## Via Capacitance

July brought HOT weather to our area. The dogs sleep inside just about all day, and the cattle can't even get up enough gumption to moo. I've been huddled up all day near the air-conditioner making good progress on my new book--just in time, apparently, to answer Juan's question below.

Hello everybody,

I write you because I'm interested in knowing if the via capacitance is a serious problem in the present designs. There is an estimation of the capacitance created by vias in the Black Magic book- -are there any other estimations about the via capacitance in addition to the Black Magic one?

Thank you, beforehand.

Thanks for your interest in High-Speed Digital Design.

Formula [7.6] in High-Speed Digital Design for the capacitance of a via is a crude approximation.

It over-estimates the capacitance by assuming the ground system is a solid cylindrical wall of ground material surrounding the via (effectively an infinite number of ground planes) with a diameter equal to the clearance hole diameter.

It further over-estimates the capacitance by assuming the via is everywhere as large in diameter as the pad diameter (essentially a cylinder with radius equal to the pad diameter).

The formula then ignores fringing-field effects at the ends (top and bottom) of the structure, using a simple coaxial approximation to derive the capacitance. The coaxial approximation assumes a length equal to the total height of the via. The coaxial approximation under-estimates the actual via capacitance by ignoring fringe-field effects at the ends (top and bottom) of the via.

Between the over-estimation due to the simplified geometry and the under-estimation due to the coaxial approximation the formula gets you within an order of magnitude of the correct answer, but not a lot closer. In the example [7.7] the answer came out within a surprisingly close ten percent or so, and I comment on the next page (258), "Don't expect the formula to be so close all the time".

I've now got some better material in .pdf format that might interest you. This is a pre-production excerpt from my new book "High-Speed Signal Propagation". This excerpt includes two tables, one listing via capacitance data for simple cases showing one reference plane, and the other showing the effect of back drilling. The book includes four other tables that show the effects of using multiple reference planes.

Best Regards,
Dr. Howard Johnson