Fourier Series Harmonics Any periodic function f(t)=f(t+T) can be expressed as a Fourier series of sines and cosines: 00 00 bm f(t)=ao + Σa cos(no ot) + Σb sin(noot) n= n= Where Period T and fundamental frequency @0 satisfy the equation T=27/000 1 Ꭲ a0= f(t) dt T 2 T an= Ꭲ T30 f(t) cos(noot)dt 2 T bn= f(t) sin(noot)dt TJ Laplace Transformation The Unit-Step Function u(t): u(t) <= ㅎ e-st The unit-impulse function (t-to): 8(t-t) <==> 0 8(t) <=>1 for to=0 The Exponential Function eat e¯atu(t) <==> (s+a) The Ramp Function tu(t): == tu(t) <==> -at The function te 'u(t): -at te 'u(t) <==> (s+a) Time Differentiation Theorem dV(t) <==> sV(s) - V(0) dt d2V(t) <==> s²V(s) - SV(0) - V'(0) dt2 In the following circuit: If vs (t) is given as a square waves as shown: If L=2H and R=492, Find i(t)? Vs (t)4 8 Solution: 3 Vs (t) + mi(1) R

Fourier Series Harmonics Any periodic function f(t)=f(t+T) can be expressed as a Fourier series of sines and cosines: 00 00 bm f(t)=ao + Σa cos(no ot) + Σb sin(noot) n= n= Where Period T and fundamental frequency @0 satisfy the equation T=27/000 1 Ꭲ a0= f(t) dt T 2 T an= Ꭲ T30 f(t) cos(noot)dt 2 T bn= f(t) sin(noot)dt TJ Laplace Transformation The Unit-Step Function u(t): u(t) <= ㅎ e-st The unit-impulse function (t-to): 8(t-t) <==> 0 8(t) <=>1 for to=0 The Exponential Function eat e¯atu(t) <==> (s+a) The Ramp Function tu(t): == tu(t) <==> -at The function te 'u(t): -at te 'u(t) <==> (s+a) Time Differentiation Theorem dV(t) <==> sV(s) - V(0) dt d2V(t) <==> s²V(s) - SV(0) - V'(0) dt2 In the following circuit: If vs (t) is given as a square waves as shown: If L=2H and R=492, Find i(t)? Vs (t)4 8 Solution: 3 Vs (t) + mi(1) R

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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