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

From: Tsuk, Michael (Michael.Tsuk@compaq.com)
Date: Mon Mar 19 2001 - 14:00:22 PST

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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```

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