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

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From: Sainath Nimmagadda (sainath@lsil.com)
Date: Mon Mar 19 2001 - 18:59:00 PST


Dear Mike,

Good point. Strictly speaking and from a closed solution (analytical) point, we
should not attach any physical significance to individual partial inductances.
But, from a discretized solution (computational) point - which is the way we are
being driven by technology, such as the finite-difference time-domain for
example, is it not a mathematical convenience to consider those individual
partial inductances - especially where one does not know how and where the
current loops are closing - to obtain some first-cut answers? Just another view.

Regards,
Sainath

Mike Jenkins wrote:

> All,
>
> FWIW, I recall that the IBM Yorktown researchers who developed the
> partial inductance concept included on the first page of the research
> report the quote from Weber to the effect that inductance makes no
> sense unless one considers the entire loop of current. I guess
> they were sensitive to not inducing readers to attach any physical
> significance to the individual partial inductances.
>
> Regards,
> Mike
>
> "Tsuk, Michael" wrote:
> >
> > Doug McKean wrote:
> >
> > ------------------------------------------------------------
> > Okay, well here goes ...
> >
> > It's easy to see that if a signal trace had a return trace as a
> > wire (shown by a dotted line), the following would cause
> > the creation of a loop.
> >
> > |
> > |
> > |
> > +----------+
> > . |
> > return . | signal
> > trace . Loop | trace
> > . |
> > +----------+
> > |
> > |
> > |
> >
> > Obviously from this construction, the inductance of the
> > return wire would be less than if the return wire was
> > underneath and following the longer path of the signal
> > trace. Thus, my questioning the path of less inductance
> > rule.
> >
> > ------------------------------------------------------------
> >
> > The confusion comes from the fact that you've ignored mutual inductance
> > here, which acts to reduce the total inductance of this circuit. The return
> > current will choose the path (or combination of paths) that minimize the
> > *total* loop inductance, not the partial inductance of the return alone.
> >
> > In general, you can never ignore mutual inductance. :-( This is
> > particularly true if you're dealing with partial inductances, which are only
> > useful if all mutuals are included.
> >
> > Even more interesting to my mind is the sign error you made in calculating
> > the direction of the magnetic force on your currents. The magnetic force
> > between two parallel currents draws them *together* if the currents are in
> > the same direction, and pushes them *apart* if they are in opposite
> > directions. Check any electromagnetics text. Your mistake is that you
> > assumed a *positive* charge when you equated the current direction with the
> > velocity of your particle, but a *negative* charge when you calculated the
> > force.
> >
> > Why the apparent effect of minimizing inductance works in the opposite
> > direction is very interesting. I think I have the answer, but I'm not sure.
> > I'd appreciate any input people might have.
> >
> > --
> > Michael Tsuk
> > Compaq AlphaServer Product Development
> > (508) 467-4621
> >
> > -----Original Message-----
> > From: Doug McKean [mailto:dmckean@corp.auspex.com]
> > Sent: Monday, March 19, 2001 4:08 PM
> > To: si-list@silab.eng.sun.com
> > Cc: Doug McKean
> > Subject: Re: [SI-LIST] : Re: approximations for partial self inductance
> > - WHY
> >
> > ------------------------------------------------------------
> > Okay, well here goes ...
> >
> > It's easy to see that if a signal trace had a return trace as a
> > wire (shown by a dotted line), the following would cause
> > the creation of a loop.
> >
> > |
> > |
> > |
> > +----------+
> > . |
> > return . | signal
> > trace . Loop | trace
> > . |
> > +----------+
> > |
> > |
> > |
> >
> > Obviously from this construction, the inductance of the
> > return wire would be less than if the return wire was
> > underneath and following the longer path of the signal
> > trace. Thus, my questioning the path of less inductance
> > rule.
> >
> > As shown above, the signal current path forms the bottom,
> > right side, and top parts of a loop. The return current path
> > forms the left side of the a loop.
> >
> > Assume the signal path is bound one-dimensionally by the
> > confines of the trace. Assume the return path is bound two
> > dimensionally by the confines of the ground plane. In other
> > words, the signal path is not free to move at all, but the
> > return path is free to move in 2-D (up, down, left, right
> > in the above picture).
> >
> > Now, assume the return path in the ground IS as shown above
> > with the signal path and the return path. We have a loop. The
> > virtual current loop if you will, circulates causing a soloenoidal
> > action creating a magnetic field in the center. As such, using
> > the right hand rule for current vs. magnetic fields, we have a
> > magnetic field coming out of the monitor. The magnetic field
> > lines are normal to the screen of the monitor.
> >
> > Using the other right hand rule for charges moving in a magnetic
> > field by way of the Lorentz force, my thumb points in the direction
> > of current flow, my fingers point in the direction of the magnetic
> > field, and my palm points in the direction that the a positive
> > charge would be pushed. With a negative charge, the push is
> > from the back of your hand or toward the signal wire. Since
> > the return current is bound only by a plane, it seeks to be
> > under the signal trace. And it would continue to balance
> > itself there.
> >
> > Turn the path of the signal current around and the return
> > current, everything reverses including the direction of the
> > magnetic field, and we still have a Lorentz force pusing the
> > return current back to the signal trace.
> >
> > A DC return current in the ground plane wouldn't cause such
> > action. It would follow only the path of least resistance.
> >
> > This is lots more wordy than if I was face to face and showed
> > with the right hand rule for negative charge in a magnetic field.
> >
> > Regards, Doug McKean
> > ------------------------------------------------------------
> >
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> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Mike Jenkins Phone: 408.433.7901 _____
> LSI Logic Corp, ms/G715 Fax: 408.433.7495 LSI|LOGIC| (R)
> 1525 McCarthy Blvd. mailto:Jenkins@LSIL.com | |
> Milpitas, CA 95035 http://www.lsilogic.com |_____|
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
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