Air bridge inductance

Updated June 7, 2008

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New for July 2008! Here we'll post some equations that will allow you to estimate the lumped inductance of an airbridge, a structure you might use to connect sources on a 100um thick MMIC to the end vias for example.

This material was provided by the Microwaves101 Professor, thank you sir!

Following the wirebond inductance rule of thumb, for 1-mil diameter bondwire rule of thumb, a good rule of thumb is 0.025 nH inductance per mil of length (one pH per micron). That shouldn't be too far off if the airbridge width and thickness aren't too different from 1 mil.

The ratios of airbridge length to width and thickness affect the inductance. Here's a formula for the inductance of a rectangular strip of ribbon, which should closely resemble an airbridge:

LR (nH) = 5.08*10-3 * L * (ln (L / (W+T)) + 1.19 + 0.22 * (W+T) / L)

Where L, W, and T are all in mils.

The formula comes from "Advances in Microwaves", Volume 8, Academic Press
1974.

Note that the "ln" function only applies to length / (width + thickness). You can think of the formula as consisting of three terms: a direct proportion to length, which is the 5.08x10-3 * 1.19 * L, a proportion to width and thickness, which is the 5.08x10-3 * 0.22 * (W+T), and one more term that's proportional to L / ln(L/(W+T))