[SI-LIST] Re: si-list Digest V3 #194
- From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
- To: "Michael Smith" <michael@xxxxxxxxxx>
- Date: Mon, 21 Jul 2003 14:01:23 -0800
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,
please
>
>check your statements.
>
>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>
>>> >Reply-To: <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>
>>> >>Reply-To: <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>
>>> >>>Reply-To: <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
>>> threads on
>>> >>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>
>>> >>>>Reply-To: <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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>>
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