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Microstrip Via Hole Inductance

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 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: equation graphic was corrected March 2016, the units are Henries, if the dimensions you enter are in meters.

Via inductance equation

Of course there is a free spreadsheet in our download area that provides this calculation and was used to prepare the plots below 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:

Microstrip Via Hole Inductance

Microstrip Via Hole Inductance

Microstrip Via Hole Inductance

Microstrip Via Hole Inductance

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)

Microstrip Via Hole Inductance 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 these rules are most accurate for D/H aspect ratio of about 0.5.

 

 References

 "Modeling Via Grounds in Microstrip" IEEE Microwave and Guided Wave Letters, Vol. 1, No. 6, June 1991, by Goldfarb and Pucel.

Author: Unknown Editor
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Dak0taD's Avatar
Dak0taD replied the topic: #158 2 years 3 months ago
I'm assuming the variable D is the diameter of the via hole and H is the substrate height, it would be helpful if this were explicitly stated.
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