partial fraction expansion and decomposition

Hello,

I'm facing the following problem: I'm trying to get a model for an
electrical dipole made of series and parallel simple elements in ladder
network (R and C). With Maxima, I obtain the admittance as f.i.
1/(1/(1/(1/(C2p2*s+1/R2p2)+1/(C2p1*s))+1/R2p1)+1/(C2s*s))
where s is the Laplace variable, C2s is the first series capacitor, R2p1
the first parallel element, C2p1 comes in parallel with R2p1 and in series
with the next stage, and so on. Having admittance measurements on a
circuit, I can model the admittance as a function of frequency as
N(s)/D(s), where N(s) is a third degree with no independent term, and D(s)
is second degree, with the independent term equal to one.

If I use ratsimp on the admittance expression, I can then match the
expanded fraction coefficients with the identified coefficients, but the
result is non-linear. For instance, the numerator coefficient associated
with s^3 is the product of the three capacitors and of the two resistors.

As the poles are distinct, I would like to obtain a simpler expression, as
Y(s) = T2 s^2 + T1 s + P0/(s-p0) + P1/(s-p1)
in order to match them against the output of Octave "residue" function. 
This is to say that I search an analytical simple fractional expansion of
Y(s). Is it possible with Maxima ?

Regards

Pascal Dupuis
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