EEVblog Electronics Community Forum
Electronics => Projects, Designs, and Technical Stuff => Topic started by: T. Mandresy Billy on December 02, 2018, 05:37:25 pm
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In my textbook, Engineering Circuit Analysis 8.Ed by William H. Hayt (Chapter 14, Section 14.1 page 536) I stumbled across a section explaining the complex frequency. The goal is to cover the concept of complex frequency when it comes to exponentially damped sinusoidal functions.
(https://my.pcloud.com/publink/show?code=XZPPlg7ZngPpIC2dhafb9scO3EVjpHvok5py)
https://my.pcloud.com/publink/show?code=XZPPlg7ZngPpIC2dhafb9scO3EVjpHvok5py
HOW DID THIS HAPPEN?
How did eσt become ejσt out of the blue?
And why did ej(ωt) become ej(jωt) ? Any help would be much appreciated.
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It comes from Eulers relationship
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Thanks for stopping by. I know this Euler's relationship. The real mystery is below. Look at it and you will find, from the mathematical expressions that:
exp(σt) become exp(jσt). How did this happen?
why did exp(jωt) become exp(jjωt)?
AN ADDITIONAL j SUDDENTLY APPEARS.
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Sorry...when the image came on my screen i did not see the last line.
It is just algebra to get to the last step. First get all terms in the form of e^x and then recombine.
There is a typo in the book. That accounts for the extra j. It should not be there.
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Glad to be reassured it was just a typo. I will email the editor about this then.
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Yes it's incorrect. They introduce the notion of complex frequency:
s = σ + jω
probably as a preliminary to get you to the Laplace transform.
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Glad to be reassured it was just a typo. I will email the editor about this then.
LOL...I am an author of an EE textbook. I hate it when someone informs me of an error...but they creep in, no matter how hard you try.