[SI-LIST] Re: Fwd: Re: si-list Digest V3 #194
- From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
- To: "SIMSCO_RADT" <simsoc_radt@xxxxxxxxxxx>
- Date: Thu, 24 Jul 2003 15:49:05 -0800
I'm not a psychic, but I can hear a toddler in the back seat saying "Are
we there yet?". Just kidding!
---
Dear Unsigned:
>When our you going to put this item to BED, it has been going on for
>at least 2 weeks.
FYI, this item has been in BED for a long time. I'm just scratching the
surface to wake her up, just to make sure ...
>You have basiclly had everybody else do your work for you.
It's learning-through-discussion and that's just what we're doing. BTW,
do you have a Sr. Manager req?
>This site was made for giving people a direction not doing their
complete analysis for them.
I agree, but in some rare cases it works out differently.
---
I appreciate your heartfelt comments, will keep the message in mind and
try to fine-tune my style.
Thanks,
Sainath
---------Included Message----------
>Date: Thu, 24 Jul 2003 11:10:03 -0400
>From: "SIMSCO_RADT" <simsoc_radt@xxxxxxxxxxx>
>Reply-To: "SIMSCO_RADT" <simsoc_radt@xxxxxxxxxxx>
>To: <gigabit@xxxxxxxxxx>, <howiej@xxxxxxxxxx>
>Cc: <si-list@xxxxxxxxxxxxx>
>Subject: Re: [SI-LIST] Fwd: Re: si-list Digest V3 #194
>
>Sainath
>
>
>When our you going to put this item to BED, it has been going on for at
least 2 weeks.
>You have basiclly had everybody else do your work for you.
>This site was made for giving people a direction not doing their
complete analysis for them.
> ----- Original Message -----
> From: Sainath Nimmagadda
> To: howiej@xxxxxxxxxx
> Cc: si-list@xxxxxxxxxxxxx
> Sent: Thursday, July 24, 2003 2:49 AM
> Subject: [SI-LIST] Fwd: Re: si-list Digest V3 #194
>
>
> Dear Howard,
>
> What was the original source for the concept and illustration of Fig.
> 5.2(high-frequency return-current path)in Black Magic book?
>
> Thanks,
> Sainath
>
> ---------Included Message----------
> >Date: Tue, 22 Jul 2003 18:30:09 -0800
> >From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
> >Reply-To: <gigabit@xxxxxxxxxx>
> >To: <howiej@xxxxxxxxxx>
> >Cc: <si-list@xxxxxxxxxxxxx>, <gigaabit@xxxxxxxxxx>
> >Subject: [SI-LIST] Re: si-list Digest V3 #194
> >
> >Dear Howard,
> >
> >I appreciate your participation, time and views. I have some issues
but
>
> >let us consider the most important one. I've reproduced portions of
> your
> >text(in quotes) for discussion convenience. Any text without quotes
is
>
> >mine. It's unusual and uncomfortable to read, but please bear with
me.
>
> >
> >"The stored energy for inductive problems is: E =
> >(1/2)*L*(I^^2), where where L is the system inductance and
> >I^^2 is the total current squared. As you can see, stored
> >magnetic energy E and inductance L vary in direct proportion
> >to one another. Therefore, the distribution of current on
> >the reference plane that minimizes the total stored magnetic
> >energy and the distribution of current that minimizes the
> >inductance are one and the same."
> >
> >For a microstrip, "Most of the current flows on the
> >reference plane right under the trace, with less and less as
> >you move away from the trace" as shown in Fig. 5.3 in Black Magic
> book.
> >
> >Using above formula and figure, "the distribution of current on
> >the reference plane that minimizes the total stored magnetic
> >energy" occurs near the tail portions(away from the trace). This
> >distribution is "one and the same" as "distribution of current that
> >minimizes the inductance".
> >
> >So, it appears to me that the path of least inductance for the
return
> >current is away from the trace where the current is minimum.
> >
> >However, it is generally believed that the path of least inductance
for
>
> >the return current is on the reference plane right under the trace.
> >Using above formula and figure and the fact that "stored magnetic
> energy
> >E and inductance L vary in direct proportion to one another", right
> >under the trace, current is maximum => stored energy is maximum =>
> >inductance is maximum.
> >
> >What's wrong with my line of reasoning?
> >
> >Sainath
> >
> >---------Included Message----------
> >>Date: Tue, 22 Jul 2003 10:58:27 -0700
> >>From: "Dr. Howard Johnson" <howiej@xxxxxxxxxx>
> >>Reply-To: <howiej@xxxxxxxxxx>
> >>To: "Si-List@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
> >>Subject: [SI-LIST] Re: si-list Digest V3 #194
> >>
> >>Those of you interested in magnetic field theory may find
> >>Sainath's questions about the integration of magnetic flux a
> >>fascinating subject; others may find this a good time to
> >>step out for a cup of tea...
> >>
> >>
> >>Dear Sainath,
> >>
> >>The mysteries of magnetic-field integration are indeed
> >>sometimes difficult to comprehend. In answer to your
> >>question about the surface of integration, the best mental
> >>image for this appears in the famous work by James Clerk
> >>Maxwell,
> >>"A Treatise on Electricity and Magnetism". The first volume
> >>of this work (Electricity) is available on www.amazon.com as
> >>a modern reprint of an old Dover version, circa 1954. I read
> >>a copy of the work in preparation for writing my latest
> >>book, "High-Speed Signal Propagation", and found it most
> >>enlightening.
> >>
> >>>From the preface of Maxwell's book, here is the key idea
> >>that renders sensible this whole business of integration of
> >>magnetic field intensity over a surface: "Faraday, in his
> >>mind's eye, saw lines of force traversing all space".
> >>
> >>It's the "lines of force" concept that makes everything
> >>work. What you need to know about Faraday's "lines of force"
> >>idea, in the context of your problem having to do with
> >>evaluating the inductance of your trace, is that magnetic
> >>lines of force form continuous loops having no beginning and
> >>no end. The total number of lines extant is a measure of the
> >>total magnetic flux produced by a magnetized structure.
> >>
> >>Of course you can re-normalize any magnetic field picture to
> >>produce a different number of lines by declaring each line
> >>to represent a different quantity of flux, for example
> >>1/10th the original amount would produce 10x the number of
> >>lines, etc. Presumably you have scaled the flux represented
> >>in your (mental) magnetic field picture in such a way as to
> >>produce a manageable number of lines that is at once enough
> >>to represent accurately the pattern of field intensity and
> >>also not too many to clutter the image. Keep in mind,
> >>however, that regardless of the number of lines, there are a
> >>finite number of them and each is a continuous entity
> >>forming a complete, unbroken loop.
> >>
> >>In Maxwell's view, integrating the magnetic flux passing
> >>through a surface is simply a matter of simply COUNTING how
> >>many lines pass through it.
> >>
> >>For example, consider a closed surface (a sphere) in space.
> >>Any particular line that enters the ball must, since it
> >>cannot end within the sphere, exit at some other point.
> >>Therefore, when counting the number of lines penetrating the
> >>surface, since each line must both enter (a positive count)
> >>and also exit (a negative count), the sum of entrances and
> >>exits penetrating the sphere must be zero. From this simple
> >>idea Maxwell derives the idea that the integral of flux over
> >>any closed surface (of any shape) must be zero.
> >>
> >>[Mathematical aside: you may be familiar with certain
> >>complications having to do with the integration of field
> >>vectors penetrating a surface whereby you have to dot
> >>product the field intensity direction vector with a vector
> >>normal to the surface--these difficulties dissappear when
> >>you simply "count lines", which is the beauty of Faraday's
> >>brilliant intuitive approach. When the surface is tilted so
> >>that the lines intersect the surface at an oblique angle,
> >>the number of lines penetrating each square area of surface
> >>is naturally reduced. This reduction is precisely accounted
> >>for, in multidimensional vector calculus, by the dot
> >>product.]
> >>
> >>Now let's apply the line-counting analogy to your
> >>trace-inductance problem. Imagine a certain finite number of
> >>magnetic lines of force wrapped around your trace. [I'll
> >>assume the reference plane is infinite in the x-y
> >>directions. The plane is located at z=0, and the trace is at
> >>z=1. Since the plane is infinite, no lines of force exist
> >>below z=0.]
> >>
> >>Assume I hook up my inductance meter to one end of the
> >>trace. Connect the other end of the trace to the reference
> >>plane. Now stretch an imaginary "soap bubble" in the region
> >>between the trace and the reference plane. Beginning at my
> >>end of the trace the edges of the bubble touch the trace all
> >>along its length, following along at the end down to the
> >>reference plane, returning along the plane to the source.
> >>For completeness, let's also consider how at the source the
> >>edges of the bubble also must track along the ground lead of
> >>my inductance meter up to the instrument and then back down
> >>the signal lead of the instrument to the beginning of the
> >>trace. We'll assume the meter is really tiny compared to the
> >>size of the trace so we don't have to worry too much about
> >>the shape of the source end of the bubble (this is a serious
> >>real-life complication in the measurement of tiny
> >>inductances).
> >>
> >>Next step: apply 1-amp of current to the trace, and count
> >>the number of field lines penetrating the soap bubble. Since
> >>the bubble is an "open" shape (i.e., it is bounded at the
> >>edges in such a way that it does not enclose any space), you
> >>will record some non-zero amount of flux penetrating the
> >>bubble. NOW comes the really cute part of this mental
> >>experiment. I want you to blow on the bubble, stretching it.
> >>It's still anchored at the edges, but no longer a flat
> >>sheet. The remarkable thing that happens is that the number
> >>of magnetic field lines penetrating the bubble does not
> >>change. It doesn't matter how you stretch or modify the
> >>shape of the bubble, or how far you blow it out of position,
> >>as long as you don't change where the bubble is anchored
> >>around the edges, you haven't changed the number of lines
> >>penetrating it. That property (of the total flux not
> >>changing regardless of the exact shape of the surface of
> >>integration used) is essential to understanding how to
> >>calculate inductance.
> >>
> >>To prove that distorting the bubble doesn't change the total
> >>flux, Maxwell imagines two surfaces, A and B, both anchored
> >>to the trace and plane just like your soap bubble. When
> >>connected together, these two surfaces A and B form a single
> >>closed surface. Therefore, using our earlier reasoning about
> >>the sphere, the total number of lines penetrating the
> >>combined object A+B (that is, coming into A and leaving
> >>through B) must equal zero--from which you may correctly
> >>deduce that when measured separately the total flux passing
> >>through A must precisely equal the total flux passing
> >>through B.
> >>
> >>In a minute I'm going to directly address your question
> >>about making "the area of the surface extend to infinity to
> >>catch all
> >>the field lines", but first I need to go over one more
> >>detail. That detail has to do with how an 2-dimensional
> >>surface with infinite extent acts kinds of like a closed
> >>surface, in that it partitiions space into two regions.
> >>Instead of the regions being "inside" and "outside" as they
> >>are for an ordinary closed surface, the regions are "this
> >>side" and the "other side", but the partition exists just
> >>the same. I bring this up because the partition idea helps
> >>you see why the total flux penetrating any infinite plane
> >>must equal zero. Just like with the sphere, any line of flux
> >>that passes through the infinite sheet to the other side (a
> >>positive count) must eventually make its way back (a
> >>negative count), making the total number of crossings equal
> >>zero. I'm now going to apply this idea (finally) to your
> >>problem.
> >>
> >>I want you to turn your mental picture so you are looking at
> >>the side of the trace (a broadside view of your soap
> >>bubble). Color the bubble pink. Now, pick some particular
> >>line of magnetic flux that penetrates the pink region. If it
> >>passes through the pink region then there are two
> >>possibilities for how it returns to its source (completing
> >>the loop): either it comes back through the pink region, in
> >>which case it cancels itself out contributing nothing to the
> >>total count of flux penetrating the the pink region, or it
> >>comes back SOME OTHER WAY. The only other way back is
> >>through the "white space" that you see above, below, and to
> >>the sides of the apparatus. Therefore if you errect a white
> >>curtain above, below, and to the sides of the apparatus,
> >>covering all the space you see that isn't already pink
> >>(looking from your perspective like a photographic negative
> >>of the pink region), and anchored at its edges along the
> >>trace and plane precisely coincident with the edges of the
> >>pink soap bubble, you may rightly conclude that any flux
> >>that contributes to the total flux count in the pink region
> >>must also penetrate the white sheet. In other words, you can
> >>count the flux passing through the pink region, or count the
> >>flux passing through the white sheet, either way you get the
> >>same answer. This property directly relates to the
> >>discussion above about the infinite plane partitioning
> >>space. As long as the pink and white surfaces, when
> >>combined, form an infinite partition of space, the total
> >>flux through that partition must be zero, ergo, the flux
> >>through the pink and white surfaces must be the same. This
> >>is what I think Andy was talking about when he said that if
> >>you extended the area of integration to infinity you could
> >>catch all the flux.
> >>
> >>The total flux passing through the pink region in reaction
> >>to a current on the trace of 1 amp is defined as the
> >>inductance of the circuit formed by the trace and its
> >>associated reference plane.
> >>
> >>I hope this rather lengthy discussion helps you sort out
> >>some of the paradoxes associated with magnetic-field
> >>integration.
> >>
> >>Buried in the definition of inductance is the assumption
> >>that current always assumes minimum-inductance distribution.
> >>We say, "Current always follows the path of least
> >>inductance", or more precisely, "Current at high
> >>frequencies, if not altered by significant amounts of
> >>resistance, always assumes a distribution that minimizes the
> >>inductance of the loop formed by the signal and return
> >>paths". If you put something in the way of your current that
> >>alters the distribution of current on the return path (like
> >>a hole in the reference plane), then the current assumes
> >>some alternate distribution which must necessarily raise the
> >>inductance of the configuration (moving to any distribution
> >>other than the minimum-inductance distribution must
> >>necessarily raise the inductance).
> >>
> >>Regarding your interest in the exact distribution of current
> >>in the "least-inductance" configuration, let me propose an
> >>analogy that I find quite helpful in working through that
> >>problem. This analogy I've developed in the course of making
> >>up laboratory demonstrations for my new class on Advanced
> >>High-Speed Signal Propagation.
> >>
> >>First replace your dielectric medium (the space between the
> >>trace and reference plane) with a slightly resistive
> >>material. I like to imagine salt water occupying that space.
> >>Leave the trace open-circuited at both ends, and apply 1-V
> >>DC to the trace. A certain pattern of current will flow
> >>through the salt water to the reference plane. I'll bet you
> >>could draw a picture showing the pattern of current flow in
> >>this situation. Start with a cross-sectional view of the
> >>trace. Suppose you use 100 lines for the picture, each line
> >>representing a certain fraction of the total current. Each
> >>line emanates from the trace and terminates on the plane
> >>(unlike magetic lines of force these current density lines
> >>have beginnings and endings). A great density of lines will
> >>flow directly between the trace and plane, with the lines
> >>feathering out to lower and lower densities as you work your
> >>way further from the trace. The lines always leave the
> >>surface of the trace in a direction perpindicular to the
> >>surface of the trace, and land perpindicular to the
> >>reference plane.
> >>
> >>Here's why I like this exercise: Your picture of the DC
> >>current flow exactly mimics the picture of lines of electric
> >>flux in a dielectric medium operated at high frequency. I
> >>find many people have no difficulty imagining how DC
> >>currents would behave in salt water--and it's the same
> >>problem figuring out how AC currents behave in a dielectric
> >>medium.
> >>
> >>Now we get to the part of this discussion about the density
> >>of current in the reference plane. Your electric-field
> >>picture shows a great density of current flowing from trace
> >>to plane at a position directly underneath the trace, and
> >>less and less density of current flowing to positions on the
> >>plane remote from the trace. This picture shows precisely
> >>how the current gets from trace to plane (i.e., it flows
> >>through the parasitic capacitance between trace and plane).
> >>If you assume that once the current arrive on the plane it
> >>flows parallel to the trace (making the cross-sectional
> >>picture the same at each position along the trace, as
> >>required by symmetry), then you can see that the picture
> >>also shows the density of current flowing on the plane as a
> >>function of position. Most of the current flows on the
> >>reference plane right under the trace, with less and less as
> >>you move away from the trace (it happens to fall off
> >>approximately quadratically for microstrips, even faster for
> >>striplines).
> >>
> >>Of course, you are going to want to know "why" current
> >>should behave in such a manner. The principle in question
> >>here is the "minimum energy" principle. My recollection of
> >>Maxwell's equations (specifically I *think* it's the ones
> >>that say the Laplacian of both electric and magnetic fields
> >>are zero within source-free regions) is that the
> >>distributions of charge and current in a statics problem
> >>fall into a pattern that satisfies all the boundary
> >>conditions around the edges of the region of interest,
> >>satisfies the Laplacian conditions in the middle, AND ALSO
> >>just happens to store the *minimum* amount of energy in the
> >>interior fields. In other words, you aren't going to get
> >>huge, unexplained, spurrious magnetic fields in the middle
> >>of an otherwise quiet region (unless you believe in vaccuum
> >>fluctuations, which is a different subject entirely...).
> >>
> >>The stored energy for inductive problems is: E =
> >>(1/2)*L*(I^^2), where where L is the system inductance and
> >>I^^2 is the total current squared. As you can see, stored
> >>magnetic energy E and inductance L vary in direct proportion
> >>to one another. Therefore, the distribution of current on
> >>the reference plane that minimizes the total stored magnetic
> >>energy and the distribution of current that minimizes the
> >>inductance are one and the same.
> >>
> >>In answer to what might logically be your next question,
> >>"Why do electromagnetic fields tend towards the
> >>minimum-stored-energy distribution?", I can only say that
> >>I'm not sure anyone really knows -- we just observe that
> >>this is the way nature seems to operate. Perhaps someone
> >>more well-versed in electromagnetic theory can provide an
> >>answer.
> >>
> >>By assuming the current is *NOT* in the minimum-energy
> >>distribution you can demonstrate the existance of a mode of
> >>current that leads to a lower-energy state, but that
> >>demonstration would convince you of the absurdity of the
> >>non-minimum energy situation only if you also intuitively
> >>believe that nature is not absurd. Further discussion of
> >>*that* issue is probably best left to
> >>physicist-philosophers.
> >>
> >>I hope this discussion is helpful to you, and doesn't just
> >>stir up a lot of other doubts.
> >>
> >>For further reading, try the following articles: "High-Speed
> >>Return Signals", "Return Current in Plane", "Proximity
> >>Effect", "Proximity Effect II", "Proximity Effect III", and
> >>"Rainy-Day Fun", (see http:\\sigcon.com, under "archives",
> >>look for the alphabetical index).
> >>
> >>Best regards,
> >>Dr. Howard Johnson, Signal Consulting Inc.,
> >>tel +1 509-997-0505, howiej@xxxxxxxxxx
> >>http:\\sigcon.com -- High-Speed Digital Design articles,
> >>books, tools, and seminars
> >>
> >>
> >>
> >>-----Original Message-----
> >>From: si-list-bounce@xxxxxxxxxxxxx
> >>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Sainath
> >>Nimmagadda
> >>Sent: Thursday, July 17, 2003 11:44 PM
> >>To: andrew.c.byers@xxxxxxxxxxxxxx
> >>Cc: si-list@xxxxxxxxxxxxx
> >>Subject: [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), then all of the
> >>magnetic field
> >>>>associated with that signal trace will pass through this
> >>rectangle. It
> >>
> >>>is
> >>>>kind of like a net. Magnetic field lines always have to
> >>end up in the
> >>
> >>>same
> >>>>place they started, completing the circle. Also, in this
> >>configuration,
> >>>all
> >>>>your field lines are perpendicular to the integrating
> >>rectangle. So
> >>>>inductance is flux/I = B*A/I. In this case, you will
> >>actually have
> >>>>inductance per unit length because your net had a specific
> >>z-length.
> >>>>
> >>>>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.
> >>>>By placing it between the signal line and the return path,
> >>you capture
> >>
> >>>all
> >>>>the field lines. So you have one number for inductance if
> >>you account
> >>
> >>>for
> >>>>all the B field lines. An inductance "distribution" would
> >>indicate
> >>that
> >>>you
> >>>>are not catching all the magnetic field lines with your
> >>integrating
> >>>surface.
> >>>>
> >>>>
> >>>>This might open up a talk about internal inductance, when
> >>you have
> >>>magnetic
> >>>>field lines (ie current) INSIDE the conductors. As
> >>frequency
> >>increases,
> >>>the
> >>>>current crowds to the surface, and the internal inductance
> >>diminishes.
> >>
> >>>But
> >>>>at lower or intermediate frequencies, this internal
> >>inductance can be
> >>
> >>>a
> >>>>contributing factor. For PCB's, this is typically in the
> >>low MHz
> >>range.
> >>>But
> >>>>for square conductors on silicon, measuring a few microns
> >>wide and a
> >>>few
> >>>>microns high, the internal inductance might have to be
> >>considered up
> >>>to
> >>>>several GHz. Does this affect you? Do you electrical
> >>models consider
> >>>this
> >>>>effect? How about internal inductance of the ground plane?
> >>Interesting
> >>
> >>>stuff
> >>>>here.
> >>>>
> >>>>Salud,
> >>>>
> >>>>Andy Byers
> >>>>
> >>>>-----Original Message-----
> >>>>From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
> >>>>Sent: Thursday, July 17, 2003 9:25 AM
> >>>>To: beneken@xxxxxxxxxxxx
> >>>>Cc: si-list@xxxxxxxxxxxxx; gigabit@xxxxxxxxxx
> >>>>Subject: [SI-LIST] Re: si-list Digest V3 #194
> >>>>
> >>>>
> >>>>Thomas,
> >>>>
> >>>>Thank you. I agree, you get one value of inductance for
> >>one
> >>>integration.
> >>>>If you repeat this for a number of 'concentric spheres',
> >>you will get
> >>a
> >>>
> >>>>number of inductances- ranging from minimum to maximum.
> >>Does that make
> >>
> >>>
> >>>>sense?
> >>>>
> >>>>Sainath
> >>>>
> >>>>---------Included Message----------
> >>>>>Date: Thu, 17 Jul 2003 12:04:57 +0200
> >>>>>From: "Thomas Beneken" <beneken@xxxxxxxxxxxx>
> >>>>>Reply-To: <beneken@xxxxxxxxxxxx>
> >>>>>To: <si-list@xxxxxxxxxxxxx>
> >>>>>Subject: [SI-LIST] Re: si-list Digest V3 #194
> >>>>>
> >>>>>Hello Sainath,
> >>>>>
> >>>>>inductance is the proportional factor between the current
> >>and the
> >>>>magnetic
> >>>>>flux. So far Your idea is ok. But calculating magnetic
> >>flux from
> >>>>magnetic
> >>>>>field requires an integration across a closed surface
> >>surrounding
> >>the
> >>>>>conductor carrying the current. So - as You see - You
> >>will not get a
> >>>>>inductance distribution over conductor length but only an
> >>integral
> >>>>value for
> >>>>>the conductor enclosed in the chosen sphere.
> >>>>>
> >>>>>Sorry,
> >>>>>Thomas
> >>>>>
> >>>>>> Msg: #12 in digest
> >>>>>> Date: Wed, 16 Jul 2003 11:55:35 -0800
> >>>>>> From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx>
> >>>>>> Subject: [SI-LIST] Microstrip Inductance
> >>>>>>
> >>>>>> Hello experts:
> >>>>>>
> >>>>>> For a microstrip, we know the magnetic field
> >>distribution(for
> >>>>>> example,
> >>>>>> Fig. 2.3 Stephen Hall's book) and current density
> >>>>>> distribution(Fig. 4.5
> >>>>>> same book). Given these, how would you obtain the
> >>inductance
> >>>>>> distribution?
> >>>>>>
> >>>>>> Thanks in advance,
> >>>>>> Sainath
> >>>>>
> >>>>>
> >>>>>---------------------------------------------------------
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_____________________________________________________________
-- HTML Attachment decoded to text by Ecartis --
-- File: attach01
Sainath
When our you going to put this item to BED, it has been going on for at
least 2 weeks. You have basiclly had everybody else do your work for you.
This site was made for giving people a direction not doing their complete
analysis for them. ----- Original Message ----- From: Sainath Nimmagadda[1]
To: howiej@xxxxxxxxxx[2] Cc: si-list@xxxxxxxxxxxxx[3] Sent: Thursday, July
24, 2003 2:49 AM Subject: [SI-LIST] Fwd: Re: si-list Digest V3 #194
Dear Howard,
What was the original source for the concept and illustration of Fig.
5.2(high-frequency return-current path)in Black Magic book?
Thanks,
Sainath
---------Included Message----------
>Date: Tue, 22 Jul 2003 18:30:09 -0800
>From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx[4]>
>Reply-To: <gigabit@xxxxxxxxxx[5]>
>To: <howiej@xxxxxxxxxx[6]>
>Cc: <si-list@xxxxxxxxxxxxx[7]>, <gigaabit@xxxxxxxxxx[8]>
>Subject: [SI-LIST] Re: si-list Digest V3 #194
>
>Dear Howard,
>
>I appreciate your participation, time and views. I have some issues but
>let us consider the most important one. I've reproduced portions of
your
>text(in quotes) for discussion convenience. Any text without quotes is
>mine. It's unusual and uncomfortable to read, but please bear with me.
>
>"The stored energy for inductive problems is: E =
>(1/2)*L*(I^^2), where where L is the system inductance and
>I^^2 is the total current squared. As you can see, stored
>magnetic energy E and inductance L vary in direct proportion
>to one another. Therefore, the distribution of current on
>the reference plane that minimizes the total stored magnetic
>energy and the distribution of current that minimizes the
>inductance are one and the same."
>
>For a microstrip, "Most of the current flows on the
>reference plane right under the trace, with less and less as
>you move away from the trace" as shown in Fig. 5.3 in Black Magic
book.
>
>Using above formula and figure, "the distribution of current on
>the reference plane that minimizes the total stored magnetic
>energy" occurs near the tail portions(away from the trace). This
>distribution is "one and the same" as "distribution of current that
>minimizes the inductance".
>
>So, it appears to me that the path of least inductance for the return
>current is away from the trace where the current is minimum.
>
>However, it is generally believed that the path of least inductance for
>the return current is on the reference plane right under the trace.
>Using above formula and figure and the fact that "stored magnetic
energy
>E and inductance L vary in direct proportion to one another", right
>under the trace, current is maximum => stored energy is maximum =>
>inductance is maximum.
>
>What's wrong with my line of reasoning?
>
>Sainath
>
>---------Included Message----------
>>Date: Tue, 22 Jul 2003 10:58:27 -0700
>>From: "Dr. Howard Johnson" <howiej@xxxxxxxxxx[9]>
>>Reply-To: <howiej@xxxxxxxxxx[10]>
>>To: "Si-List@xxxxxxxxxxxxx[11]" <si-list@xxxxxxxxxxxxx[12]>
>>Subject: [SI-LIST] Re: si-list Digest V3 #194
>>
>>Those of you interested in magnetic field theory may find
>>Sainath's questions about the integration of magnetic flux a
>>fascinating subject; others may find this a good time to
>>step out for a cup of tea...
>>
>>
>>Dear Sainath,
>>
>>The mysteries of magnetic-field integration are indeed
>>sometimes difficult to comprehend. In answer to your
>>question about the surface of integration, the best mental
>>image for this appears in the famous work by James Clerk
>>Maxwell,
>>"A Treatise on Electricity and Magnetism". The first volume
>>of this work (Electricity) is available on www.amazon.com[13] as
>>a modern reprint of an old Dover version, circa 1954. I read
>>a copy of the work in preparation for writing my latest
>>book, "High-Speed Signal Propagation", and found it most
>>enlightening.
>>
>>>From the preface of Maxwell's book, here is the key idea
>>that renders sensible this whole business of integration of
>>magnetic field intensity over a surface: "Faraday, in his
>>mind's eye, saw lines of force traversing all space".
>>
>>It's the "lines of force" concept that makes everything
>>work. What you need to know about Faraday's "lines of force"
>>idea, in the context of your problem having to do with
>>evaluating the inductance of your trace, is that magnetic
>>lines of force form continuous loops having no beginning and
>>no end. The total number of lines extant is a measure of the
>>total magnetic flux produced by a magnetized structure.
>>
>>Of course you can re-normalize any magnetic field picture to
>>produce a different number of lines by declaring each line
>>to represent a different quantity of flux, for example
>>1/10th the original amount would produce 10x the number of
>>lines, etc. Presumably you have scaled the flux represented
>>in your (mental) magnetic field picture in such a way as to
>>produce a manageable number of lines that is at once enough
>>to represent accurately the pattern of field intensity and
>>also not too many to clutter the image. Keep in mind,
>>however, that regardless of the number of lines, there are a
>>finite number of them and each is a continuous entity
>>forming a complete, unbroken loop.
>>
>>In Maxwell's view, integrating the magnetic flux passing
>>through a surface is simply a matter of simply COUNTING how
>>many lines pass through it.
>>
>>For example, consider a closed surface (a sphere) in space.
>>Any particular line that enters the ball must, since it
>>cannot end within the sphere, exit at some other point.
>>Therefore, when counting the number of lines penetrating the
>>surface, since each line must both enter (a positive count)
>>and also exit (a negative count), the sum of entrances and
>>exits penetrating the sphere must be zero. From this simple
>>idea Maxwell derives the idea that the integral of flux over
>>any closed surface (of any shape) must be zero.
>>
>>[Mathematical aside: you may be familiar with certain
>>complications having to do with the integration of field
>>vectors penetrating a surface whereby you have to dot
>>product the field intensity direction vector with a vector
>>normal to the surface--these difficulties dissappear when
>>you simply "count lines", which is the beauty of Faraday's
>>brilliant intuitive approach. When the surface is tilted so
>>that the lines intersect the surface at an oblique angle,
>>the number of lines penetrating each square area of surface
>>is naturally reduced. This reduction is precisely accounted
>>for, in multidimensional vector calculus, by the dot
>>product.]
>>
>>Now let's apply the line-counting analogy to your
>>trace-inductance problem. Imagine a certain finite number of
>>magnetic lines of force wrapped around your trace. [I'll
>>assume the reference plane is infinite in the x-y
>>directions. The plane is located at z=0, and the trace is at
>>z=1. Since the plane is infinite, no lines of force exist
>>below z=0.]
>>
>>Assume I hook up my inductance meter to one end of the
>>trace. Connect the other end of the trace to the reference
>>plane. Now stretch an imaginary "soap bubble" in the region
>>between the trace and the reference plane. Beginning at my
>>end of the trace the edges of the bubble touch the trace all
>>along its length, following along at the end down to the
>>reference plane, returning along the plane to the source.
>>For completeness, let's also consider how at the source the
>>edges of the bubble also must track along the ground lead of
>>my inductance meter up to the instrument and then back down
>>the signal lead of the instrument to the beginning of the
>>trace. We'll assume the meter is really tiny compared to the
>>size of the trace so we don't have to worry too much about
>>the shape of the source end of the bubble (this is a serious
>>real-life complication in the measurement of tiny
>>inductances).
>>
>>Next step: apply 1-amp of current to the trace, and count
>>the number of field lines penetrating the soap bubble. Since
>>the bubble is an "open" shape (i.e., it is bounded at the
>>edges in such a way that it does not enclose any space), you
>>will record some non-zero amount of flux penetrating the
>>bubble. NOW comes the really cute part of this mental
>>experiment. I want you to blow on the bubble, stretching it.
>>It's still anchored at the edges, but no longer a flat
>>sheet. The remarkable thing that happens is that the number
>>of magnetic field lines penetrating the bubble does not
>>change. It doesn't matter how you stretch or modify the
>>shape of the bubble, or how far you blow it out of position,
>>as long as you don't change where the bubble is anchored
>>around the edges, you haven't changed the number of lines
>>penetrating it. That property (of the total flux not
>>changing regardless of the exact shape of the surface of
>>integration used) is essential to understanding how to
>>calculate inductance.
>>
>>To prove that distorting the bubble doesn't change the total
>>flux, Maxwell imagines two surfaces, A and B, both anchored
>>to the trace and plane just like your soap bubble. When
>>connected together, these two surfaces A and B form a single
>>closed surface. Therefore, using our earlier reasoning about
>>the sphere, the total number of lines penetrating the
>>combined object A+B (that is, coming into A and leaving
>>through B) must equal zero--from which you may correctly
>>deduce that when measured separately the total flux passing
>>through A must precisely equal the total flux passing
>>through B.
>>
>>In a minute I'm going to directly address your question
>>about making "the area of the surface extend to infinity to
>>catch all
>>the field lines", but first I need to go over one more
>>detail. That detail has to do with how an 2-dimensional
>>surface with infinite extent acts kinds of like a closed
>>surface, in that it partitiions space into two regions.
>>Instead of the regions being "inside" and "outside" as they
>>are for an ordinary closed surface, the regions are "this
>>side" and the "other side", but the partition exists just
>>the same. I bring this up because the partition idea helps
>>you see why the total flux penetrating any infinite plane
>>must equal zero. Just like with the sphere, any line of flux
>>that passes through the infinite sheet to the other side (a
>>positive count) must eventually make its way back (a
>>negative count), making the total number of crossings equal
>>zero. I'm now going to apply this idea (finally) to your
>>problem.
>>
>>I want you to turn your mental picture so you are looking at
>>the side of the trace (a broadside view of your soap
>>bubble). Color the bubble pink. Now, pick some particular
>>line of magnetic flux that penetrates the pink region. If it
>>passes through the pink region then there are two
>>possibilities for how it returns to its source (completing
>>the loop): either it comes back through the pink region, in
>>which case it cancels itself out contributing nothing to the
>>total count of flux penetrating the the pink region, or it
>>comes back SOME OTHER WAY. The only other way back is
>>through the "white space" that you see above, below, and to
>>the sides of the apparatus. Therefore if you errect a white
>>curtain above, below, and to the sides of the apparatus,
>>covering all the space you see that isn't already pink
>>(looking from your perspective like a photographic negative
>>of the pink region), and anchored at its edges along the
>>trace and plane precisely coincident with the edges of the
>>pink soap bubble, you may rightly conclude that any flux
>>that contributes to the total flux count in the pink region
>>must also penetrate the white sheet. In other words, you can
>>count the flux passing through the pink region, or count the
>>flux passing through the white sheet, either way you get the
>>same answer. This property directly relates to the
>>discussion above about the infinite plane partitioning
>>space. As long as the pink and white surfaces, when
>>combined, form an infinite partition of space, the total
>>flux through that partition must be zero, ergo, the flux
>>through the pink and white surfaces must be the same. This
>>is what I think Andy was talking about when he said that if
>>you extended the area of integration to infinity you could
>>catch all the flux.
>>
>>The total flux passing through the pink region in reaction
>>to a current on the trace of 1 amp is defined as the
>>inductance of the circuit formed by the trace and its
>>associated reference plane.
>>
>>I hope this rather lengthy discussion helps you sort out
>>some of the paradoxes associated with magnetic-field
>>integration.
>>
>>Buried in the definition of inductance is the assumption
>>that current always assumes minimum-inductance distribution.
>>We say, "Current always follows the path of least
>>inductance", or more precisely, "Current at high
>>frequencies, if not altered by significant amounts of
>>resistance, always assumes a distribution that minimizes the
>>inductance of the loop formed by the signal and return
>>paths". If you put something in the way of your current that
>>alters the distribution of current on the return path (like
>>a hole in the reference plane), then the current assumes
>>some alternate distribution which must necessarily raise the
>>inductance of the configuration (moving to any distribution
>>other than the minimum-inductance distribution must
>>necessarily raise the inductance).
>>
>>Regarding your interest in the exact distribution of current
>>in the "least-inductance" configuration, let me propose an
>>analogy that I find quite helpful in working through that
>>problem. This analogy I've developed in the course of making
>>up laboratory demonstrations for my new class on Advanced
>>High-Speed Signal Propagation.
>>
>>First replace your dielectric medium (the space between the
>>trace and reference plane) with a slightly resistive
>>material. I like to imagine salt water occupying that space.
>>Leave the trace open-circuited at both ends, and apply 1-V
>>DC to the trace. A certain pattern of current will flow
>>through the salt water to the reference plane. I'll bet you
>>could draw a picture showing the pattern of current flow in
>>this situation. Start with a cross-sectional view of the
>>trace. Suppose you use 100 lines for the picture, each line
>>representing a certain fraction of the total current. Each
>>line emanates from the trace and terminates on the plane
>>(unlike magetic lines of force these current density lines
>>have beginnings and endings). A great density of lines will
>>flow directly between the trace and plane, with the lines
>>feathering out to lower and lower densities as you work your
>>way further from the trace. The lines always leave the
>>surface of the trace in a direction perpindicular to the
>>surface of the trace, and land perpindicular to the
>>reference plane.
>>
>>Here's why I like this exercise: Your picture of the DC
>>current flow exactly mimics the picture of lines of electric
>>flux in a dielectric medium operated at high frequency. I
>>find many people have no difficulty imagining how DC
>>currents would behave in salt water--and it's the same
>>problem figuring out how AC currents behave in a dielectric
>>medium.
>>
>>Now we get to the part of this discussion about the density
>>of current in the reference plane. Your electric-field
>>picture shows a great density of current flowing from trace
>>to plane at a position directly underneath the trace, and
>>less and less density of current flowing to positions on the
>>plane remote from the trace. This picture shows precisely
>>how the current gets from trace to plane (i.e., it flows
>>through the parasitic capacitance between trace and plane).
>>If you assume that once the current arrive on the plane it
>>flows parallel to the trace (making the cross-sectional
>>picture the same at each position along the trace, as
>>required by symmetry), then you can see that the picture
>>also shows the density of current flowing on the plane as a
>>function of position. Most of the current flows on the
>>reference plane right under the trace, with less and less as
>>you move away from the trace (it happens to fall off
>>approximately quadratically for microstrips, even faster for
>>striplines).
>>
>>Of course, you are going to want to know "why" current
>>should behave in such a manner. The principle in question
>>here is the "minimum energy" principle. My recollection of
>>Maxwell's equations (specifically I *think* it's the ones
>>that say the Laplacian of both electric and magnetic fields
>>are zero within source-free regions) is that the
>>distributions of charge and current in a statics problem
>>fall into a pattern that satisfies all the boundary
>>conditions around the edges of the region of interest,
>>satisfies the Laplacian conditions in the middle, AND ALSO
>>just happens to store the *minimum* amount of energy in the
>>interior fields. In other words, you aren't going to get
>>huge, unexplained, spurrious magnetic fields in the middle
>>of an otherwise quiet region (unless you believe in vaccuum
>>fluctuations, which is a different subject entirely...).
>>
>>The stored energy for inductive problems is: E =
>>(1/2)*L*(I^^2), where where L is the system inductance and
>>I^^2 is the total current squared. As you can see, stored
>>magnetic energy E and inductance L vary in direct proportion
>>to one another. Therefore, the distribution of current on
>>the reference plane that minimizes the total stored magnetic
>>energy and the distribution of current that minimizes the
>>inductance are one and the same.
>>
>>In answer to what might logically be your next question,
>>"Why do electromagnetic fields tend towards the
>>minimum-stored-energy distribution?", I can only say that
>>I'm not sure anyone really knows -- we just observe that
>>this is the way nature seems to operate. Perhaps someone
>>more well-versed in electromagnetic theory can provide an
>>answer.
>>
>>By assuming the current is *NOT* in the minimum-energy
>>distribution you can demonstrate the existance of a mode of
>>current that leads to a lower-energy state, but that
>>demonstration would convince you of the absurdity of the
>>non-minimum energy situation only if you also intuitively
>>believe that nature is not absurd. Further discussion of
>>*that* issue is probably best left to
>>physicist-philosophers.
>>
>>I hope this discussion is helpful to you, and doesn't just
>>stir up a lot of other doubts.
>>
>>For further reading, try the following articles: "High-Speed
>>Return Signals", "Return Current in Plane", "Proximity
>>Effect", "Proximity Effect II", "Proximity Effect III", and
>>"Rainy-Day Fun", (see http:\\sigcon.com, under "archives",
>>look for the alphabetical index).
>>
>>Best regards,
>>Dr. Howard Johnson, Signal Consulting Inc.,
>>tel +1 509-997-0505, howiej@xxxxxxxxxx[14]
>>http:\\sigcon.com -- High-Speed Digital Design articles,
>>books, tools, and seminars
>>
>>
>>
>>-----Original Message-----
>>From: si-list-bounce@xxxxxxxxxxxxx[15]
>>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Sainath
>>Nimmagadda
>>Sent: Thursday, July 17, 2003 11:44 PM
>>To: andrew.c.byers@xxxxxxxxxxxxxx[16]
>>Cc: si-list@xxxxxxxxxxxxx[17]
>>Subject: [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[18]>
>>>Reply-To: <andrew.c.byers@xxxxxxxxxxxxxx[19]>
>>>To: <gigabit@xxxxxxxxxx[20]>
>>>Cc: <si-list@xxxxxxxxxxxxx[21]>
>>>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[22]
>>>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[23]>
>>>>Reply-To: <andrew.c.byers@xxxxxxxxxxxxxx[24]>
>>>>To: <gigabit@xxxxxxxxxx[25]>, <beneken@xxxxxxxxxxxx[26]>
>>>>Cc: <si-list@xxxxxxxxxxxxx[27]>
>>>>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), then all of the
>>magnetic field
>>>>associated with that signal trace will pass through this
>>rectangle. It
>>
>>>is
>>>>kind of like a net. Magnetic field lines always have to
>>end up in the
>>
>>>same
>>>>place they started, completing the circle. Also, in this
>>configuration,
>>>all
>>>>your field lines are perpendicular to the integrating
>>rectangle. So
>>>>inductance is flux/I = B*A/I. In this case, you will
>>actually have
>>>>inductance per unit length because your net had a specific
>>z-length.
>>>>
>>>>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.
>>>>By placing it between the signal line and the return path,
>>you capture
>>
>>>all
>>>>the field lines. So you have one number for inductance if
>>you account
>>
>>>for
>>>>all the B field lines. An inductance "distribution" would
>>indicate
>>that
>>>you
>>>>are not catching all the magnetic field lines with your
>>integrating
>>>surface.
>>>>
>>>>
>>>>This might open up a talk about internal inductance, when
>>you have
>>>magnetic
>>>>field lines (ie current) INSIDE the conductors. As
>>frequency
>>increases,
>>>the
>>>>current crowds to the surface, and the internal inductance
>>diminishes.
>>
>>>But
>>>>at lower or intermediate frequencies, this internal
>>inductance can be
>>
>>>a
>>>>contributing factor. For PCB's, this is typically in the
>>low MHz
>>range.
>>>But
>>>>for square conductors on silicon, measuring a few microns
>>wide and a
>>>few
>>>>microns high, the internal inductance might have to be
>>considered up
>>>to
>>>>several GHz. Does this affect you? Do you electrical
>>models consider
>>>this
>>>>effect? How about internal inductance of the ground plane?
>>Interesting
>>
>>>stuff
>>>>here.
>>>>
>>>>Salud,
>>>>
>>>>Andy Byers
>>>>
>>>>-----Original Message-----
>>>>From: Sainath Nimmagadda [mailto:gigabit@xxxxxxxxxx]
>>>>Sent: Thursday, July 17, 2003 9:25 AM
>>>>To: beneken@xxxxxxxxxxxx[28]
>>>>Cc: si-list@xxxxxxxxxxxxx[29]; gigabit@xxxxxxxxxx[30]
>>>>Subject: [SI-LIST] Re: si-list Digest V3 #194
>>>>
>>>>
>>>>Thomas,
>>>>
>>>>Thank you. I agree, you get one value of inductance for
>>one
>>>integration.
>>>>If you repeat this for a number of 'concentric spheres',
>>you will get
>>a
>>>
>>>>number of inductances- ranging from minimum to maximum.
>>Does that make
>>
>>>
>>>>sense?
>>>>
>>>>Sainath
>>>>
>>>>---------Included Message----------
>>>>>Date: Thu, 17 Jul 2003 12:04:57 +0200
>>>>>From: "Thomas Beneken" <beneken@xxxxxxxxxxxx[31]>
>>>>>Reply-To: <beneken@xxxxxxxxxxxx[32]>
>>>>>To: <si-list@xxxxxxxxxxxxx[33]>
>>>>>Subject: [SI-LIST] Re: si-list Digest V3 #194
>>>>>
>>>>>Hello Sainath,
>>>>>
>>>>>inductance is the proportional factor between the current
>>and the
>>>>magnetic
>>>>>flux. So far Your idea is ok. But calculating magnetic
>>flux from
>>>>magnetic
>>>>>field requires an integration across a closed surface
>>surrounding
>>the
>>>>>conductor carrying the current. So - as You see - You
>>will not get a
>>>>>inductance distribution over conductor length but only an
>>integral
>>>>value for
>>>>>the conductor enclosed in the chosen sphere.
>>>>>
>>>>>Sorry,
>>>>>Thomas
>>>>>
>>>>>>Msg: #12 in digest
>>>>>>Date: Wed, 16 Jul 2003 11:55:35 -0800
>>>>>>From: "Sainath Nimmagadda" <gigabit@xxxxxxxxxx[34]>
>>>>>>Subject: [SI-LIST] Microstrip Inductance
>>>>>>
>>>>>>Hello experts:
>>>>>>
>>>>>>For a microstrip, we know the magnetic field
>>distribution(for
>>>>>>example,
>>>>>>Fig. 2.3 Stephen Hall's book) and current density
>>>>>>distribution(Fig. 4.5
>>>>>>same book). Given these, how would you obtain the
>>inductance
>>>>>>distribution?
>>>>>>
>>>>>>Thanks in advance,
>>>>>>Sainath
>>>>>
>>>>>
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