What is a S domain ,and how can i convert normal electrical circuit parameters to S domain?
- LawrenceLv 61 decade agoFavorite Answer
The S domain is the complex frequency domain which is represented by the application of the Laplace transform.
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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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'
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....