What is Laplace Transform? Why Laplace Transform is used in Circuit Analysis?

This video explains What is Laplace Transform and Why it is used in the Circuit analysis (Advantage of using the Laplace Transform in the Circuit Analysis)
The following topics are covered in the video:
0:00 What is Laplace Transform?
1:00 Advantage of using a Laplace Transform in the Circuit Analysis
3:33 Laplace Transform Formula (One-sided Laplace Transform)
6:08 Condition for the existence of the Laplace Transform
7:55 Region of Convergence (ROC) in Laplace Transform
10:42 Inverse Laplace Transform Formula
What is Laplace Transform:
The Laplace transform is integral transform which convert the time domain function into the complex frequency domain. The complex frequency is usually represented using the variable S. (S = σ + jω)
Why Laplace Transform is used in Circuit Analysis:
Following are the advantages of using the Laplace Transform in the Circuit Analysis:
1) Using Laplace Transform, Differential Equations turns into Algebraic equation
2) Initial conditions are taken care during the transformation
3) In a single operation, the total response of the circuit (CF + PI) can be found
4) Laplace Transform can be applied to wide variety of inputs
In this video, the definition of Laplace Transform is explained, the condition for the existence of the Laplace Transform and the Region of Convergence (ROC) in Laplace Transform is explained.
And in the end, the definition of Inverse Laplace Transform is also explained.
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This video will be helpful to all the students of science and engineering in understanding what is Laplace Transform and why it is used in the Circuit Analysis ?
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[@ALLABOUTELECTRONICS]

For videos on Network Analysis / Network Theory, check this playlist:
ua-cam.com/play/PLwjK_iyK4LLBN9RIDQfl9YB4caBYyD_uo.html

[@poojashah6183]

Excellent explanation, amazing 🎉

[@mayurshah9131]

Very nice 👍

[@NadeemKhan-ei2we]

Very good explanation

[@patelraju2882]

Super 👍

[@Rocky-st1wo]

Suuper Lec& keep it up

[@_Singh.7]

Thanks❤

[@sanjayshah9838]

V. Good 👌

[@styrishrodrigues]

I have laplace transform chapter in engineering maths. I skipped that module for exam 😢

[@maxopgod1700]

💀broo

[@joewade4154]

Very good 😂

[@shtappy]

7:14 please can someone explain how |e^(-jwt)| = (sin^2(wt) + cos^2(wt))^0.5

[@ALLABOUTELECTRONICS]

As per Euler's e^jx = cos (x) + j sin (x).
And e^-jx = cos (x) - j sin (x)
If you just consider the magnitude then that is equal to sqrt (cos^2 x + sin^2 x) for both the cases.
For example, if you have a complex number A + j B, then its magnitude is sqrt (A^2 + B^2)
So, similarly, | e^-jwt| = sqrt (cos^2 (wt) + sin^2 (wt)) = 1

[@shtappy]

​@@ALLABOUTELECTRONICS Thanks a lot for quick ve detailed answer!

[@zoro.73]

Why are you using "j" to represent imaginary number
Didn't the representation of imaginary number "i" comes from the term "imaginary"
Using "j" just doesn't make any sense

[@shtappy]

Because i used for current, j used for imajinary in electrical engineering. By the way, I prefer in-phase (I) and quadrature (Q) as an electrical engineer because there is no imaginary thing in real world. Mathematicians loves abstraction so they call it imaginary.

[@husnainhyder6713]

Can you please explain how we will going to use Laplace transform in circuits involving diode and transistors of all kinds.
I was working with clippers and clampers lately but I wasn't achieving desired results with that.,
If you have any idea regarding that then please help

[@ALLABOUTELECTRONICS]

The Laplace Transform will be useful when we are dealing with a source which is not DC or sinusoidal signal. (e.g ramp signal, exponential decaying signal, step function etc). If the clipper or clamper circuit contains a conventional source like DC, square wave, triangular wave, or sinusoidal wave) then it is better to deal such circuits with the conventional circuit analysis. I have already covered how to analyze clipper and clamper circuits. For more info, you can check those videos and the solved problems related to them.

[@AllenSA_Lily]

Super👍