[SI-LIST] Re: si-list Digest V3 #194
- From: Wen Fred-Q16099 <fred.wen@xxxxxxxxxxxx>
- To: "'gigabit@xxxxxxxxxx'" <gigabit@xxxxxxxxxx>
- Date: Mon, 21 Jul 2003 12:35:22 +0800
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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