[SI-LIST] Re: Can L12 ever exceed L1 or L2 ??
- From: "Chan, Edward K" <edward.k.chan@xxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Sun, 30 Oct 2005 15:59:55 -0800
I've been thinking about this problem for a while too, and here's what I
think I figured out:
The requirement for an inductance matrix to be physical is that it is
positive definite. Thus L11 * L22 - L12 * L12 > 0. This is similar to
other equations described by others previously.
Hence, it is possible that L12 is larger than the smaller of L11, L22.
So what physical system exhibits this --> essentially transformers:
Imagine two concentric coils with identical loop area placed infinitely
close to each other. Then L12 is very close to L11 (and L22).=20
Now we double the windings of the second coil. If we integrate the flux
over the area of the first coil (single winding), we find that the flux
from the second coil (two windings) is larger than the flux from itself
(first coil with one winding). Therefore, L12 is larger than L11.
Now, what structures on typical PCBs exhibit this behavior?
Imagine a microstrip line over a ground plane has a certain L11 and L22.
Now put a ground plane over this microstrip to create a stripline. With
the top and bottom planes tied together at the near and far ends, we
will get a 2x2 inductance matrix. When the signal trace is narrower
(~<0.5X) than the ground planes, the additional ground plane will reduce
the effective inductance of the ground plane such that it is less than
the mutual inductance between the signal and ground.=20
I haven't investigated all the conditions under which these observations
are true, but I believe L12 can exceed L11 or L22.
I have simulated the coils and the stripline in Fasthenry, and can
provide the simple input decks to anyone interested.
Edward Chan
Intel
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Zhou, Xingling (Mick)
Sent: Saturday, October 29, 2005 6:44 AM
To: eric@xxxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx; ray.anderson@xxxxxxxxxx
Cc: susan@xxxxxxxxxxxxxxx
Subject: [SI-LIST] Re: Can L12 ever exceed L1 or L2 ??
Eric,
Seems we have talked about signal lines a lot. Those lines are self-L
dominated as we know. I don't remember any physics law prohibits
L12>L1,or L2 other than K<=3D3D1 and some intuitive arguments. One =
special
case can break the statement if we do not have solid foundation. If a
law is pointed out or newly proven in general, the argument will be much
easier. If not, it may be considered as a conjecture based on some
observations at most.=3D20
How about when planes are involved? For example, for a package, L_vss is
generally low referring to PCB GND. However, there are signals/planes
that couple with VSS strongly.=3D20
Even for regular lines, is it possible to construct a case that breaks
the statement? For example, when line loops cross each other in complex
ways in 3D (not as simple as we have in regular designs).=3D20
Of course, numerical problems are always questionable. This is why the
question confuses many of us. Is it because of the numerical errors or
physically possible in some cases? Or in any case, we should check the
numerical problems and force the vendor to satisfy us.
Finding out when the statement is true (if not always) is also very
helpful.
Just some wild thoughts.
Thanks.
Mick
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Eric Bogatin
Sent: Saturday, October 29, 2005 8:58 AM
To: si-list@xxxxxxxxxxxxx; ray.anderson@xxxxxxxxxx
Cc: eric@xxxxxxxxxxxxxxx; susan@xxxxxxxxxxxxxxx
Subject: [SI-LIST] Can L12 ever exceed L1 or L2 ??
Ray-
I completely agree with Steve Weir's comment that it is not
physically possible for L12 > L11, whether we use these
terms as loop inductance elements or partial inductance
elements.
The self inductance is the number of loops of magnetic field
lines that surround one conductor per amp of its current.
The mutual inductance is the number of loops of magnetic
field lines that surrounds both conductor, per amp of
current in one. All the mutual field lines from one
conductor must also, by definition surround its own
conductor and be part of its self inductance. This is true
for loop inductance or partial inductance.
The real question is why your vendor supplied you with
matrix elements where you got L21 =3D3D 3 x L11. I've gotten
similar comments from other end users. The answer is that
when the vendor ran their field solver, they did not use a
fine enough mesh. If you have radically different conductor
geometries, like a short, wide conductor and a long,
meandering trace, you will often see on the first pass
calculation of the field solver that the partial self
inductance of the short trace is less than the partial
mutual between them.=3D20
Your vendor needs to refine their mesh. When the mesh is
refined so that the matrix elements do not change by more
than about 1% for a 10-20% increase in mesh elements in the
high field regions, the mesh is refined enough.
Perhaps if your vendor were to read chapter 6 in my book
Signal Integrity-Simplified, they would have a better chance
of providing you more accurate and meaningful models.
Hope this helps.
--eric
***************************************
Eric Bogatin
Bogatin Enterprises
OnLine Lectures on Signal Integrity
26235 w 110th terr
Olathe, KS 66061
v:913-393-1305
cell: 913-424-4333
f:913-393-0929
e:eric@xxxxxxxxxxxxxxx
www.BeTheSignal.com <http://www.BogEnt.com>=3D20
Signal Integrity- Simplified
published by Prentice Hall
*****************************************
Msg: #7 in digest
Subject: [SI-LIST] Can L12 ever exceed L1 or L2 ??
Date: Fri, 28 Oct 2005 12:21:06 -0700
From: "Ray Anderson" <ray.anderson@xxxxxxxxxx>
A question for the E&M gurus on the list:
=3D20
Are there any conditions (pathological or not) that the
mutual inductance between two conductors can be greater than
the self inductance of either one?
=3D20
Since L12 =3D3D k * sqrt(L1*L2) and the coupling factor k must
be -1 < k < 1 then this would seem to imply that L12 must
be less than or equal to geometric mean of the self
inductances. However this leaves open the possibility the Lm
could be > than one or the other which flies in the face of
the commonly made assertion that Lm must be less than
either. It seems that there must be other qualifying
statements to made regarding the relationship to the self
and mutual inductances.
=3D20
Going back to some of the basic fundamental relationships
(such as Grover's formulas) I can convince myself that for
circular conductors
L12 must be less than or equal to either L1 or L2, but how
about the mutual coupling between some other structures say
a signal trace and large planar structure that isn't
intended to be be a signal return path but very well may be
?
=3D20
I've got a field solver reporting Lm being 2 to 3 times
Lself on one particular problem. I'm trying to determine if
the solver is having a difficult time dealing with the
particular geometries involved or if it is indeed possible
despite the common wisdom to the contrary.
=3D20
Any comments one way or the other are appreciated.
=3D20
Regards,
=3D20
-Ray
=3D20
=3D20
Raymond Anderson
Senior Signal Integrity Staff Engineer
Product Technology Department
Advanced Package R&D
Xilinx Inc.
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