Laplace Transform

## $F(s) = L(f) = \int_0^{\infty}e^{-st}f(t)dt$

 f(t) L(f) 1 $\frac{1}{s}$ t $\frac{1}{s^2}$ $t^2$ $\frac{2!}{s^3}$ $t^n$ $\frac{n!}{s^{n+1}}$ $t^a$ $\frac{\Gamma (a+1)}{s^{a+1}}$ $e^{at}$ $\frac{1}{s-a}$ $coswt$ $\frac{s}{s^2+w^2}$ $sinwt$ $\frac{w}{s^2+w^2}$ $cosh at$ $\frac{s}{s^2-a^2}$ $sinh at$ $\frac{a}{s^2-a^2}$ $e^{at}coswt$ $\frac{s-a}{{(s-a)}^2+w^2}$ $e^{at}sinwt$ $\frac{w}{{(s-a)}^2+w^2}$
• s-Domain Circuit Element Model

$v(t)=Ri(t) \Rightarrow V(s)=R I(s)$
$Z_R(s)=\frac{V_R(s)}{I_R(s)}=R$

page revision: 63, last edited: 10 Feb 2011 14:24