Wirebond inductance

Updated August 3, 2008

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New for July 2008! This page accompanies our new page on wirebonding. The material below was contributyebty the "official" Microwaves101 Professor, thanks Dude!

Wirebond inductance rule of thumb

A good rule of thumb is that for wire, the length in millimeters is equal to its inductance in nano-henries.

The formula for bondwire inductance looks similar to that of airbridge inductance:

Lw (nH) = 5.08x10-3 * L * (ln(4*L/D) - 1)

Wirebond inductance is roughly proportional to the length, but there's also a factor that accounts for the shape (length over diameter) of the wire. That may come from the fact that there are two contributors to the inductance of a wire (as opposed to a coil): one depends on the area of the loop, and the other comes from the skin effect, and it's a surface reactance that's equal to the surface resistance. The second term is pretty small compare with the first one.

The formula for bondwire inductance, plus another one that accounts for the ground plane can be found in "Computer-Aided Design of Microwave Circuits", by K.C. Gupta, Ramesh Garg and Rakesh Chadha, Artech House 1981. That book also has the same formula for inductance of a ribbon. You can find (and order) this book and many others from our microwave books page.

K.C. Gupta's book also has a correction for ribbon inductance in the presence of a ground plane. It shows the inductance of the ribbon goes down from its free-space value when a ground plane is nearby, and continues to decrease as the ground plane is brought nearer.

Gupta's book mentions the inductance of ribbon strips going down as frequency increases, to a point. This happens because of the part of the inductance that comes from the surface reactance. That reactance goes up only as the square root of frequency, which means the surface inductance is going down with the square root of frequency. At some frequency that term becomes insignificant and the other term takes over. He refers to "Calculation of Inductance of Finite-Length Strips and Its Variations with Frequency", IEEE MTT, Vol. MTT-21, 1973.

Does anyone have a formula for wire resistance that takes into account skin depth? Please shoot it in, we need that!