[SI-LIST] Partial Inductance

From: Albert Ruehli <ruehli@xxxxxxxxxx>
To: si-list@xxxxxxxxxxxxx
Date: Fri, 23 Sep 2005 15:19:51 -0400
Hi
once we learn to think in terms of partial inductances it becomes a very 
useful concept.
Assuming that we have a rectangular loop, then its inductance (loop) is 
given by
L(loop) = Lp_11 + Lp_22 + Lp_33 + Lp_44 - 2 Lp_13 - 2 Lp_24

where Lp_ij are the partial inductances.   Intuitively, we have the 
partial self inductances
which have a flux associated with them to infinity.  However for each of 
the partial self
inductances, there is a partial mutual inductance associated to subtract 
the flux to infinity
(from the other side)  so that only the flux in the loop remains.   So, 
partial inductances
are very useful for inductance computations. 

Now assume that we have a solder ball and we know its partial self 
inductance.  Is this 
number useful or not?   So essentially we have Lp_11 and we don't exactly 
know where
the return current is going to be.  If the distance to the ground return 
is large compared 
to the length of the via, then the partial mutual inductance Lp_13 is 
relatively small
and we can estimate the loop inductance as  L(loop)  as  Lp_11 + Lp_33. If 
there 
are many ground returns, Lp_33 may be small.   Also, we have assumed a 
quasi- 2D
situation with respect to the top and bottom loop closure.   However, the 
point I am 
trying to make is that the  solder ball partial inductance can be a good 
rough estimate
for the inductive discontinuity. 

Another point I want to make is that we don't need closed loops for 
partial inductances.
We can make a PEEC model for a lambda/4 antenna where the end is open, 
from a 
direct current path point of view.   So the partial inductances of the 
antenna wires do
not form a loop.
 
Regards,
Al 

Albert Ruehli 
ruehli@xxxxxxxxxx
914-945-1592  TL  862-1592, Fax  914-945-4244 



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[SI-LIST] Partial Inductance

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