Introduction to Electric Circuits -...

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Introduction to Electric Circuits Chapter 14 The Laplace Transform Part 1

Transcript of Introduction to Electric Circuits -...

Page 1: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Introduction to Electric Circuits

Chapter 14 The Laplace TransformPart 1

Page 2: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Laplace Transform

Page 3: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 4: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Inverse Laplace Transform

Page 5: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 6: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Linearity

Page 7: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 8: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Laplace Transform of Derivative

Integration by parts

d du dv dv d duuv v u u uv vdt dt dt dt dt dt

dv duu uv vdt dt

00 0

, ,

( ) (0 )

st st

st st st

dv df duu e v f sedt dt dt

df e dt e f s fe dt sF s fdt

Page 9: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 10: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 11: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 12: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 13: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 14: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 15: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 16: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Pulse Inputs

Unit step function

Page 17: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Impulse Function

Page 18: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Impulse Function

Page 19: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Time-shifted Function

Page 20: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 21: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 22: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Inverse Laplace Transform

Page 23: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 24: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Simple Complex Conjugate Poles

Page 25: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 26: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 27: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 28: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 29: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 30: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.

Repeated Poles

Page 31: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 32: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.
Page 33: Introduction to Electric Circuits - ccrs.hanyang.ac.krccrs.hanyang.ac.kr/webpage_limdj/circuit2/Chapter14_1.pdf · EXAMPLE 14. —st 2-1 Laplace Transform Pairs —at where a > 0.