Re: [SI-LIST] : Inductance vs. frequency

Wai-Yeung Yip (yip@lantern1)
Tue, 21 Apr 1998 09:05:11 -0700 (PDT)

Lidu,

My understanding is, there are two reasons inductance decreases with frequency.
First is skin effect. As frequency increases and current is gradually pushed out
to the skin of the conductor, internal inductance due to the conductor material
is gradually reduced. At very high frequency, internal inductance becomes
essentially zero compared to external inductance and the total inductance should
then level off.

How much is internal inductance compared to external inductance depends on your
particular geometry. But I would say for packaging interconnects expect internal
inductance to be around 10% of total inductance. So the drop you saw in your
modeling seems a little large.

As an example, here is the formula for a coaxial transmission line:
L=(Uo/8pi)+(Uo/2pi)*ln(b/a) H/m
where the first term is the internal inductance and the second term the external
inductance which depends on the inner and outer radii a & b of the line.

Second cause for inductance drop with frequency is drop in relative permeability
of the material with frequency. However, if you happened to use constant
relative permeability in your finite element analysis, this would not show up.
I don't know exactly the general relationship between relative permeability and
frequency. Experiment shows that for alloy 42 which is a magnetic material it
is a logarithmic relationship.

If you are interested in reading more about inductance and resistance
measurements and modeling and how they change with frequency,
I would like to refer you to a paper entitled "High-Frequency Inductance
Measurements and Characterization of Alloy 42 and Copper Packages" by Dr. Chi-
Taou Tsai et al of Motorola published in the Proceedings of the 43rd ECTC in
1993, pp. 635-640.

Hope this helps.

Regards,
Wai-Yeung Yip
CPU Module Design Engineer
Sun Microsystems

> Date: Tue, 21 Apr 1998 10:52:51 -0400
> From: Lidu Huang <a0754116@pan.mc.ti.com>
> Mime-Version: 1.0
> To: si-list@silab.Eng.Sun.COM
> Subject: [SI-LIST] : Inductance vs. frequency
>
> Hello all,
>
> Would anyone provide me some formula to calculate the
> inductance for a busbar with rectangular cross section?
> Information on inductance changes with frequency (kHz to
> 100MHz) is also helpful.
>
>
>
> This is the inductance resulted from finite element
> analysis. Do you think the inductance vs. frequency
> tendency is reasonable?
>
> Any thoughts or leads would be appreciated!
>
>
> Lidu Huang
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