Introduction to Electrical Engineering

Transcription

1 DR. GYURCSEK ISTVÁN Introduction to Electrical Engineering Sources and additional materials (recommended) Dr. Gyurcsek Dr. Elmer: Theories in Electric Circuits, GlobeEdit, 2016 ISBN: gyurcsek.istvan@mik.pte.hu

2 Introduction (Bio-1) At a glance Contact DR. GYURCSEK ISTVÁN Department of Electrical Networks Institute of Information and Electrical Technology University of Pécs Office: Boszorkány street 2 Room: B.232 Web: gyurcsek.istvan@mik.pte.hu Phone: / [msc: electrical engineer] - [dr.univ: physics] [text books:08] [periodicals:10] [patents:06] [conferences:15] [pmmff-a] - [tkb] 2 gyurcsek.istvan@mik.pte.hu

3 Introduction (Bio-2) [budapest] [münchen] [berlin] [frankfurt] [wien]-[moscow] [samara]-[hhi,sc/usa] [hiking] [swimming] [photography] [blue track:5705] [dubai]-[kuwait] [yerevan] [peterborough] [london] [warsaw]-[lodz]-[pécs] [2 children] [2 locations] [1 car] 3 gyurcsek.istvan@mik.pte.hu

4 Course Introduction Topics and Requirements Mathematics Background 4 gyurcsek.istvan@mik.pte.hu

5 The Method I hear and I forget I see and I remember I do and I understand 5 gyurcsek.istvan@mik.pte.hu

6 Language The book of nature is written in the language of mathematics. 6 gyurcsek.istvan@mik.pte.hu

7 How to TRUE USEFUL ESTHETIC MIN REQ: 2 OUT OF 3 THE ONLY QUESTION IS WHY? 7 gyurcsek.istvan@mik.pte.hu

8 Course Introduction Topics and Requirements Mathematics Background 9 gyurcsek.istvan@mik.pte.hu

9 Presence

10 Prerequisites FOUR BASIC OPERATIONS ( IN ENGINEERING ) Differential calculus f(t) t Integral calculus Laplace transform Fourier transform L f(t), t2, න f t dt t1 F f(t) L 1 f(t), F 1 f(t) 11 gyurcsek.istvan@mik.pte.hu

11 Electrical Engineering 1 INTRODUCTION Course overview (covered topics and required background in mathematics) ELECTROMAGNETIC FIELDS Electric field (characteristics of static electric field, Gauss law, energy of the electric field, interaction with matter, characteristics of stationary electric field, theoretical background of Ohm s law and Kirchhoff s laws) (examples) Magnetic field (Energy in static and stationary magnetic field, interaction with matter, induction, self and mutual inductance, Amperee s excitation law, Faraday s induction law, Time varying electric and magnetic fields, Maxwell equations) DC CIRCUIT ANALYSIS Concepts and definitions (charge and current, voltage, power and energy, circuit elements) (examples) Basic laws (Ohm s Law, nodes, branches, and loops, Kirchhoff s laws, series resistors and voltage division, parallel resistor and current division, wye-delta transformations) (examples) Methods of analysis (nodal analysis, mesh analysis, applications: DC transistor circuits) (examples) Circuit theorems (linearity property, superposition, source transformation, Thevenin s theorem, Norton s theorem, maximum power transfer) (examples) Operational amplifiers (ideal op amp, inverting amplifier, noninverting amplifier, summing amplifier, difference amplifier, cascaded op amp circuits) (examples) BASIC AC CIRCUITS Capacitors and inductors (capacitors, series and parallel capacitors, inductors, series and parallel inductors, applications) (examples) Sinusoids and phasors (sinusoids, phasors, phasor relationships for circuit elements, impedance and admittance, Kirchhoff s laws in the frequency domain, impedance combinations) (examples) Sinusoidal steady-state analysis (nodal analysis, mesh analysis, superposition theorem, source transformation, Thevenin and Norton equivalent circuits, op amp AC circuits) AC power analysis (instantaneous and average power, maximum average power transfer, effective or RMS value, apparent power and power factor, complex power, conservation of AC power, power factor correction) (examples) 13 gyurcsek.istvan@mik.pte.hu

12 Electrical Engineering 2 ADVANCED AC CIRCUITS Three-phase circuits (balanced three-phase voltages, balanced wye-wye, wye-delta, delta-delta, delta-wye connections, power in a balanced system, unbalanced three-phase systems, applications) (examples) Magnetically coupled circuits (mutual inductance, energy in a coupled circuit, linear transformers, ideal transformers, three-phase transformers, applications) (examples) Frequency response (transfer function, decibel scale, Bode plots) (examples) Resonance circuits (series and parallel resonances, passive and active filters, applications) (examples) Circuits with general periodic excitations (trigonometric and exponential Fourier series, symmetry considerations, frequency spectra, circuit applications, average power and RMS values) (examples) Two-port networks (impedance and admittance parameters, hybrid parameters, transmission parameters, relationships between parameters, interconnection of networks, symmetric two-ports, applications) (examples) DYNAMIC CIRCUITS First-order circuits (source-free RC and RL circuits, singularity functions, step response of RC and RL circuits, applications) (examples) Second-order circuits (finding initial and final values, source-free series and parallel RLC circuits, step response of a series and parallel RLC circuits, general second-order circuits, electrical duality, applications) (examples) INTEGRAL TRANSFORMS IN CIRCUIT ANALYSIS The Laplace transform (definitions, properties, inverse Laplace transform,, application to integrodifferential equations, convolution integral, circuit element models, circuit analysis, transfer functions in s-domain) (examples) The Fourier transform (definitions, properties, circuit applications, Parseval s theorem, comparing the Fourier and Laplace transforms, applications) (examples) 14 gyurcsek.istvan@mik.pte.hu

13 Required Performance 1 Requirements Two approved classroom studies (scheduled during the semester) Written examination (scheduled for the exam terminus) Grading guidelines Outstanding work (mark 5, %). Execution of work is thoroughly complete and demonstrates a superior level of achievement overall with a clear attention to details. The student is able to synthesize the course material with new concepts and ideas in a thoughtful manner and is able to express those ideas in clear way. High quality work (mark 4, 76-89%). Student work demonstrates a high level of knowledge with consistency. The student demonstrates a level of thoughtfulness in addressing concepts and ideas. Work demonstrates excellence but less consistency than a 5 student. Satisfactory work (mark 3, 63-75%). Student work addresses all of the task and assignment objectives with few minor or major problems. Less than satisfactory work. (mark 2, 51-62%). Work is incomplete in significant ways and lacks attention to details. Unsatisfactory work (mark 1, 0-50%). Work exhibits several major and minor problems with basic conceptual premise, lacking both intention and resolution. Results are severely lacking and are weak in clarity and completeness. 15 gyurcsek.istvan@mik.pte.hu

14 Readings, Sources (EN) Globe Edit, ISBN:

15 Readings, Sources (HU) Torda B.: Bevezetés az elektrotechnikába 1-2. SZIE 2005 (kézirat) Simonyi K.: Villamosságtan. AK Budapest 1983, ISBN: Simonyi K. - Zombory L.: Elméleti villamosságtan. MK Budapest 2000, ISBN: Zombory L.: Elektromágneses terek. MK Budapest 2006, ( Dr.Selmeczi K. - Schnöller A.: Villamosságtan 1. MK Budapest 2002, TK szám: 49203/I Dr.Selmeczi K. - Schnöller A.: Villamosságtan 2. TK Budapest 2002, ISBN: Fodor Gy.: Elméleti elektrotechnika 1-2. TK Budapest 1974, TK. szám: Fodor Gy.: Hálózatok és rendszerek. Műegyetemi Kiadó Budapest Fodor Gy.: Villamosságtan példatár. TK Budapest Simonyi K.- Fodor Gy. Vágó I.: Elméleti villamosságtan példatár. TK Bp. 1967, TK szám: gyurcsek.istvan@mik.pte.hu

16 Course Introduction Topics and Requirements Mathematics Background

17 Functions

18 Linearity Conditions of linearity Homogenity y = h(x) a y = h(a x) Additivity y 1 = h x 1, y 2 = h x 2 y 1 + y 2 = h x 1 + x 2 Example 1 Differential calculus Example 2 - Relationship bw. excitation and response Homogenity y = dx dt Additivity a y = d a x dt y 1 = dx 1 dt, y 2 = dx 2 dt = a dx dt Homogenity V = R I a V = R (a I) Additivity V 1 = R I 1, V 2 = R I 2 y 1 + y 2 = d x 1 + x 2 dt = dx 1 dt + dx 2 dt V = R I 1 + I 2 = R I 1 + R I 2 = V 1 + V 2 21 gyurcsek.istvan@mik.pte.hu

19 Matrix 1 R = R 11 R 1N R N1 R NN R 11 R 1N R N1 R NN i 1 i N = v 1 v N M = a 11 a 12 a 21 a 22 = a 11 a 22 a 12 a 21 I = i 1 i N V = v 1 v N R 11 i 1 + R 12 i R 1N i N = v 1 R 21 i 1 + R 22 i R 2N i N = v 2 adjm = a 22 a 12 a 21 a 11 adjoint M 1 = 1 adjm = R I = V R N1 i 1 + R N2 i R NN i N = v N = a 22 a 12 a 21 a gyurcsek.istvan@mik.pte.hu

20 Matrix 2 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 x 1 x 2 x 3 = b 1 b 2 b 3 Cramer s rule (n n) x 1 = 1, x 2 = 2, x 3 = 3 = det a 11 a 12 a 13 a 21 a 22 a 23 1 = det a 31 a 32 a 33 = det b 1 a 12 a 13 a 11 b 1 a 13 b 2 a 22 a 23 2 = det a 21 b 2 a 23 b 3 a 32 a 33 a 31 b 3 a 33 3 a 11 a 12 b 1 a 21 a 22 b 2 a 31 a 32 b 3 Sarrus rule 3 3 = a 11 a 22 a 33 + a 12 a 23 a 31 + a 13 a 21 a 32 a 13 a 22 a 31 a 11 a 23 a 32 a 12 a 21 a 33 extension right OR extension down 23 gyurcsek.istvan@mik.pte.hu

21 Differential Calculus f x + x f x x + x x = f x x df x dx = f (x) (slope at arbitrary point x) f(x) g(x) = f x g x g x f(x) g(x) 2 df g x dx = df g x dg x dg x dx example. 1; sin ωt = ω cos ωt example. 2; cos ωt = ω sin ωt example.3; e st = s e st 24 gyurcsek.istvan@mik.pte.hu

22 Integral Calculus i b f(x i) x න f(x) dx a S ab below f(x) b න f(x) dx = F(x) b a = F b F(a) a example. 1; F = F s W ab F s, example. 2; U avg = 1 T න 0 T u(t) dt W ab = example. 3; ර A i b F(s i) s න F(s) ds = න a a B da = 0 b F (s) cos α ds 25 gyurcsek.istvan@mik.pte.hu

23 Trigonometry 2 cos x cos y = cos x y + cos x + y sin x ± y = sin x cos y ± cos x sin y cos x ± y = cos x cos y sin x sin y sin 2x = 2 sin x cos x cos 2x = cos 2 x sin 2 x cos 2 x + sin 2 x = 1 Calculus f(x) f (x) F(x) sin x cos x cos x cos x sin x sin x tan x 1 + tan 2 x ln cos x 26 gyurcsek.istvan@mik.pte.hu

24 Complex Numbers Complex number SCALAR z ҧ = x + j y or z = x + j y (signed simply bold although not a vector) z = x + j y = r cos φ + j sin φ = r e jφ j = 1 = 1 e jπ = 1 e jπ/2 Calculus e jφ = cos φ + j sin φ Euler z 1 = x 1 + j y 1, z 2 = x 2 + j y 2 r = x 2 + y 2, φ = tan 1 y x z 1 + z 2 = x 1 + x 2 + j y 1 + y 2 x = r cos φ, y = r sin φ z 1 z 2 = r 1 r 2 e j φ 1+φ 2 * cos φ = ejφ + e jφ 2 sin φ = ejφ e jφ j 2 z 1 z 2 = r 1 r 2 e j φ 1 φ 2 z = x j y = r e jφ HW: j 2j =? 27 gyurcsek.istvan@mik.pte.hu

25 Function Transform 1 v t = V cos ω t + φ v t = V m e j ω t+φ = V m e jφ jω t e v t V, V v t, PHASOR(supressing time factor) V = V e jφ v t = Re v t 28 gyurcsek.istvan@mik.pte.hu

26 Function Transform 2 x t, τ = rect t, τ X Ω, τ = F x t, τ = τ sin Ωτ/2 Ωτ/2 = τ sinc Ωτ/2 (sinc cardinal sine) f t F ω = F f(t) = න f(t)e jωt dt F ω f t = F 1 F(ωt = 1 2π න F jω e jωt dω 29 gyurcsek.istvan@mik.pte.hu

27 Questions