From: [email protected]
Date: Tue Nov 09 1999 - 17:05:33 PST
CT,
The impedance of an infinitely-long unloaded transmission line is Zo = sqrt( Lu
/ Cu ), where Lu is the unit-length inductance in Henries/meter and Cu is the
unit-length capacitance in Farads/meter. If the vias are close together and
relatively-uniformly spaced along the transmission line (with respect to the
signal rise-/fall-time), you can add an equivalent capacitance to Cu to get the
loaded transmission-line impedance. If the vias are all in a small area you may
be able to treat them as a single-point capacitive load, and use a Smith Chart
to analyze the transmission line. If the vias occur in clusters, you might be
able to analyze it as a series of transmission lines in series, loaded sections
connected by unloaded sections.
I recall reading in some microwave book/magazine about making the traces
narrower in the vicinity of vias or at sharp bends, to try to hold the
transmission-line impedance constant. The idea was to raise Lu to match the
percentage increase in Cu from the parasitic capacitance. Doug Smith's webpage
http://emcesd.com/ has a Technical Tidbit ( http://emcesd.com/tt101899.htm
) showing a T-pad attenuator that uses a similar scheme to provide flat
frequency response from DC to 10's of GHz.
John Barnes Advisory
Engineer
Lexmark International
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