via hole inductance
here to go to our main page on microstrip
here to go to our page on inductor mathematics
here to go to our main page on MMIC design
Here we will provide an equation
that allows you to calculate the inductance of a single ground via
in a microstrip circuit board.
This is based on the IEEE paper
"Modeling Via Grounds in Microstrip" IEEE Microwave and
Guided Wave Letters, Vol. 1, No. 6, June 1991, by Goldfarb and Pucel.
It is Equation 3 in the reference.
Note that this is an empirical
solution that was found to fit data where the height was between
100 um and 631 microns. It is supposed to be valid for heights less
that 3% of a wavelength. Note: this equation was slightly wrong
until August 2009, sorry for the inconveinece. Thanks, Vitaley!
The plots below were correct, just the equation graphic.
New for August 2009! We
placed a spreadsheet in the download
area that provides this calculation and was used to prepare
the plots on this page.
Although Goldfarb and Pucel didn't
tell you, the units of all of the lengths have to be in meters,
then the answer comes out in Henries. We entered the equation into
a spreadsheet. Here is the inductance for a via hole in on 15, 10,
4 and 2 mil substrates:
In many cases it
is desirable to keep the D/H ratio to 0.5 to minimize the catch-pad
area (especially on MMICs).
inductance rule of thumb(s)
On two-mil (50 micron) GaAs, Lvia is about 10 pico-henries.
For four-mil (100 um) GaAs, it is about 20 pico-Henries. Note that
thes rules are most accurate for D/H aspect ratio of about 0.5.