# Significance of s

Discussion in 'General Electronics Chat' started by aamirali, Apr 25, 2012.

1. ### aamirali Thread Starter Member

Feb 2, 2012
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2
1. What's signigfance of s (used in Ls, 1/Cs) inductors & capacitors.

2. I read that s=jw. Why we want to introduce imaginary component in our circuit analysis, but in real we have to wok for real components only

2. ### Papabravo Expert

Feb 24, 2006
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2,697
It allows us to keep track of both magnitude and phase.

3. ### WBahn Moderator

Mar 31, 2012
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7,653
Note that 's' is a complex variable with real and imaginary components. Setting it equal to jw isn't 'introducing' an imaginary component, but rather keeping only the imaginary part and getting rid of the real part.

What background do you have at this point? Are you at all familiar with Laplace and Fourier transforms yet?

Depending on your answer, I can probably direct you to another thread where this is answered in some detail.

4. ### crutschow Expert

Mar 14, 2008
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6,744
The s is used to signify the reactive component of an impedance. It allows you to use the imaginary number system to easily calculate the impedance of a circuit and the phase shift the reactive components cause between the current and the voltage. If you didn't use imaginary numbers, these would be very difficult to calculate.

The s term has both transient and steady-state components from the Laplace transforms of the calculus equations. If you are only interested in the steady-state term (constant AC voltages) then you substitute jω for s.

Imaginary doesn't mean imaginary components. Imaginary is perhaps an unfortunate term for the complex number system but that is what the original mathematicians that developed the system called it so we live with it. The imaginary or complex number system just gives an easy way to mathematically calculate the behavior of circuits that contain both resistive and reactive components. It allows us to use algebra to calculate the parameters rather than the more complex basic calculus equations that describe the circuit behavior.

5. ### aamirali Thread Starter Member

Feb 2, 2012
415
2

Thanks everyone for reply.
yes I am grad student & went through laplace & fourier

6. ### WBahn Moderator

Mar 31, 2012
24,454
7,653
So how much circuit analysis have you had? Have you taken a Transform Methods course?

Short answer: The s comes from taking the Laplace transform of the differential equations governing the V-I relationship for a capacitor and an inductor. Setting s=jw is simply converting it to the Fourier transform. The former allows you to obtain the complete solution, including the transient response, while the latter only lets you get the steady state response.

7. ### kelvin_mksinst New Member

Apr 28, 2012
3
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Laplace or Fourier transform is to remove the time from the equation, and engineer not longer need to due with complicated differential equation in circuit analysis. s-domain and frequency domain is very useful for example in control theory.