[SI-LIST] Re: Microstrip Inductance (Old Wine in New Bottle)

Probably the high-frequency current distribution on the trace itself, which 
thus far not entered the discussion, holds key to the dilemma. It should have 
current minimum at the center of trace and maximum values at the edges.
 
Sainath
"Dr. Sainath Nimmagadda" <intrinsi@xxxxxxxxx> wrote:
Novices and experts,
 
First, my thanks to Dr. Johnson for seconding my conjucture that there is a 
distribution of inductance. In fact, that is how/where I started this thread. 
What kind of distribution ?, least inductance or otherwise, is a matter of 
follow up. Also, I am glad that Dr. Johnson supported my view that " the 
"distribution of least inductance" includes the current flowing at positions 
remote from the trace."
 
Discussion turned off momentarily-
 
I couldn't access my gigabit@xxxxxxxxxx mail since last Friday because mail 
server was down or some such thing. So, this is an old thread with a new email 
address. Those numerous readers who sent private emails encouraging this 
thread, I appreciate your support, please note my new address 
intrinsi@xxxxxxxxx . I checked out the list archives periodically but didn't 
see anything new on this thread.
 
I was expecting to get a response to "What was the original source for the 
concept and illustration of Fig. 5.2(high-frequency return-current path)in 
Black Magic book?"  but didn't. If any of you have any clue on source 
reference, please let me know.
 
Back to the discussion-
 
I'm surprised that the discussion side-stepped from 'stored energy' (which is 
appropriate for inductance) to 'power dissipation' (which is a resistance 
property). It looks to me that we are simply trying to extrapolate what we know 
about (current flow in) simple resistance to what we possibly don't know about 
the more evolved and subtle inductance. 
 
Please allow me to modify (for a better mental picture) Dr. Johnson's ribbon 
cable analogy of the reference plane. Let us consider the reference plane as 
comprised of a number of tiles, each identical in geometry with our trace. We 
keep one reference tile, R, directly under the trace tile, T.
 
We would like, in a "most--of-the-current" sense, the current flowing out in T 
to return back through R. For the time being, other reference tiles are just 
"sitting in position" and watching the game. Later, when they play T as a team, 
they will reduce the flux contribution due to reference plane (i.e., lower 
inductance). Bad game! But, that doesn't affect the focus of our reasoning. 
Similar is the contribution from mutuals.
 
According to the popular screw rule, flux due to currents in T and R (flowing 
in opposite directions) add up and the resulting flux concentration (per unit 
area sense) will be maximum right under the trace. This leads me to believe 
that inductance is maximum there. We know that as we move away from T, along an 
imaginary line between T and R, 
the flux falls off inversely(1/r). So, remote from T, while still the flux due 
to T and R currents keep adding up, the resulting flux concentration (per unit 
area sense) gets smaller and smaller. Thus, contributing to lower and lower 
inductance as we move away from T.
 
If the above makes sense, there is a distribution of inductance which is 
maximum right under T (where current is maximum) and falls off toward those 
edges, away from trace, of reference plane (where the current goes to minimum). 
Current and stored energy distributions, which we already know, show a similar 
behavior.
 
Dr. Johnson has already subscribed to possibility of least inductance away from 
the trace. Question is how are you guys able to find least inductance right 
under the trace where the fields are roaring. Please do tell me what I'm not 
getting right.
 
Sainath
 
===============================================================
[SI-LIST] Re: si-list Digest V3 #194
---------------------------------

   To: "Si-List@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx> 
   Subject: [SI-LIST] Re: si-list Digest V3 #194 
   From: "Dr. Howard Johnson" <howiej@xxxxxxxxxx> 
   Date: Thu, 24 Jul 2003 11:30:18 -0700 

---------------------------------

Dear Sainath,Let's work for a minute on your concept of the "path ofleast 
inductance".I think a better wording here would be the "distribution ofleast 
inductance".<skip>

Imagine you have a long, straight pcb trace carrying acertain amount of signal 
current.Underneath that trace I want you to construct not a plane,but an array 
of wires (kind like a ribbon cable). Place thewires on a very fine spacing so 
that (in the limit) theyapproximate a plane, but keep them as individual wires.

<skip>

You will findthat the particular return wire that generates the leastinductance 
is the one directly underneath the trace.

<skip>

You are indeed correct that the "distribution of leastinductance" includes the 
current flowing at positions remotefrom the trace.<skip>

Suppose now you connect individual current sources to theindividual resistors 
so you can adjust the current separtelyin each. I claim that, of all possible 
distributions ofcurrent adding up to 1 mA, the particular distribution "A"is 
the one that minimizes the total dissipated power.



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