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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
ECE137A, Notes Set 15:
LaPlace Transforms
Mark Rodwell, Doluca Family Chair, ECE DepartmentUniversity of
California, Santa [email protected]
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Goals of this note set:
response.ansient circuit tr find to themuse tohowRemember
from. comesit where....and
.*is* transformLaPlace a what Understand
*LaPlace Tranforms are slightly modified Fourier
Transforms.*
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
The LaPlace Transform
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
The LaPlace Transform
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Multiply our Function with an Decaying Exponential:
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Multiply our Function with an Decaying Exponential:
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Fourier Transform of G(t)=F(t)*exp(-st)
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
LaPlace Transform=Fourier Transform of G(t)=F(t)*exp(-st)
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Who Gets Credit ?
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Why use the LaPlace Transform ?
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Transforms of Derivative and Integrals
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Inductor
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Inductor
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Capacitor
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Capacitor
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Resistors
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Independent Sources
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: *De*pendent Sources
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
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ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
function Step
finally... ...and
