Laplace Transform Inverse by
Partial Fraction Expansion
Cuthbert Nyack
Consider a Laplace Transform F(s) which can be represented as a
ratio of 2 polynomials as shown below.
If the denominator can be factorised with simple roots at r1,
r2 etc. then F(s) can be expanded as:-
With coefficients
If Q(s) has a multiple zero of order m
(F(s) has a multiple pole of order m)
then the expansion of
F(s) must be written
with coefficients
Example
Consider finding the inverse f(t) of F(s) below
Since F(s) has a second order pole at the origin and complex
conjugate poles at -1/2 ± j0.866, then it can be expanded to
The coefficient a1 is calculated
a2 is
a3 is
and a4 is
The Expansion for F(s) now becomes
with inverse
and simplifies to
Return to main page
Return to page index
Copyright 1996 © Cuthbert A. Nyack.