[SI-LIST] Re: Help Explaining Microstrip
- From: "Kihong Joshua Kim" <joshuakh@xxxxxxxxx>
- To: levinpa@xxxxxxxxxxxxx, eric@xxxxxxxxxxxxxxx
- Date: Fri, 26 Oct 2007 17:09:39 -0500
Dear SI-listers,
Here I try to make it more clear for any further discussions on the
Hall-effect and the original question about microstrip.
When I introduced "Hall Effect" in this e-mail thread, it was intended just
for "Side-Bar" with no exact mapping between this to the original question,
as I stated in the previous e-mail,
".... using magnetic field NORMAL (not tangential) to the metal (or
semiconductor) surface....".
Now, in this microstrip case as we focused, there is No(or negligibly
small) magnetic field Normal to ground plane by the current
density developed by AC field applied onto this transmission line. This is
from the well-known boundary condition derived from Maxwell's curl-H and J
relationship (One can refer to any EM text book about line path integral
alongside the infinitesimal closed loop at the metal surface).
Thus, in this case, Hall-effect is NOT applied to answer the
original question unless we are interested in the MICROSCOPIC displacement
as in the previous e-mail.
And, because of that boundary condition, the magnetic field in this geometry
is always TANGENTIAL to the ground plane at least under TEM mode assumption
as a major mode for our two-conductor system which has a narrow spatial
distance between them compared to the wavelength of the electromagnetic
wave under consideration.
Therefore, (to answer my 'gedanken' experiment,) even with corrugated
ground plane there is no Lorentz' force to make the electrons or currents to
be bunched up sideways (horizontally) but, of course, negligibly in vertical
way (a displacement less than 100um(about 3-4oz copper thickness) to build
up a micro-volt quoted from the privous e-mail).
Hope this explains a little bit better ...
Cheers,
Kihong Joshua Kim
SI in Photonics and Electronics
On 10/25/07, Eric Bogatin <eric@xxxxxxxxxxxxxxx > wrote:
>
> Paul, Dave and other-
>
> I thought I would shed a little light on this question of understanding
> the
> current distribution in microstrip at some high frequency, and at the same
> time, the repulsive force between two currents, traveling in the same
> direction.
>
> Here is fair warning- if you are not interested in this topic,
>
> DON'T READ ANY FURTHER. DELETE THIS NOTE NOW.
>
> You are both correct, but these observations apply to two very different
> situations.
>
> It is absolutely correct that there is an attractive force between two
> adjacent currents traveling in the same direction, and a repulsive force
> between them when traveling in opposite directions.
>
> This is a DC to daylight effect and is independent of the frequency of the
> current. This arises due to the force on a moving charge in a magnetic
> field
> and is the principle which gives rise to the Hall Effect. A current
> flowing
> down a wire, in a magnetic field which is at right angles to the current,
> will experience a force.
>
> The direction of the force on the moving charges is at right angles to
> both
> the direction of the current (the Ben Franklin positive current) and the
> direction of the B field. This force points transverse to the direction of
> motion, to the side of the wire.
>
> If you hold the wire in place and prevent it from moving, the charges will
>
> move to the side of the wire, push against the side of the wire and you
> feel
> it. If you hold the wire, the charge carriers will bunch up, creating a
> charge concentration. This charge concentration will produce its own
> electric field inside the wire, preventing any net current transverse to
> the
> wire. The re-distribution in current density due to this charge
> re-distribution is a tiny, negligible effect on the current distribution.
>
> In the presence of the external magnetic field, the moving charges-
> electrons, in most conductors- are pushed to the side of the conductor,
> while the ion cores of the metal atoms are held in place by the crystal
> lattice of the metal.
>
> At DC, in the magnetic field, the current distribution in the wire is
> uniform, it's just that there is an ever so slight shift in the charge
> density of the electrons compared to the ion cores, to one side of the
> wire.
>
> When the wire is held in place so it doesn't move, the electrons, bunching
> to one side push on the side of the wire and the person holding the wire
> feels the force. They also create an internal electric field, due to the
> higher negative charge density on one side compared to the ion core
> density.
> The voltage between the two sides of the wire- the internal field times
> the
> wire diameter- can be easily measured- this is the Hall voltage and is
> typically on the order of microvolts for most realistic situations.
>
> Now comes a completely different effect related to the current
> distribution
> in a wire which is strongly frequency dependent. This is not a net charge
> re-distribution, it is a current density re-distribution. There is no net
> force on electrons pushing them to the outer surface of a wire, causing
> them
> to move.
>
> When you look at the current distribution in a microstrip and see current
> flowing to the outside of the conductor and in proximity to the return
> current, it looks like there is a repulsive force inside the conductors
> and
> an attractive force between opposite going conductors, but this is an
> illusion. There is no force between the currents, other than the one
> referred to above.
>
> The current density is re-distributed throughout the conductors, but there
> is no net charge density re-arrangement. The charge density through out
> the
> wire is still locally neutral. This is not the case for the Hall effect,
> where there is a local charge density variation.
>
> The simplest way of thinking about this effect, which we lump under the
> heading of skin depth, is to consider a wire made from a material that has
> a
> resistivity that is higher in its center and lower at its outer surface.
>
> What would the current density be in this case when you launch a DC
> current
> down this conductor? It would distribute based on the local resistivity-
> more current flowing down the path of lowest resistance. There is no net
> shift of electric charge distribution- it is a shift of current density,
> with everywhere local neutrality. Is there a force on the currents pushing
>
> them to the outer surface in this case? No, it is current taking the path
> of
> lowest impedance.
>
> What determines the precise current density is the balance of the voltage
> drop from the current density through the resistivity at each location.
> There should not be a voltage difference between the center and the outer
> edge of the wire. If there were, current will flow in that direction,
> transverse to the wire, until the voltage is reduce to zero. So, the
> current
> density x the resistivity should be constant everywhere along the cross
> section.
>
> If there is higher resistivity in the center, there will be lower current
> density. If too much current flows in the center, there will be a larger
> voltage drop down the length of the wire compared to the voltage drop down
> the wire at the outer edge and current will flow between the edge and
> center
> to equalize the voltage.
>
> The current distribution is based on the map of the resistivity of the
> wire.
>
> Now substitute the idea of resistance or resistivity, with impedance and
> recognize that impedance is really the series resistance + i x 2 pi f x L
> and you see that as frequency goes up, the impedance where there is higher
>
> inductance, goes up faster. This means, where there is higher inductance,
> there will be lower current density.
>
> It is the total inductance per length of a path that the current sees.
> This
> is a combination of the partial self inductance of the path minus the
> partial mutual from the adjacent, return current. The combination of these
> two inductances generates a total inductance per length profile that has
> higher inductance in the center of each conductor and lower inductance
> toward the outer surface.
>
> In addition, between the conductors, the total inductance is reduced due
> to
> field cancellation.
>
> The current distribution maps inversely with the impedance profile. The
> lower the impedance- toward the outer surface and between the conductors,
> the higher the current density. The higher the frequency, the bigger the
> difference between the impedance in the center and the outer regions.
>
> We often say - and I am as guilty as everyone- that the currents inside
> the
> conductor are repelling and the currents between the conductors are
> attracting each other, but this is not the mechanism giving rise to the
> current distribution. There are no net forces on the currents. There would
>
> be a net force on the currents if they did NOT follow these paths of
> lowest
> impedance.
>
> The fact they look like they are attracting each other between conductors
> and repelling inside the same conductor is an illusion.
>
> I hope this helps. If you want more details about this effect, see chapter
> 6
> of my book, Signal Integrity Simplified, or check out some of the articles
> I've written about Inductance on my web site- they are free for download.
>
> Ok, I now return control of your television set.....
>
> --eric
>
>
>
> **************************************
> Dr. Eric Bogatin, President
> Bogatin Enterprises, LLC
> Setting the Standard for Signal Integrity Training
> 26235 w 110th terr
> Olathe, KS 66061
> v: 913-393-1305
> f: 913-393-0929
> c:913-424-4333
> e:eric@xxxxxxxxxxxxxxx
> www.BeTheSignal.com <http://www.bethesignal.com/>
> Spring 2008 Signal Integrity Training Institute
> EPSI, SIAA, BBDP
> April 7-11, 2008, San Jose, CA
> ****************************************
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> On
> Behalf Of Paul Levin
> Sent: Thursday, October 25, 2007 5:02 AM
> To: dave.instone@xxxxxxxxxx; Si-List (E-mail)
> Subject: [SI-LIST] Re: Help Explaining Microstrip
>
> Dear Dave,
>
> That demonstration is exactly my problem.
>
> Were those two feeders carrying current in opposite directions? If so, I
> believe Oersted says that they should spring apart. Were those two wires
> part of a single-turn inductor? Then minimizing energy (=L*I*I/2) says
> minimize L (mu0*Area), hence minimize Area, or get closer together.
>
> These two things seem to be in opposition to each other.
>
> Regards,
>
> Paul Levin
> Xyratex
>
> -----Original Message-----
> >From: David Instone <dave.instone@xxxxxxxxxx >
> >Sent: Oct 25, 2007 2:14 AM
> >To: "Si-List (E-mail)" <si-list@xxxxxxxxxxxxx >
> >Subject: [SI-LIST] Re: Help Explaining Microstrip
> >
> >More than 40 years ago, one of the members of the amateur radio group I
> >belonged to at the time was shown round the VLF high power transmitting
> >station at Rugby UK. He said that what most demonstrated the power of
> >the Tx was seeing the two wires of the open wire feeders springing
> >towards each other every time the morse key was pressed. No need for
> >a strain gauge there.
> >
> >Regards
> >Dave Instone
> >+44 (0)1235 824963
> >
> >OXFORD SEMICONDUCTOR LIMITED
> >25 MILTON PARK
> >ABINGDON
> >OXFORDSHIRE
> >OX14 4SH
> >Registered in England no 2733820
> >Registered Address: As above
> >
> >
> >
> >Loyer, Jeff wrote:
> >> I've been thinking (and reading a bit) about this, so thought I'd throw
> >> in my thoughts/questions...
> >>
> >> Reference: http://www.physics.upenn.edu/~uglabs/exp68_doc.pdf, among
> >> others
> >>
> >> Two conductors close together, carrying the same DC current (connected
> >> in series, resistors not shown), but in opposite directions.=20
> >>
> >> V+ -------------------------------
> >> |
> >> |
> >> |
> >> -----<<<<<<<<<<<<<<<<<<<<<--------
> >> |
> >> ----->>>>>>>>>>>>>>>>>>>>>--------
> >> |
> >> |
> >> | =20
> >> V- -------------------------------
> >>
> >> Assuming the "<" and ">" sections are close together, they will repulse
>
> >> following the formula: F =3D I^2 * (u0 * 2L)/(4 * pi * d0).
> >>
> >> But, there's no mention of the currents in the conductors being
> affected
> >> by this. I've only heard of the currents in the conductors remaining
> >> distributed thoughout their entire cross-sectional areas to maintain
> the
> >> smallest impedance (resistance, in this case). =20
> >>
> >> Why aren't the DC currents influenced by the repulsive force? =20
> >>
> >> If they are influenced by the force (and the effective cross sectional
> >> area diminishes accordingly), the DC resistance would have to go up,
> yet
> >> I've never heard of DC resistance going up because 2 DC conductors are
> >> placed closed together. What am I missing?
> >>
> >> Moving this to a PCB microstrip...
> >> Start with the current we're talking about causing the repulsion:
> DC. I
> >> wonder if we would measure some repulsion between microstrip traces and
>
> >> the adjacent ground, if we had small enough strain gauges. I suspect
> >> not, since the current in the ground plane would be distributed
> >> throughout its entire area to minimize resistance. Force that ground
> >> plane to be very small (such that it becomes a trace), and directly
> >> below the microstrip trace, and I think you would have to see
> repulsion.
> >> But again, I haven't heard of any change in current distribution due to
>
> >> the repulsive force (and, it seems that this would apply to coplanar
> >> traces).
> >>
> >> Now moving to AC in a PCB microstrip...
> >> As we move to AC, the current in the conductors distributes itself
> >> differently to minimize impedance - the current in the plane bunches
> >> under the trace. Again, we end up with 2 conductors close together,
> >> carrying current in opposite directions. I suspect the conductors must
>
> >> be repulsed, though I haven't heard of the distribution of the currents
> >> in the conductors being affected. And, as was pointed out, the
> adhesion
> >> to the substrate is strong enough to keep the traces from separating.
> >>
> >> So: for the AC-case, very sensitive strain gauges would detect the
> >> microstrip trace being repulsed by the ground plane, but why the
> current
> >> distributions (and subsequent impedance) aren't affected isn't clear to
>
> >> me.
> >>
> >> Still left wondering...
> >>
> >> Jeff Loyer
> >>
> >> -----Original Message-----
> >> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx
> ]
> >> On Behalf Of Paul Levin
> >> Sent: Wednesday, October 17, 2007 1:44 PM
> >> To: SI-LIST Reflector
> >> Subject: [SI-LIST] Help Explaining Microstrip
> >>
> >> Dear SI-LIST'ers,
> >>
> >> I'm working on a presentation to explain transmission line to
> >> non-engineers and I find myself stumbling over some of the basics.
> >> (There's nothing like explaining something to bring out all of the
> >> glitches in what you were sure you
> >> understood!)
> >> I'm hoping that one of you may be able to supply the missing link.
> >>
> >> Nearly two hundred years ago Oersted and Ampere figured out that if you
>
> >> have two conductors carrying current in the same direction, they would
> >> would to pull in close to each other whereas if you had two conductors
> >> carrying current in opposite directions, they would want to separate.
> >>
> >> If one were to apply just these observations to microstrip, you would
> >> expect to see all of the trace current bunched on the side away from
> the
> >> ground plane and the return plane current in two bunches to either side
>
> >> of the trace and as far away from the trace as possible, if not on the
> >> bottom.
> >>
> >> Of course, this is almost exactly opposite from what we know happens.
> >>
> >> What is the force that overcomes Oersted and Ampere and causes the
> trace
> >> and return currents to be so heavily attracted to each other?
> >>
> >> Thank you in advance.
> >>
> >> Regards,
> >>
> >> Paul Levin
> >> Senior Principal Engineer
> >> Xyratex
> >>
> >>
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