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]
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Goals of this note set:
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.*is* transformLaPlace a what Understand
*LaPlace Tranforms are slightly modified Fourier Transforms.*
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
The LaPlace Transform
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
The LaPlace Transform
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Multiply our Function with an Decaying Exponential:
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Multiply our Function with an Decaying Exponential:
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Fourier Transform of G(t)=F(t)*exp(-st)
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
LaPlace Transform=Fourier Transform of G(t)=F(t)*exp(-st)
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Who Gets Credit ?
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Why use the LaPlace Transform ?
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Transforms of Derivative and Integrals
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Inductor
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Inductor
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Capacitor
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Capacitor
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Resistors
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: Independent Sources
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Applications to Circuit Elements: *De*pendent Sources
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
Example Problem---with Initial Conditions
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
ECE137A class notes, UCSB, Mark Rodwell, copyright 2019
For Reference: LaPlace Transform Pairs
function Step
finally... ...and
