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

• From: "Dr. Sainath Nimmagadda" <intrinsi@xxxxxxxxx>
• To: Ed Priest <epriest@xxxxxxxxxxxxxxxxxxx>, si-list@xxxxxxxxxxxxx
• Date: Mon, 28 Jul 2003 23:23:49 -0700 (PDT)

```Ed,

That is precisely what I meant by extrapolating resistance ideas to inductance.

>Think of the impedance due to L. The current will flow in the lowest
>impedance [L(s)]. If you have a ribbon of parallel cable - current will
>flow in all of them but will be max in the ribbon that has the lowest
>impedance - which is under the trace.

Where do we expect to find this lowest impedance [L(s)]? On the reference
plane, like the lowest resistance, as shown in Fig. 5.1(Black Magic)?

>You get max flux because of the large current not because the inductance is
>higher.

I didn't say that max flux is because inductance is higher. Please see again,
what I said is reproduced below. Apparently, you are agreeing that flux is max
under the trace because of the large current. You have a situation with max
flux and min loop area. How would you show that inductance is minimum?

"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."
>Inductance is a function of the area of the current loop - the minimum
>is closest to the trace.

Can we make this statement- unconditionally?

Sainath

Ed Priest <epriest@xxxxxxxxxxxxxxxxxxx> wrote:

Think of the impedance due to L. The current will flow in the lowest
impedance [L(s)]. If you have a ribbon of parallel cable - current will
flow in all of them but will be max in the ribbon that has the lowest
impedance - which is under the trace. You get max flux because of the
large current not because the inductance is higher.

Inductance is a function of the area of the current loop - the minimum
is closest to the trace.

-----Original Message-----
Sent: Monday, July 28, 2003 4:44 PM
To: si-list@xxxxxxxxxxxxx
Cc: intrinsi@xxxxxxxxx
Subject: [SI-LIST] Microstrip Inductance (Old Wine in New Bottle)

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
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"
Subject: [SI-LIST] Re: si-list Digest V3 #194
From: "Dr. Howard Johnson"
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".

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.

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

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

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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