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ECE 3336 Introduction to Circuits & Electronics

ECE 3336 Introduction to Circuits & Electronics. Lecture Set #9 Linear Circuit-Fourier-Digital. Dr. Han Le ECE Dept. Introduction to Circuits & Electronics. Input. Output. It does something useful: information power. Concept of System (Contraption). R. Control. C.

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ECE 3336 Introduction to Circuits & Electronics

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  1. ECE 3336 Introduction to Circuits & Electronics Lecture Set #9 Linear Circuit-Fourier-Digital Dr. Han Le ECE Dept.

  2. Introduction to Circuits & Electronics Input Output • It does something useful: • information • power

  3. Concept of System (Contraption)

  4. R Control C input vin[t] i(t) output vout[t] System (circuits) Input Output xk(t) yj(t) k=1,..., m C j=1,..., p i(t) R output vout[t] Concept of System in Electronics Low pass High pass input vin[t]

  5. Control System (circuits) Input Output xk(t) yj(t) k=1,..., m j=1,..., p Linear (Time-Invariant) System Output Input This is called “linear” Time-invariant DOES NOT mean time-constant. It means that it does not matter when you input the signals (today or 1,000,000 yr BC), you’ll get the same output

  6. The most significant application of electronic systems is signal processing: • generating: signal synthesis: converting information (logic) into electrical signal (voltage or current), encoding • conditioning (transforming): signal shaping, filtering, amplifying • transmitting: sending signal to other parts of the circuit, or over transmission media: conductor, air (EM waves), fiber optics (for long distance) • receiving: transforming the signal, converting into information

  7. Harmonic function Fourier transform Phasors Complex numbers &analysis

  8. Applications of mathematical techniques Harmonic function Fourier transform • Signal and AC circuit problems • RLC or any time-varying linear circuits. Applicable to linear portion of circuits that include nonlinear elements • Signal processing • signal analysis (spectral decomposition) • filtering, conditioning (inc amplification) • synthesizing Phasors Complex number &analysis

  9. Outline • Time-varying circuits and signals • Introduction to mathematical techniques: • Harmonic functions • Complex analysis • Phasors • Fourier analysis and transform • Applications of mathematical techniques to physical problems and circuits

  10. Link to Mathematica file

  11. the digital electronic trend

  12. Automatic Fan Control: The Analog Way We have +-15 V and 5 V DC power input. +15 V Temperature sensor input (low=0.5 V; high=4 V) Voltage comparator User preset (controllable) voltage input. -15 V

  13. Automatic Fan Control: The Digital Way We have +-15 V and 5 V DC power input. Temperature sensor Micro-processor User preset digital: 10101101 The digital core However, the physical world is analog; the digital core is still based on the analog circuit principle. And outside the digital core, it is still an analog periphery.

  14. Digital Electronics • Signal processing is fundamentally mathematical operation • In the past, electronic circuits were used to do signal processing mathematics directly on the signal voltage or current (analog). • With digital electronic, voltage and current no longer represents the signal directly, they represent the numerical (digital) value of the signal • Electronic circuits (ICs) are designed to perform numerical (digital) mathematical operations: microcontrollers, digital signal processors, FPGA, microprocessors…

  15. Logical layer (Digital design) Physical layer (Analog implementation) • Electronics become “mathematical operation”-oriented at the functional design level • However, fundamental electrical circuit behavior is still essential at the physical implementation level

  16. A summary of phasor, Fourier, signal processing and all that

  17. The basics • Voltage or current signal is time-dependent (otherwise, there is no information transmitted) • Solving time-dependent differential equations for circuits involving R, L, C is difficult & tedious • But if the signal is a pure harmonic of single frequency, we can use phasor transform, which is easy • As it turns out, even if the signal is not a harmonic, Fourier theorem tells us that it can be break down as a sum (or integral) of harmonics • Hence, we can use phasor method, along with Fourier theorem to solve for any signal

  18. Linear Circuit - Frequency domain Circuit Arbitrary input Output Input Fourier Fourier Phasor Harmonic function Harmonic transfer function

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