Electronics/Laplace Transform pairs

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Electronics | Foreword | Basic Electronics | Complex Electronics | Electricity | Machines | History of Electronics | Appendix | edit



f(t) F(s)
\delta(t-t_0) e^{-st_0}
u(t) \frac{1}{s}
e^{-\alpha t} u(t) \frac{1}{s+\alpha}
\sin(\beta t) u(t) \frac{\beta}{s^2+\beta^2}
\cos(\beta t) u(t) \frac{s}{s^2+\beta^2}
e^{-\alpha t}\sin(\beta t) u(t) \frac{\beta}{(s+\alpha)^2+\beta^2}
e^{-\alpha t}\cos(\beta t) u(t) \frac{s+\alpha}{(s+\alpha)^2+\beta^2}
2e^{\alpha t}(a\cos{\beta t}-b\sin{\beta t}) u(t) \frac{a+jb}{s+\alpha-j\beta}+\frac{a-jb}{s+\alpha+j\beta}
t^n \frac{n!}{s^{n+1}}
t^nf(t) (-1)^n\frac{d^nF(s)}{ds^n}
\frac{df(t)}{dt} sF(s)-f(0)
\int_0^tf(x) dx \frac{1}{s}F(s)
u_{-1}(t-t_0)f(t-t_0) e^{-t_0s}F(s), t_0 \ge 0
h(t)*f(t)=\int_0^th(t-\tau)f(\tau) d\tau H(s)F(s)
f_1(t)f_2(t) F_1(s)*F_2(s)