Đang tải... (xem toàn văn)
Những nội dung chính được trình bày trong bài giảng Electrical and electronic principles - Chương 7 gồm có: Laplace transform, circuit element models, circuit analysis, transient analysis. Mời các bạn cùng tham khảo.
TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT TP HỒ CHÍ MINH ELECTRICAL AND ELECTRONIC PRINCIPLES WEEK 7, Cuong Q Ngo Last classes • Trigonometric Fourier series • Plot function - MATLAB • Circuit Application (Applying Fourier series) Contents (Today class) • Laplace transform • Circuit element models • Circuit analysis • Transient analysis Laplace Transform • The Laplace transform is an integral transformation of a function f (t) from the time domain into the complex frequency domain, giving F (s) • Where s is a complex variable: 𝑠 = 𝜎 + 𝑗𝜔 Laplace Transform • Determine the Laplace transform of Laplace Transform • Laplace transform pairs (f(t) = 0, for t < 0) Laplace Transform • Laplace transform pairs (f(t) = 0, for t < 0) Laplace Transform • Inverse Laplace transform Decompose F(s) into simple terms using partial fraction expansion Find the inverse of each term by matching entries in the previous table Laplace Transform • Find the inverse Laplace transform of Laplace Transform • Answer: 𝑓 𝑡 = 3𝑢 𝑡 − 5𝑒 −𝑡 𝑢 𝑡 + sin 2𝑡 𝑢(𝑡) 10 Laplace Transform • Find f(t) given that 11 Laplace Transform • Answer: 𝑓 𝑡 = (2 − 8𝑒 −2𝑡 + 7𝑒 −3𝑡 )𝑢(𝑡) 12 Circuit element models • For a resistor 13 Circuit element models • Representation of an inductor: 14 Circuit element models • Representation of a capacitor: 15 Circuit element models • Impedance of elements in the s-domain (zero initial condition) 16 Circuit analysis • Steps in applying the Laplace transform Transform the circuit from the time domain to the s-domain Solve the circuit using nodal analysis, mesh analysis, sourcetransformation, superposition, or any circuit analysis techniquewith which we are familiar Take the inverse transform of the solution and thus obtain thesolution in the time domain 17 Circuit analysis • Find vo(t) in the circuit, assuming zero intial condition 18 Circuit analysis • Answer: 19 Circuit analysis • The switch closes the circuit at t = Find i(t) for t > i(t) 20 Circuit analysis • Answer: 𝑅 𝑉 −𝑡 𝐿 𝑖 𝑡 = 1−𝑒 𝑅 21 Trasient analysis (MultiSim) • Multisim computes the circuit’s response as a function of time • Each input cycle is divided into intervals, and a DC analysis is performed for each time point in the cycle 22 Transient analysis 23 ... Impedance of elements in the s-domain (zero initial condition) 16 Circuit analysis • Steps in applying the Laplace transform Transform the circuit from the time domain to the s-domain Solve the circuit... techniquewith which we are familiar Take the inverse transform of the solution and thus obtain thesolution in the time domain 17 Circuit analysis • Find vo(t) in the circuit, assuming zero intial condition...Last classes • Trigonometric Fourier series • Plot function - MATLAB • Circuit Application (Applying Fourier series) Contents (Today class) • Laplace transform