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

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From: Reid, Chris (chris_reid@mentorg.com)
Date: Thu Mar 15 2001 - 09:00:44 PST


Hello,

Actually, the statement:

> It is a principle
> of Maxwell's equations that high-speed returning signal
> current will flow in whatever path produces the
> least overall inductance.

is not really correct. Instead of inductance, think of
resistance for a moment. If you put two resistors in parallel,
one 100 Ohms and the other 1 Ohm the effective resistance is
1/(1/100 + 1/1) =~ 0.99 Ohm. Clearly most of the current
flows through the 1 Ohm resistor, but some also flows through
the 100 Ohm resistor.

Inductance is similar, only now the result depends on frequency.

Chris

-----Original Message-----
From: Sainath Nimmagadda [mailto:sainath@lsil.com]
Sent: Wednesday, March 14, 2001 6:19 PM
To: Howard Johnson; si-list@silab.eng.sun.com
Subject: Re: [SI-LIST] : Re: approximations for partial self inductance

Dear Howard,

Please see below:

Howard Johnson wrote:

> Dear Itzhak Hirshtal and Brian Young,
>
> The difficulties with approximating the inductance
> of a via are even worse than you
> may have suspected. Both approximations are flawed whether
> you use +1 or -3/4, (or, as I have also seen, -1).
>
> The issue of the exact constant (1, -3/4, or something
> else) depends critically on your assumption about
> the path of returning signal current. (Current always
> makes a loop; when signal current traverses the via,
> a returning signal current flows SOMEWHERE in
> the opposite direction.). It is a principle
> of Maxwell's equations that high-speed returning signal
> current will flow in whatever path produces the
> least overall inductance.

My question is on this last statement. I like to understand which
Maxwell's equation suggests this and how? Thanks.

Sainath

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