Microstrip via hole inductance

Updated July 7, 2008

Click here to go to our main page on microstrip

Click here to go to our page on inductor mathematics

Click here to go to our main page on MMIC design

Here we will go through the math 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.

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.

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).

Via hole inductance rule of thumb(s)

On two-mil (50 micron) GaAs, L_via 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.