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# What is a S domain ,and how can i convert normal electrical circuit parameters to S domain?

### 6 Answers

- LawrenceLv 61 decade agoFavorite Answer
The S domain is the complex frequency domain which is represented by the application of the Laplace transform.

http://en.wikipedia.org/wiki/Laplace_transform#For...

In the time domain, functions are with respect to time. In the S domain, functions are with respect "per time" or frequency.

Multiplying by s in the S domain represents differentiation in the time domain. Dividing by s in the S domain represents integration in the time domain.

A first derivative of a function F(t) in the s domain is sF(s) - F(0)

A second derivative of a function F(t) in the s domain is s²F(s) - sF(0) - F'(0)

"normal electrical circuit parameters"? I think you mean typical circuit parameters, such as voltage, current and impedance.

Ohms Law is:

V = IZ

In this example, I placed R, L & C in series. In the S domain, impedance for R, L & C can be stated in a general form as:

R + Ls + 1/(Cs)

Voltage and Current in the time domain are, V(t) and I(t) respectively. In the S domain voltage and current become, V(s) and I(s).

So a series RLC circuit in the S domain is:

V(s) = I(s)[ R + Ls + 1/(Cs) ]

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Which re-arranged is

CV(s)s = I(s)[ RCs + LCs² + 1 ]

For clarity, let I = I(s) and V = V(s)

CVs = LCs²I + RCsI + I

Applying initial conditions we have

CVs - V(0) = [ LCs²I - sI(0) - I'(0) ] + [ RCsI - I(0) ] + I

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What is a S domain ,and how can i convert normal electrical circuit parameters to S domain?

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The s domain uses the laplace transform to simplify circuit analysis. Impedance values are as follows: Resistors stay as their same value R, capacitors become 1/(sC) and inductors become sL. A step function is modelled by 1/s, an exponential decay for instance e^(-at) becomes 1/(s+a), a sinusoid sin(wt) becomes w/(s^2+w^2), cos(wt) becomes s/(s^2+w^2). These are only the most common parameters I can think of. You need an understanding of Laplace Transforms though to really understand.

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- Anonymous1 decade ago
there is two main domains time domain and frequency domain so

S domain means frequency domain

and how to convert from time to frequency you need to study 'Laplace transform'

for example

time : frequency

-----------------------------------

1 : 1/s

e^at : 1/(s-a)

sin(at) : a/(s^2-a^2)

if u search for it u will find all the other transforms

*there is also z domain means discrete (for knowledge only ) :D

- 5 years ago
ANALAYSIS IN S DOMAIN IS EASY BECAUSE CONVERT DIFFERENTIAL EQUATIONS IN SIMPLE POLYNOMIAL....