# Re: [SI-LIST] : Transmission Lines Formulae

Brian Young ([email protected])
Wed, 13 Jan 1999 08:57:11 -0600

Microstrip and stripline do not have exact analytical solutions. In
the quasi-static case, Schwarz-Christoffel transformations can be used
to
map the cross section into a parallel plate capacitor. The assumption
is that the metal is infinitely thin. That allows you to get the
capacitance
of the structure assuming uniform dielectric. You can then get the
inductance by knowing the phase velocity. Finally, you get the
characteristic impedance.

With the basic technique, the formulas do not have frequency dependence
nor non-uniform dielectric (important for microstrip). You can modify
the method to bring in the dielectric constant, but frequency dependence
and finite metal thickness and conductivity remain elusive. Full-wave
simulations and/or measurements can produce a database from which ad-hoc

There are a large number of formulas that each seek to minimize the
effect of some approximation. Depending on where you look, different
authors choose different formulas to present based on their opinion as
to which one is "best".

How do you choose which formula to use? That depends on the accuracy
you need. That begs the question as to the accuracy of the formulas,
and
you may need to dig up the original reference to find that out.

Because of tight pitches in buses, the formulas are not very accurate
anyway because they assume that the lines are isolated. It turns out to
be easier for me to simply compute the RLC matrices for a given cross
section with a full-wave 2D simulator including finite metal thickness
and conductivity. For any given cross section, it only takes a few
minutes
to draw the structure and run the problem.

One thing to keep in mind is that the formulas for microstrip and
stripline
where developed by microwave engineers to meet their needs. They have
widely spaced, wide lines (about as thick as the substrate) with thin
(compared to the width) metalization. If your cross section does not
look like that, then you need to be a little more careful when using
their formulas.

Brian

Lum Wee Mei wrote:
>
> While working on my Z calculation for transmission line, I noticed that
> different reference books provide different variations of the
> transmission line formulae be it microstrip or stipline.
>
> As a designer, I am expected to be proffesional in my work and able to
> explain the rationale why I use the formulae from this reference book
> and not the other. Can someone enlighten me on which formula to use and
> the reason, if any?

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