[SI-LIST] Re: Spreading Inductance
- From: "Hill, John" <John.Hill@xxxxxxxxxx>
- To: "Peterson, James F \(EHCOE\)" <james.f.peterson@xxxxxxxxxxxxx>, <weirsi@xxxxxxxxxx>, "silist" <si-list@xxxxxxxxxxxxx>
- Date: Tue, 26 Sep 2006 10:30:26 -0400
Jim,
It does in the far field as it radiates in a spherical wave front away
from a source, but not in a loss-less transmission line. I look at the
planes as two dimensional transmission lines. As the wave hits the open
discontinuity at the edge it will reflect off the open. This will cause
various resonance structures to be formed. This gives us insight into
how a Patch antenna works. However the Zo is very low and I don't know
how to calculate it.
One of the things that I am unsure of is if we can really use a spice
gird simulation to analyze this problem. The field from one transmission
line would not interact with the near by transmission lines.
I am sorry for rambling, but I don't have a PhD in electromagnetics.
Best regards,
John
=20
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-----Original Message-----
From: Peterson, James F (EHCOE) [mailto:james.f.peterson@xxxxxxxxxxxxx]=20
Sent: Tuesday, September 26, 2006 7:33 AM
To: weirsi@xxxxxxxxxx; Hill, John; silist
Subject: RE: [SI-LIST] Re: Spreading Inductance
very interesting discussion. I've always pictured (imagined) current
density falling off at 1/D^2 away from a direct line between the entry
and exit points of a ground plane...not a good approximation?
-Jim
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of steve weir
Sent: Monday, September 25, 2006 6:35 PM
To: Hill, John; Sirisha.Godavarthy@xxxxxxxxxxxx; Nash, Tim J (EHCOE);
silist
Subject: [SI-LIST] Re: Spreading Inductance
John,
When we are solving a simple plane spreading inductance problem we
integrate dB to find total B around the port, in this case a circle.
Your discomfort with integrating around a circle is no doubt from your
expectation that yields a zero result. But for these types of problems
it does not. This is not the same as say integrating spring force over
distance where if we finish where we start we end up with a zero result.
At each point around the path we have a nonzero increment that adds to
the final result.
As to the current path spreading out diminishing to zero, well, yes and
no. What happens is that the field intensity falls away very quickly
with initial distance, and then proceeds to fall off slower and slower,
but it never falls to zero. So yes, from a practical standpoint for
digital and basic power distribution, there is a distance beyond which B
is so small as to be negligible. If we are dealing with a problem with
a lot of dynamic range we would not want to use that approximation.
This is why sometimes moating is a good thing.
I have attached an H field plot that may be helpful. For anyone who
cares, this is slide 10 from my 2005 SVCEMC meeting presentation. As
you can see, the current distribution concentrates around the ports sure
enough, but remains pretty intense in all of the area directly between
the capacitor and the test port, as well as substantially beyond.
Inductance yields frequency dependent impedance, so I am not sure what
additional effect you are looking for. If I had superconducting planes
separated by a loss less diectric, at low frequency I would have
essentially no impedance, whereas the dimensions of the features yield
an inductance, and therefore impedance at any higher frequencies.
Best Regards,
Steve.
At 03:03 PM 9/25/2006, Hill, John wrote:
>Steve,
>
>I am not comfortable with the idea of integrating around a circle.=20
>Could you describe the integration path?
>
>I expect the current will lump up in a line between the source (the
>capacitor) and the load (the chip). In the extreme, if the board was a=20
>mile wide, the current would not reach the edge. There is a limit where
>further width will not have an effect.
>
>The current path will spread out, but I am unsure of how wide it is=20
>going to spread perpendicular to the path of the current. I would also=20
>expect the width of the spreading to be dependant on frequency. But=20
>there is no dependence on frequency or dielectric constant in your=20
>equation. I don't understand how that can be true.
>
>Best regards,
>
>John
>
>-----Original Message-----
>From: steve weir [mailto:weirsi@xxxxxxxxxx]
>Sent: Monday, September 25, 2006 5:38 PM
>To: Hill, John; Sirisha.Godavarthy@xxxxxxxxxxxx;=20
>Tim.J.Nash@xxxxxxxxxxxxx; silist
>Subject: RE: [SI-LIST] Re: Spreading Inductance
>
>John we solve for inductance between two circular ports by performing=20
>integration of the incremental field intensity using the Law of Biot=20
>and Savart. That states that
>
>dB =3D uo*i/4pi * dl sin theta / r^2, magnitude only
>
>alternatively
>
>dB =3D u0i/4pi*dl x r / r^2 to obtain both direction and magnitude
>
>Integrate this formula and you get B. Since L =3D B/H, and we =
stipulate=20
>H, this gives us L.
>
>So, back to our planes. When we look at power delivery to an IC die,=20
>it is not at the end of a long skinny transmission line, it is inside=20
>the extents of the planes. Current density and hence B both rise as we
>approach the IC, and diminish as we move away. This is analagous to=20
>what happens with spreading resistance. In a planar structure we yield
>resistance per square.
>
>Best Regards,
>
>
>Steve.
>
>At 02:14 PM 9/25/2006, Hill, John wrote:
> >Steve,
> >
> >I understand that in a transmission line the inductance per unit=20
> >length and capacitance per unit length are related. As you know, the=20
> >equation
> >is:
> >
> >The relative permeability times the relative dielectric constant
>divided
> >by the speed of light squared is equal to the inductance per unit
>length
> >times the capacitance per unit length.
> >
> >I believe we can model the power planes as a transmission line=20
> >connecting the decoupling capacitor and the load (chip). Given a BC24
> >material with a Capacitance of 1 nF per inch (39 nF per meter) with a
> >dielectric constant of 4.5. I expect the inductance per unit length=20
> >to be 1.27 nF per meter (32.2 pH per inch)
> >
> >L=3D(4.5 * 1)/(c^2 * 39 nF per meter)
> >
> >The Zo would be 179 milliohms. Remember to terminate the transmission
> >line or it will show a low impedance resonance at a quarter=20
> >wavelength of electrical length.
> >
> >Now we still need to deal with the inductance of the connecting vias,
> >but I am planning on using an array of laser drilled micro vias.
> >
> >How did you derive the equation shown below for the L of
PLANE_CAVITY?
> >It does not contain the things that I would be looking for in such an
> >equation. It looks like the equation for the inductance of a via.
> >
> >So again I ask: Why are you using Ohms per Square?
> >
> >Best regards,
> >
> >John
> >
> >
> >
> >-----Original Message-----
> >From: steve weir [mailto:weirsi@xxxxxxxxxx]
> >Sent: Monday, September 25, 2006 11:46 AM
> >To: Hill, John; Sirisha.Godavarthy@xxxxxxxxxxxx;=20
> >Tim.J.Nash@xxxxxxxxxxxxx; silist
> >Subject: RE: [SI-LIST] Re: Spreading Inductance
> >
> >John, it is just English / Metric conversion:
> >
> >1.257E-6 H/m * 0.0254 m/inch =3D 31.92 H/inch
> >
> >Best Regards,
> >
> >
> >Steve.
> >At 08:27 AM 9/25/2006, Hill, John wrote:
> > >Steve,
> > >
> > >I was under the impression that the Permeability of free space was
>4PI
> > >times 10 to the -7. That is 1.257 X 10 to the -6 henrys per meter.
> > >
> > >This comes from the square of the speed of light being equal to one
> >over
> > >the permeability time the dielectric constant. The dielectric
>constant
> > >of free space being equal to 8.85 X 10 to the -12 farads per meter.
> > >
> > >Where does the per square come from?
> > >
> > >Best regards,
> > >
> > >John
> > >
> > >-----Original Message-----
> > >From: si-list-bounce@xxxxxxxxxxxxx
> >[mailto:si-list-bounce@xxxxxxxxxxxxx]
> > >On Behalf Of steve weir
> > >Sent: Monday, September 25, 2006 10:59 AM
> > >To: Hill, John; Sirisha.Godavarthy@xxxxxxxxxxxx;=20
> > >Tim.J.Nash@xxxxxxxxxxxxx; silist
> > >Subject: [SI-LIST] Re: Spreading Inductance
> > >
> > >John, this is the permeability of free space. It is an observed=20
> > >constant behavior.
> > >
> > >Best Regards,
> > >
> > >
> > >Steve.
> > >At 07:30 AM 9/25/2006, Hill, John wrote:
> > > >Steve,
> > > >
> > > >Where does the 31.9nH/Square come from?
> > > >
> > > >Best regards,
> > > >
> > > >John
> > > >
> > > >
> > > >
> > > >
> > > >---------------------------------------
> > > >The information in this email and attachments hereto may contain=20
> > > >legally privileged, proprietary or confidential information that=20
> > > >is intended for a particular recipient. If you are not the=20
> > > >intended recipient(s), or the employee or agent responsible for=20
> > > >delivery of this message to the intended recipient(s), you are=20
> > > >hereby notified that any disclosure, copying, distribution,=20
> > > >retention or use of the contents of this e-mail information is=20
> > > >prohibited and may be unlawful. When addressed to Takata=20
> > > >customers or vendors, any information contained in this e-mail is
> > > >subject to the terms and conditions in the governing contract, if
> > > >applicable. If you have received this communication in error,=20
> > > >please immediately notify us by return e-mail, permanently delete
> > > >any electronic copies of this communication and destroy any paper
copies.
> > > >---------------------------------------
> > > >-----Original Message-----
> > > >
> > > >From: si-list-bounce@xxxxxxxxxxxxx
> > >[mailto:si-list-bounce@xxxxxxxxxxxxx]
> > > >On Behalf Of steve weir
> > > >Sent: Tuesday, September 19, 2006 12:28 AM
> > > >To: Sirisha.Godavarthy@xxxxxxxxxxxx; Tim.J.Nash@xxxxxxxxxxxxx;
>silist
> > > >Subject: [SI-LIST] Re: Spreading Inductance
> > > >
> > > >Tim, those equations come from a presentation I made to the=20
> > > >SCVEMC January 2005. You can find the presentation in whole on=20
> > > >both the X2Y, and Teraspeed web
> > > >sites: =20
> > > >http://www.x2y.com/bypass/method/does_position_matter.pdf,
> > > >and http://www.teraspeed.com/publications.html Note that they
>apply
> > > >for specific circumstances of calculating spreading inductance=20
> > > >between a power ring, and a surrounding bypass capacitor ring.
>This
> > > >would also work for a single Vdd / Vss pair. However for more=20
> > > >complex pin arrays, you really need to solve the plane. Tools=20
> > > >from IBM, KAW, Ansoft, or Sigrity are all capable of that task.
> > > >
> > > >Steve.
> > > >At 05:57 AM 9/18/2006, Sirisha Godavarthy wrote:
> > > > >Hi Tim,
> > > > >I got some info regarding spreading inductance.
> > > > >Hope it helps.
> > > > >
> > > > >Plane spreading inductance:
> > > > >
> > > > >- L of PLANE_CAVITY =3D3D u0 / 2=3DF0 * H * (( ln( R2/R1 ) * =
KPERF=20
> > > > >)
>+
> > > > >ln( R3/R2 ))
> > > > >- u0 =3D3D 31.9nH/square
> > > > >- H =3D3D cavity height
> > > > >- R3 =3D3D radius from die center to bypass cap ring
> > > > >- R2 =3D3D radius from die center to via field edge
> > > > >- R1 =3D3D radius from die center to pkg power / ground
>attachments.
> > > > >- KPERF scaling factor for perforation in via field
> > > > >* For perforations small compared to wavelength area ratio
> > > > >
> > > > >Thanks&Regards,
> > > > >Sirisha.
> > > > >
> > > > >Thanks&Regards,
> > > > >Sirisha.
> > > > >=3D20
> > > > >
> > > > >-----Original Message-----
> > > > >From: si-list-bounce@xxxxxxxxxxxxx
> > > >[mailto:si-list-bounce@xxxxxxxxxxxxx] =3D
> > > > >On Behalf Of Nash, Tim J (EHCOE)
> > > > >Sent: Friday, September 15, 2006 7:56 PM
> > > > >To: silist
> > > > >Subject: [SI-LIST] Spreading Inductance
> > > > >
> > > > > From what I have gathered, spreading inductance of a plane is=20
> > > > >=3D dimensionless (i.e. nH/sq) and not a function of the =
distance
> > > > >between two
>points,
> >=3D
> > > > >rather a
> > > > >function of aspect ratio of the plane - L x W. So, the size of
>the
> >=3D
> > > > >plane
> > > > >isn't what affects spreading inductance, but its shape does. =20
> > > > >Are
> > >these
> > > >=3D
> > > > >true
> > > > >statements? I want to make sure I understand this correctly.
> > > > >Best Regards,
> > > > >Tim
> > > > >
> > > > >
> > > > >-- Binary/unsupported file stripped by Ecartis --
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> > > > >
> > > >
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