopper: DC-DC converter applications – Buck, Boost, etc. › Rectifier: AC-DC converter. › Inverter: DC-AC converter. › Matrix converter (cyclo-converter): AC-AC converter. 13 Electric Motor Drive Rectifier Inverter Matrix Converter 14 Single Phase Uncontrolled Half Wave Rectifier 15 Single Phase Uncontrolled Full Wave Rectifier 16 Single Phase Uncontrolled Full Wave Rectifier 17 Three Phase Uncontrolled Full Wave Rectifier 18 Motor Drive 19 Self-Commissioning & Auto-Diagnostic Drives 20 What is Analog and Digital Analog: – Most of the world that we experience is Analog: There are an infinite number of ‘increments’ There are an infinite number of colors to paint an object There are an infinite number of sounds levels 21 What is Analog and Digital Digital: – Digital signals and objects deal in the realm of the discrete or finite things. This means there is a limited set of values through which they can be represented. This could mean 2 possible values, 255, or anything ridiculously large, provided it's not infinity. 22 Challenges of Analog Systems Noise and Interference ✓ Analog signals are exposed to noise and signal degradation, especially over long distances or in electrically noisy environments. This is a major limitation compared to digital systems. Precision ✓ Analog signals are continuous, the precision is often limited by noise and the quality of the components. ✓ Small variations in signal can lead to inaccuracies in measurement or control. 23 Challenges of Digital Systems Latency ✓ Delays in real-time applications due to signal conversion and processing. Power Consumption ✓ It needs more energy due to increased processing and data handling. Complexity ✓ In design, debugging, and synchronization. 24 Analog or Digital? 𝑨𝒏𝒂𝒍𝒐𝒈 𝑫𝒊𝒈𝒊𝒕𝒂𝒍 25 𝑨𝒏𝒂𝒍𝒐𝒈 𝑫𝒊𝒈𝒊𝒕𝒂𝒍 Analog or Digital? 26 Analog or Digital? Resolution and Precision ✓ Analog systems offer infinite resolution because the signals can take any value within a range. ✓ Digital systems, however, have limited resolution due to the discrete nature of digital signals. Processing and Control ✓ Digital systems are easier to program and reconfigure. ✓ Analog systems may provide smoother and faster real-time responses but are harder to modify once implemented. 27 Digital or Analog? Accuracy: – For analog, 0.1% is very good accuracy. – For digital, add more circuitry to get more accuracy. Subject to accuracy of analog sensor input. Long Term Storage: – Analog circuits store data as a voltage on a capacitor. Max storage time is in minutes. – Digital circuits store data in memory. Max storage time is years. 28 Digital or Analog? Speed – Fastest circuits are analog. – The highest frequency circuits in your cell-phone etc. are analog. Design Cost/Time – Analog designers have to worry about: noise, power-supply variation, cross-talk between-wires, inaccurate values, temperature variation of component values, ground bounce, clock feed-through,... To digital designers, these are 2nd order effects. 29 Digital or Analog? Design Cost/Time cont. – Analog designers typically need several years experience. – There are many more people doing digital design than analog. – Analog circuits are rapidly being redesigned in digital. Digital is Essentially Analog – Analog problems become especially important in digital for: very fast circuits. very low supply voltages (1.0 V). very large circuits (5 million gates per chip). 30 When to Choose Analog vs. Digital Analog: ✓ High precision. ✓ Real-time response. ✓ When the physical variable is continuous. ✓ Traditional control systems without a lot of data processing. Digital: ✓ If you need flexibility and programmability for changing system requirements. ✓ For noise immunity and long-distance communication, as digital signals are less affected by interference. ✓ When integrating with computers, microcontrollers, or any system requiring 31 digital processing. Summary Analog Digital Continuous signals Discrete Infinite possible values Finite values (0,1) High Noise Sensitivity Low Noise Sensitivity Complex Hardware Simple Hardware High resolution and accuracy Can lose information during sampling 32 Hybrid System Hybrid system use both analog and digital components. For example, a sensor might produce an analog signal that is then converted to digital using an Analog-to-Digital Converter (ADC), allowing a microcontroller to process the data. In many applications, analog systems (sensors, amplifiers) combined with digital control systems (microcontrollers, programmable logic controllers) for optimized performance. 33 Hybrid System Applications Communication systems Hybrid systems are common in radio transceivers, where analog components process signals over the air and digital components manage data processing and storage. Control systems Many industrial control systems use analog inputs (from sensors) that are converted into digital signals for more accurate and complex processing. Audio and video equipment Analog sound and video inputs (e.g., microphones or cameras) are converted to digital for processing, storage, and editing, then converted back to analog for playback. 34 Hybrid System 35 Digital Signals: What is Binary? 36 https://perexpteamworks.com/en/binary-number-system/ Digital Signals: What is Binary? Binary is a number system that consists of only two digits: 0 and 1. It's also known as Base-2, unlike the decimal system (Base-10) that uses ten digits (0-9). Binary is the foundation of digital computing since it maps easily onto the two states of electrical circuits: on (1) and off (0). 37 Digital Signals: Binary (Base-2) Before we look at digital signals in depth, first we need to know how to represent them. To do this we use the Binary system. The binary number system (base-2) is an alternative to the decimal numbering system that we use every day. In the decimal system we have 10 symbols to represent numbers – The symbols are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. – After 9 we run out of symbols, so instead we ‘carry’ the 1 to the left and reset the symbol to the right to 0, resulting in 10 (ten). 38 Digital Signals: Binary (Base-2) After 1, we run out of symbols, so we ‘carry’ the 1 to the left and reset the symbol to the right to 0, resulting in 10 (two). Each of these 1s or 0s is called a ‘bit’ A group of 4 bits is called a ‘nibble’ and 8 bits is called a ‘byte’ ‘Word’ is another group of bits whose length is processor dependent. It could be 16, 32, or 64 bits, etc. 39 Why Binary is Important Digital systems, like computers and electronic devices, use binary to process data. Binary simplifies the design of circuits in processors, memory, and data storage. Logic gates (AND, OR, NOT) in computers operate using binary. Binary data can represent anything: numbers, text (ASCII), images, and more. 40 Application of Binary Computers All software and hardware operate in binary (e.g., binary code, machine code). Networking IP addresses and network protocols use binary for routing and data transfer. Data Storage Files (text, images, video) are stored in binary form. 41 Decimal versus 4-bit Binary Numbers Try converting 1 to 15 into a 4-bit binary equivalent Decimal Binary Decimal Binary 0 0000 8 1000 1 0001 9 1001 2 0010 10 1010 3 0011 11 1011 4 0100 12 1100 5 0101 13 1101 6 0110 14 1110 7 0111 15 1111 42 Digital Signals: Binary (Base-2) In an n-bit word we can represent up to 2n states ( 0 to 2n – 1) For example: – A 4-bit word can represent up to 24 ( 1 6 ) states which are numbered from 0 to 24 – 1 = 15 after which we run out of bits. The state 15 would be represented by 1111. 𝑵𝒖𝒎𝑴𝑨𝑿 = 𝟐𝒏 − 𝟏 We can rearrange this equation to determine the minimum number of bits we need to represent a number: 𝒏𝒎𝒊𝒏𝒊𝒎𝒖𝒎 = 𝒍𝒐𝒈𝟐(𝑵𝒖𝒎 + 𝟏) As we can only have an integer number of bits, we must round this up to represent the number. 43 Converting between Binary and Decimal Exp. 1: Convert 21 to binary We can check the minimum number of bits required 𝒏𝒎𝒊𝒏𝒊𝒎𝒖𝒎 = 𝒍𝒐𝒈𝟐(𝑵𝒖𝒎 + 𝟏) 𝒏𝒎𝒊𝒏𝒊𝒎𝒖𝒎 = 𝟒. 𝟒𝟔 = 𝟓 𝑨𝒏𝒔: 𝟏𝟎𝟏𝟎𝟏 44 Converting between Binary and Decimal Exp. 2: Convert 11011 to decimal 𝑵𝒖𝒎𝑴𝑨𝑿 = 𝟐𝒏 − 𝟏 𝑵𝒖𝒎𝑴𝑨𝑿 = 𝟑𝟏 𝑨𝒏𝒔: 𝟐𝟕 45 Digital Signal Waveform Typical digital signal waveform: Von Voltage Voff Time These 1s and 0s are in fact a range of voltages, and are not very sensitive to noise (temperature, supply voltage, etc.) The ‘On’ and ‘Off’ voltages can be different values, 5V, 3.3V, 1.2V, etc. depending on the device. 46 Introduction to Boolean Logic/Algebra Two value algebra: – Values are ‘0’ or ‘1’, ‘True’ or ‘False, and ‘High’ or ‘Low’ Variables: – Variables, for example ‘X’, can have values of 1 or 0 Operations: – Complement, Not, or Inverse: X is the opposite of X 47 Introduction to Boolean Logic/Algebra Operations cont.: – AND (ab or a⋅b): 𝑋 is 1 if variables a and b are both 1 – OR (a + b): 𝑋 is 1 if a or b or both are 1 – Exclusive OR (XOR) (𝑎 ⊕ 𝑏) 𝑋 is 1 if exactly one of a or b is 1 48 Introduction to Boolean Logic/Algebra Operations cont.: – NAND (𝑎𝑏 or a ⋅ 𝑏): 𝑋 is 0 if variables a and b are both 1 – NOR (𝑎 + 𝑏 ): 𝑋 is 0 if a or b or both are 1 – X-NOR (𝑎 ⊕ 𝑏 ) 𝑋 is 0 if exactly one of a or b is 1 49 Introduction to Boolean Logic/Algebra 50 Equations from Digital Circuits Ex.1: Determine the equation for ‘T’ 𝑻 = 𝑨𝑩 + 𝑪 51 Equations from Digital Circuits Ex.2: Determine the equation for ‘U’ 𝑼 = 𝑫𝑬(𝑭 + 𝑮) 52 Equations from Digital Circuits Ex.3: Determine the equation for ‘V’ 𝑽 = 𝑯𝑰 + 𝑱 + 𝑲 53 XOR and XNOR The formulas for XOR and XNOR are combinations of AND as well as OR gates 54 Introduction to Boolean Logic/Algebra What if we have more than 2 inputs? 𝑋 =𝑎⋅𝑏⋅𝑐 55 Formulas From Truth Tables Exp. 1: Determine the equation for ‘J’ given the following: A B J 0 0 0 0 1 1 1 0 0 1 1 1 𝑱 = 𝑨𝑩 + 𝑨𝑩 56 Formulas From Truth Tables Exp. 2: Determine the equation for ‘K’ given the following: A B C K 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 𝑲 = 𝑨𝑩𝑪 + 𝑨𝑩𝑪 + 𝑨𝑩𝑪 57 Formulas From Truth Tables A B C D L 0 0 0 0 0 Exp. 3: Determine the equation for ‘L’ for: 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 L = 𝑨𝑩𝑪𝑫 + 𝑨𝑩𝑪𝑫 + 𝑨𝑩𝑪𝑫 + 𝑨𝑩𝑪𝑫 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 58 Questions? 59