# RE: [SI-LIST] : Calculating Trace Inductance

Eric Bogatin ([email protected])
Tue, 24 Nov 1998 19:25:09 -0600

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Doug-

If you know the characteristic impedance of the trace, Z0, and the
"effective" dielectric constant of the dielectric, e_eff, then the "loop"
inductance of the trace is:

L_loop =3D 0.086 Z0 sqrt(e_eff) nH/inch

and while we're at it, the capacitance per length of a microstrip is:

C =3D 85/Z0 x sqrt(e_eff) pF/in

For example, in FR4, the effective dielectric constant of a 50 Ohm
microstrip is about 3.0, given the bulk dielectric constant of 4.0. This
yields the following for the capacitance and inductance per length:

L_loop =3D 7.4 nH/inch
C =3D 2.9 pF/in

( if you use 4.0 for e_eff, its not that big an effect, since its in the
sqrt. If you are worried about the difference between 1.73 and 2.0, don't
use an approximation, use a field solver to get a value you have confiden=
ce
in to better than 3%. I am giving a paper at Design Con 99 on this topic =
and
will be happy to send folks a copy of the paper, when it comes out, if yo=
u
send me a note off line.)

hope this helps.

--eric

ps- for those of you that notice this sort of thing, my affiliation and
email address has changed since the last time I sent a note to this

*************************************************************
Dr. Eric Bogatin
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26235 W 110th Terr.
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(f) 913-393-1306
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************************************************************

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Douglas McKean
Sent: Tuesday, November 24, 1998 4:07 PM
To: [email protected]
Subject: [SI-LIST] : Calculating Trace Inductance

What is the formula for calculating the
inductance/inch of a microstrip Cu trace?

Regards, Doug

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