[SI-LIST] Re: Help Explaining Microstrip
- From: "Eric Bogatin" <eric@xxxxxxxxxxxxxxx>
- To: <levinpa@xxxxxxxxxxxxx>, <dave.instone@xxxxxxxxxx>, "'Si-List \(E-mail\)'" <si-list@xxxxxxxxxxxxx>
- Date: Thu, 25 Oct 2007 19:42:20 -0500
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
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
>>
>>
>> ------------------------------------------------------------------
>> To unsubscribe from si-list:
>> si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
>>
>> or to administer your membership from a web page, go to:
>> //www.freelists.org/webpage/si-list
>>
>> For help:
>> si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
>>
>>
>> List technical documents are available at:
>> http://www.si-list.net
>>
>> List archives are viewable at: =20
>> //www.freelists.org/archives/si-list
>> or at our remote archives:
>> http://groups.yahoo.com/group/si-list/messages
>> Old (prior to June 6, 2001) list archives are viewable at:
>> http://www.qsl.net/wb6tpu
>> =20
>> ------------------------------------------------------------------
>> To unsubscribe from si-list:
>> si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
>>
>> or to administer your membership from a web page, go to:
>> //www.freelists.org/webpage/si-list
>>
>> For help:
>> si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
>>
>>
>> List technical documents are available at:
>> http://www.si-list.net
>>
>> List archives are viewable at:
>> //www.freelists.org/archives/si-list
>> or at our remote archives:
>> http://groups.yahoo.com/group/si-list/messages
>> Old (prior to June 6, 2001) list archives are viewable at:
>> http://www.qsl.net/wb6tpu
>>
>>
>>
>>
>------------------------------------------------------------------
>To unsubscribe from si-list:
>si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
>
>or to administer your membership from a web page, go to:
>//www.freelists.org/webpage/si-list
>
>For help:
>si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
>
>
>List technical documents are available at:
> http://www.si-list.net
>
>List archives are viewable at:
> //www.freelists.org/archives/si-list
>or at our remote archives:
> http://groups.yahoo.com/group/si-list/messages
>Old (prior to June 6, 2001) list archives are viewable at:
> http://www.qsl.net/wb6tpu
>
>
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list
For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
List technical documents are available at:
http://www.si-list.net
List archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list
For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
List technical documents are available at:
http://www.si-list.net
List archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
Other related posts:
