Jim, for a transmission line over a plane, the image in the plane drops off like that. But for parallel plates of like size the distribution is quite different. Regards, Steve At 04:33 AM 9/26/2006, Peterson, James F \(EHCOE\) wrote: >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. > >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 > >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 > >going to spread perpendicular to the path of the current. I would also > >expect the width of the spreading to be dependant on frequency. But > >there is no dependence on frequency or dielectric constant in your > >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; > >Tim.J.Nash@xxxxxxxxxxxxx; silist > >Subject: RE: [SI-LIST] Re: Spreading Inductance > > > >John we solve for inductance between two circular ports by performing > >integration of the incremental field intensity using the Law of Biot > >and Savart. That states that > > > >dB = uo*i/4pi * dl sin theta / r^2, magnitude only > > > >alternatively > > > >dB = u0i/4pi*dl x r / r^2 to obtain both direction and magnitude > > > >Integrate this formula and you get B. Since L = B/H, and we stipulate > >H, this gives us L. > > > >So, back to our planes. When we look at power delivery to an IC die, > >it is not at the end of a long skinny transmission line, it is inside > >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 > >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 > > >length and capacitance per unit length are related. As you know, the > > >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 > > >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 > > >to be 1.27 nF per meter (32.2 pH per inch) > > > > > >L=(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 > > >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; > > >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 = 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; > > > >Tim.J.Nash@xxxxxxxxxxxxx; silist > > > >Subject: [SI-LIST] Re: Spreading Inductance > > > > > > > >John, this is the permeability of free space. It is an observed > > > >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 > > > > >legally privileged, proprietary or confidential information that > > > > >is intended for a particular recipient. If you are not the > > > > >intended recipient(s), or the employee or agent responsible for > > > > >delivery of this message to the intended recipient(s), you are > > > > >hereby notified that any disclosure, copying, distribution, > > > > >retention or use of the contents of this e-mail information is > > > > >prohibited and may be unlawful. When addressed to Takata > > > > >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, > > > > >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 > > > > >SCVEMC January 2005. You can find the presentation in whole on > > > > >both the X2Y, and Teraspeed web > > > > >sites: > > > > >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 > > > > >between a power ring, and a surrounding bypass capacitor ring. > >This > > > > >would also work for a single Vdd / Vss pair. However for more > > > > >complex pin arrays, you really need to solve the plane. Tools > > > > >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 =3D u0 / 2=F0 * H * (( ln( R2/R1 ) * KPERF > > > > > >) > >+ > > > > > >ln( R3/R2 )) > > > > > >- u0 =3D 31.9nH/square > > > > > >- H =3D cavity height > > > > > >- R3 =3D radius from die center to bypass cap ring > > > > > >- R2 =3D radius from die center to via field edge > > > > > >- R1 =3D 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. > > > > > >=20 > > > > > > > > > > > >-----Original Message----- > > > > > >From: si-list-bounce@xxxxxxxxxxxxx > > > > >[mailto:si-list-bounce@xxxxxxxxxxxxx] = > > > > > >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 > > > > > >= dimensionless (i.e. nH/sq) and not a function of the distance > > > > > > >between two > >points, > > >= > > > > > >rather a > > > > > >function of aspect ratio of the plane - L x W. So, the size of > >the > > >= > > > > > >plane > > > > > >isn't what affects spreading inductance, but its shape does. > > > > > >Are > > > >these > > > > >= > > > > > >true > > > > > >statements? I want to make sure I understand this correctly. > > > > > >Best Regards, > > > > > >Tim > > > > > > > > > > > > > > > > > >-- Binary/unsupported file stripped by Ecartis -- > > > > > >-- Type: application/x-pkcs7-signature > > > > > >-- File: smime.p7s > > > > > > > > > > > > > > > > > > > >------------------------------------------------------------------ > > > > > >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 FAQ wiki page is located at: > > > > > > http://si-list.org/wiki/wiki.pl?Si-List_FAQ > > > > > > > > > > > >List technical documents are available at: > > > > > > http://www.si-list.org > > > > > > > > > > > >List archives are viewable at: =20 > > > > 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