[SI-LIST] Re: si-list Digest V3 #194
- From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
- To: "Wen Fred-Q16099" <fred.wen@xxxxxxxxxxxx>
- Date: Mon, 21 Jul 2003 11:13:06 -0800
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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