Re: TC Differential Equations

• To: tesla-at-pupman-dot-com
• Subject: Re: TC Differential Equations
• From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twf-at-verinet-dot-com>)
• Date: Fri, 12 Feb 1999 19:09:41 -0700
• Approved: twf-at-verinet-dot-com

Tesla List wrote:

>         What do you mean by "The coefficients of the common Laplace
transform
> denominator"?  I'm not familiar with this nomenclature, and am curious
> about it.

I listed the coefficients for the numerators of Vc1(s), Vc2(s), Il1(s),
and
Il2(s). All have the same denominator D(s). For example, using the first
two
polynomials in my message:

                    n3 s^3 + n2 s^2 + n1 s + n0
Vc1(s) = Vc1(0) --------------------------------------
                 d4 s^4 + d3 s^3 + d2 s^2 + d1 s + d0

To obtain Vc1(t), expand this expression in partial fractions, what will
usually result in two real terms, and apply the inverse Laplace
transform
to them, what results in two sinusoids multiplied by exponential
decaying
factors. The Teslasim program lists the final expressions.

> (Of course, my last course in Laplace transforms was in the
> spring of 1948, and I'm sure the world of circuit analysis has advanced
> since then.)

Not much in this area.

Antonio Carlos M. de Queiroz

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