## [SI-LIST] Re: si-list Digest V3 #194

• From: "john lipsius" <johnlipsius@xxxxxxxxx>
• To: <gigabit@xxxxxxxxxx>
• Date: Mon, 21 Jul 2003 15:31:36 -0700

```To all pursuers of the maximum/minimum false dichotomy
and the "path of maximum annoyance"     :-)
-------------------------------------------------------

Any further contributions to this thread that adhere to that
confusion will, it seems, just confuse novices that subscribe
to this list.  Any further help from the experts is, unfortunately,
wasted I believe.

Please pick up a physics or microwave text to get it straight
and look at the illustrations.   In short, it's necessary to
dot-product one's interest with a little homework, whereupon
the path of maximum edification shall reveal itself in all its glory
and thence one shall go forth in peace and confidence.

A review of andrew's and michael's replies on this thread should
suffice, below.

Basically, claiming there's an inductance "distribution" is
confusing these two:

1. a mathematical definition of flux that relies on an abstract
surface chosen by you

2. the flux itself, which is constant for constant current, frequency,
material and geometry.

-enough said

----- Original Message -----
To: Michael Smith
Cc: si-list@xxxxxxxxxxxxx
Sent: Monday, July 21, 2003 3:01 PM
Subject: [SI-LIST] Re: si-list Digest V3 #194

Michael Smith,

>By your logic, if
>I could find a different but equally wrong way of calculating the
>inductance and it happened to come out larger than the correct
>calculation, then the correct calculation should henceforth be known
as
>the minimum inductance value.

That is what I need. Please give me a way to find an inductance value
that is larger than the correct value.

>The path of maximum inductance within the conductor would be the
current
>distribution which maximizes the open surface area required to couple
>all of the B field. The path of minimum inductance within the
conductor
>would be the current distribution which minimizes the open surface
area
>required to couple all of the B field.  The change in inductance is
>linked to the variation in loop size caused by the variation in
current
>distribution.

I don't quite follow this technical language. Is there a reference you
could suggest me on this?

>Additionally, as has been stated on this thread, the current will
>distribute itself on the path of minimum impedance or referring to the
>principle of least action, the path of least energy; depending on
>frequency this is not necessarily the path of minimum inductance.

We all seem to agree that high-frequency currents need not necessarily
follow the path of minimum inductance.

Sainath

---------Included Message----------
>Date: Mon, 21 Jul 2003 12:23:32 -0700
>From: "Michael Smith" <michael@xxxxxxxxxx>
>Reply-To: "Michael Smith" <michael@xxxxxxxxxx>
>To: <gigabit@xxxxxxxxxx>, "'Wen Fred-Q16099'" <fred.wen@xxxxxxxxxxxx>
>Cc: <si-list@xxxxxxxxxxxxx>
>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>
>Sainath,
>
>You are getting confused between the calculation of the inductance for
a
>given current distribution and the variation of inductance caused by a
>variation in current distribution.
>
>When you are calculating the inductance value for a given current
>distribution, you must integrate the normal of the B field over a
>surface area which captures ALL of the field lines surrounding
(external
>inductance) and within the current distribution (internal inductance).
>This is not the maximum inductance or the path of maximum inductance,
it
>is simply the correct inductance.  Any calculation which uses a
surface
>area which fails to have all of the field lines passing through it is
>wrong.  Inductance (not partial inductance) is defined as the ratio of
>the amount of magnetic flux coupled through and created by a given
>closed path current distribution to that current distribution.  The
>irrelevant fact that performing the calculation while ignoring some of
>the field lines happens to give a lesser inductance value does not
make
>the correct calculation the maximum inductance value.  By your logic,
if
>I could find a different but equally wrong way of calculating the
>inductance and it happened to come out larger than the correct
>calculation, then the correct calculation should henceforth be known
as
>the minimum inductance value.
>
>If I were to integrate the electric field lines passing out of a
closed
>surface and decided to ignore part of the surface, I would get a value
>for the charge within that surface which was smaller than the correct
>value.  Should I then refer to the charge within that surface as the
>maximum charge value?
>
>The path of maximum inductance within the conductor would be the
current
>distribution which maximizes the open surface area required to couple
>all of the B field. The path of minimum inductance within the
conductor
>would be the current distribution which minimizes the open surface
area
>required to couple all of the B field.  The change in inductance is
>linked to the variation in loop size caused by the variation in
current
>distribution.
>
>Additionally, as has been stated on this thread, the current will
>distribute itself on the path of minimum impedance or referring to the
>principle of least action, the path of least energy; depending on
>frequency this is not necessarily the path of minimum inductance.
>
>Thanks,
>
>Michael Smith
>iZ Technology Corp.
>Voice: (604) 395-7878 ext. 314
>Fax: (604) 395-7888
>
>
>-----Original Message-----
>From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]
>On Behalf Of Sainath Nimmagadda
>Sent: Monday, July 21, 2003 12:13 PM
>To: Wen Fred-Q16099
>Cc: si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: si-list Digest V3 #194
>
>Fred,
>
>We've been talking about magnetic flux which is the surface integral of

>the normal component of flux density vector B. Right? Given that,
>
>
>Sainath
>
>---------Included Message----------
>>Date: Mon, 21 Jul 2003 12:35:22 +0800
>>From: "Wen Fred-Q16099" <fred.wen@xxxxxxxxxxxx>
>>Reply-To: "Wen Fred-Q16099" <fred.wen@xxxxxxxxxxxx>
>>To: "'gigabit@xxxxxxxxxx'" <gigabit@xxxxxxxxxx>
>>Cc: "'si-list@xxxxxxxxxxxxx'" <si-list@xxxxxxxxxxxxx>
>>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>
>>Sainath,
>>
>>The integral (maximum or minimal) depends on the loop of the surface
>edge, not
>>the surface itself. Given a fixed loop, the integral will not vary on

>various
>>surface. Its principle comes from the physics law that tells us the
>integral on
>>a closed surface is always ZERO.
>>
>>Fred
>>
>>> -----Original Message-----
>>> From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
>>> Sent: Sunday, July 20, 2003 1:40 PM
>>> To: andrew.c.byers@xxxxxxxxxxxxxx
>>> Cc: si-list@xxxxxxxxxxxxx
>>> Subject: [SI-LIST] Re: si-list Digest V3 #194
>>>
>>>
>>> Andy,
>>>
>>> I disagree with your correction(about integrating magnetic
>>> flux lines).
>>> Please do a simple dimensional check.
>>>
>>> Yes, there is this correct inductance value which we get in
>>> the limiting
>>> case when we capture all the flux. This is also the maximum
>>> inductance.
>>> Lower inductance values are possible depending on the chosen
>>> surface and
>>> the minimum can go as low as zero, like you said. So, there is a
>>> distribution ranging from zero to the correct value. I believe the
>>> significance of this and its SI application opens up new
>>> directions...
>>>
>>>
>>> For SI application involving return current paths, I wonder
>>> how the idea
>>> of minimum(zero) inductance path stuck around so long.
>>>
>>> Sainath
>>>
>>> ---------Included Message----------
>>> >Date: Fri, 18 Jul 2003 17:29:15 -0700
>>> >From: <andrew.c.byers@xxxxxxxxxxxxxx>
>>> >To: <gigabit@xxxxxxxxxx>
>>> >Cc: <si-list@xxxxxxxxxxxxx>
>>> >Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >
>>> >Sainath,
>>> >
>>> >First of all, with your surface, either above the microstrip
>>> or below,
>>> you
>>> >are capturing magnetic field lines, not "flux lines". You integrate

>
>>> these
>>> >field lines over the area of the surface to produce a scalar number

>
>>> which is
>>> >your magnetic flux. A lot of times people get Flux and Field
>>> confused.
>>> Flux
>>> >is a scalar number, while field is a vector.
>>> >
>>> >So, like you say, if you capture all the field lines on your
>>> surface,
>>> you
>>> >should calculate the true flux and therefore the correct
inductance.
>
>
>>> Calling
>>> >it a "maximum" or "minimum" does not really fit here. If you were
to
>
>
>>> use a
>>> >surface where you did not account for all the field lines, the
>>> inductance
>>> >you calculate would indeed be smaller than the correct value. But
it
>
>
>>> would
>>> >be wrong. I guess you could say that "maximum" inductance
>>> calculation
>>> is
>>> >correct, and "minimum" inductance calculation would be zero (you
>>> capture
>>> >none of the field lines).
>>> >
>>> >Any 2D cross section of an interconnect system should have
>>> one correct
>>> >inductance value. As you move along in the 3D direction of
>>> propagation,
>>> the
>>> >2D cross sections will change and your inductance at that
>>> point might
>>> change
>>> >too. Once again this is assuming no internal inductance and a
single
>
>
>>> mode.
>>> >With internal inductance, your total inductance becomes frequency
>>> dependent.
>>> >The Ramo, Whinnery, Van Duzer book points this out as well.
>>> >
>>> >Andy
>>> >
>>> >-----Original Message-----
>>> >From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
>>> >Sent: Friday, July 18, 2003 6:07 PM
>>> >To: Byers, Andrew C
>>> >Cc: si-list@xxxxxxxxxxxxx
>>> >Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >
>>> >
>>> >Andy,
>>> >
>>> >Yes, the inductance value should remain the same for both
>>> cases. Also,
>>>
>>> >we are capturing all the magnetic flux lines in both cases.
>>> >
>>> >Now comes the real question. When you capture all the flux lines,
is
>
>
>>> the
>>> >inductance going to be maximum? or minimum?
>>> >
>>> >Sainath
>>> >
>>> >---------Included Message----------
>>> >>Date: Fri, 18 Jul 2003 09:50:57 -0700
>>> >>From: <andrew.c.byers@xxxxxxxxxxxxxx>
>>> >>To: <gigabit@xxxxxxxxxx>
>>> >>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >>
>>> >>Sainath -
>>> >>
>>> >>With the case of the surface above the microstrip, the inductance

>>> >value
>>> >>should remain the same. The integrating distance will be
>>> from the top
>>>
>>> >of the
>>> >>microstrip to infinity, and the B-field will be diminishing in
>>> >magnitude as
>>> >>you get further and further from the microstrip. The integral to
>>> >infinity
>>> >>will be equivalent to some series, and can be solved easily to a
>>> >finite
>>> >>number.
>>> >>
>>> >>Another way of looking at it - all of the fields that wrap under
>the
>>> >>microstrip will also wrap above it. You just have to have a big
>>> enough
>>> >>surface to catch them all. In practice, a surface that is about
3-4
>
>
>>> >times
>>> >>the height of the dielectric should catch most of the fields. This

>
>>> >whole
>>> >>infinite surface stuff is just for theoretical robustness.
>>> >>
>>> >>By the way, there is a paper that demonstrates this in FDTD
>>> simulation.
>>> >I
>>> >>believe it is in the 1997 EPEP conference - its written by Melinda

>
>>> >Piket-May
>>> >>and Roger Gravrok. I might be off by a year of two... if you have

>>> >those
>>> >>conference proceedings look for it. I can dig more for the
>>> name if you
>>>
>>> >would
>>> >>like.
>>> >>
>>> >>andy
>>> >>
>>> >>-----Original Message-----
>>> >>From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
>>> >>Sent: Thursday, July 17, 2003 11:44 PM
>>> >>To: Byers, Andrew C
>>> >>Cc: si-list@xxxxxxxxxxxxx
>>> >>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >>
>>> >>
>>> >>Hi Andy,
>>> >>
>>> >>Thanks again. I get the themes that inductance is a one
>>> number affair
>>>
>>> >>and current returns through the least inductance path. Is there a

>>> >>contradiction in these themes?
>>> >>
>>> >>Let me borrow the following from your previous mail.
>>> >>
>>> >>"If you were to put your integrating surface on the other
>>> side of the
>>>
>>> >>trace, extending up from the top of the trace, you
>>> theoretically would
>>>
>>> >
>>> >>have to make the area of the surface extend to infinity to
>>> "catch" all
>>>
>>> >
>>> >>the field lines."
>>> >>
>>> >>For this case, is the inductance of the microstrip going to be
>>> >>infinity(because of infinite surface)? or any other value? remains

>
>>> same
>>> >
>>> >>as what it was for the integrating surface below the trace?
>>> >>
>>> >>Sainath
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>---------Included Message----------
>>> >>>Date: Thu, 17 Jul 2003 17:37:12 -0700
>>> >>>From: <andrew.c.byers@xxxxxxxxxxxxxx>
>>> >>>To: <gigabit@xxxxxxxxxx>
>>> >>>Cc: <si-list@xxxxxxxxxxxxx>
>>> >>>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >>>
>>> >>>Hello Sainath,
>>> >>>
>>> >>>Clearing up some terminology here.
>>> >>>
>>> >>>"Least inductance" refers to the path that the current will
travel
>
>
>>> >>because
>>> >>>it has the least inductance of all possible paths in the system.

>
>>> >>Current
>>> >>>will never choose an alternate path of "most inductance".
>>> BUT you can
>>>
>>> >
>>> >>have a
>>> >>>different design in which the "path of least inductance"
>>> is longer.
>>> >>For
>>> >>>example a two wire line with no ground plane where the wires are

>>> >>extremely
>>> >>>far apart. Huge loop, huge inductance. But still the smallest
loop
>
>
>>> for
>>> >
>>> >>that
>>> >>>system. For a microstrip, a path of More Inductance would
>>> be if there
>>>
>>> >
>>> >>were a
>>> >>>gap in the ground plane under the microstrip line. The
>>> current would
>>>
>>> >>be
>>> >>>forced to diverge around the gap. This path would be more
>>> inductive
>>> >>than a
>>> >>>solid ground plane, but the current would still be
>>> following the path
>>>
>>> >
>>> >>of
>>> >>>least inductance for that particular case.
>>> >>>
>>> >>>The main challenge in most systems I've dealt with is making sure

>
>>> >that
>>> >>>return current paths have the least inductance possible.
>>> The simplest
>>>
>>> >
>>> >>way to
>>> >>>do this is go differential. Then you carry your virtual
>>> ground with
>>> >>you
>>> >>>everywhere. If single ended, then be very conscious about
>>> where the
>>> >>return
>>> >>>currents flow and try to provide a short path. Plenty of
>>> >>this
>>> >>>list about that.
>>> >>>
>>> >>>Not sure if this clears up your last question, hope it
>>> helps though.
>>> >>>
>>> >>>- Andy
>>> >>>
>>> >>>
>>> >>>
>>> >>>-----Original Message-----
>>> >>>From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
>>> >>>Sent: Thursday, July 17, 2003 4:01 PM
>>> >>>To: Byers, Andrew C
>>> >>>Cc: si-list@xxxxxxxxxxxxx
>>> >>>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >>>
>>> >>>
>>> >>>Andy,
>>> >>>
>>> >>>Thanks. I appreciate the extra effort to explain detail of
>>> >>integration.
>>> >>>In short, you've explained the current loop formed by a
>>> signal path
>>> on
>>> >
>>> >>
>>> >>>trace and signal return path beneath the trace and on the ground

>>> >plane.
>>> >>
>>> >>>Such a return path, with its minimum loop area, is widely known
to
>
>
>>> >>>provide the path of "least" inductance for high-frequency
>>> currents(for
>>> >
>>> >>
>>> >>>example, Black Magic book). If inductance is thought of as one
>>> number,
>>> >
>>> >>
>>> >>>what does "least inductance" refer to? Which is the path of
"most"
>
>
>>> >>>inductance for the microstrip? No doubt, I'm missing somethig.
>>> >>>
>>> >>>Sainath
>>> >>>
>>> >>>---------Included Message----------
>>> >>>>Date: Thu, 17 Jul 2003 10:02:49 -0700
>>> >>>>From: <andrew.c.byers@xxxxxxxxxxxxxx>
>>> >>>>To: <gigabit@xxxxxxxxxx>, <beneken@xxxxxxxxxxxx>
>>> >>>>Cc: <si-list@xxxxxxxxxxxxx>
>>> >>>>Subject: RE: [SI-LIST] Re: si-list Digest V3 #194
>>> >>>>
>>> >>>>Sainath,
>>> >>>>
>>> >>>>As Thomas pointed out, inductance is the ratio of
>>> magnetic flux to
>>> >>>current
>>> >>>>in the conductor. Magnetic flux is the integral of B dot
>>> dA, or the
>>>
>>> >>>magnetic
>>> >>>>field [dot product] the surface you are integrating over.
>>> The "dot
>>> >>>product"
>>> >>>>is the same as multiplying the B-field by the area by the
>>> cosine of
>>>
>>> >>>the
>>> >>>>angle between the B-vector and the normal to the area. So if the

>
>>> >>>B-vector is
>>> >>>>perpendicular to the area surface, then the B-vector is
>>> parallel to
>>>
>>> >>the
>>> >>>unit
>>> >>>>normal vector of the area surface, cosine of this zero
>>> degree angle
>>>
>>> >is
>>> >>
>>> >>>1,
>>> >>>>and you simply multiply B*area. Here's an example to illustrate.

>
>>> >>>>
>>> >>>>You have a rectangular metal trace over a ground plane, length
in
>
>
>>> >the
>>> >>>>z-direction, height in the y, width in the x. Stretch a
>>> rectangle in
>>>
>>> >
>>> >>>the yz
>>> >>>>plane between the trace and the ground plane. Make it any length

>
>>> >>>(smaller if
>>> >>>>you are simulating with EM tool). If we assume perfect
conductors
>
>
>>> (ie
>>> >
>>> >>
>>> >>>no
>>> >>>>internal-conductor magnetic fields
>>> ---------End of Included Message----------
>>> _____________________________________________________________
>>>
>>>
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>>
>---------End of Included Message----------
>_____________________________________________________________
>
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```