RE: [SI-LIST] : Re: approximations for partial self inductance

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From: Grossman, Brett (brett.grossman@intel.com)
Date: Thu Mar 15 2001 - 17:14:14 PST


Dr. Johnson, all,

A question rather than noting any errors.

---- I erased the dissertation I was about to create, and will simplify
with:

1. I understand the derivation of [1], but where does the ln(2) come from in
expressions [2] and [3]?
2. From a first inspection it seems to me that the derivation of [3] has
selectively eliminated some of the couplings from the expression. If I was
to represent the structure as:

        G1
G2 S G3
        G4

Where S is the source via and G1-G4 are the four return vias. Can the G1-G2,
G2-G4, G4-G3, G3-G1 or G1-G4, G2-G3 coupling be safely omitted?

Thanks for any assistance that can be offered.

Regards,

-Brett

>>>>>> Cut and paste <<<<<<<<<

L = 5.08*H*(2*ln(2*S/D)) [1]

If the return current is carried mainly on two vias
equally spaced on either side of the signal via,
where the spacing from signal via to either return via
is S and the via diameter is D:

L = 5.08*H*(1.5*ln(2*S/D) + 0.5*ln(2)) [2]

If the return current is carried mainly on four vias
equally spaced in a square pattern on four sides
of the signal via, where the spacing from signal via
to any return via is S and the via diameter is D:

L = 5.08*H*(1.25*ln(2*S/D) + 0.25*ln(2)) [3]

If the return current is carried mainly on a
coaxial return path completely encircling the signal
via, where the spacing from signal via
to the return path is S and the via diameter is D:

L = 5.08*H*(ln(2*S/D)) [4]

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