[SI-LIST] Re: Via Inductance Formula Assumptions
- From: "Mike Degerstrom" <degers@xxxxxxxxxxxxxxxxxxxx>
- To: "Moeller, Merrick" <mmoeller@xxxxxxxxxxxxxxx>
- Date: Thu, 28 Aug 2003 12:21:50 -0500
Merrick,
One potential problem with the via inductance formulas is that I assume they
do not account for the return path between vias - which in this case the
return path is probably comprised of ground plane paths.
Also you should short your probe by touching down on an area of metal on your
board then subtract that inductance from your total inductance. Maybe you've
done this already as part of your equipment calibration?
Mike
On Thu August 28 2003 11:40 am, Moeller, Merrick wrote:
> Below is a portion of the thread in the archives.
> If you read through you will find that the assumption
> made by Johnson give a return path at 5.43*H. This is
> much more than my return path, but the results from
> this formula seem to match my measurements (approx 1.2nh).
> At the very end the formula using the "-1" assumes a return path at .735*H
> which is just about exactly where my return vias are located at a 1.12mm
> pitch on a .062" board. This
> equation however gives a seemingly low value (approx .313nh).
> I made the measurements using 2 450um pitch Picoprobes across the top of
> two vias surrounded by 10 others shorted together on the top and bottom of
> the board. The 2 vias of concern have
> pads and antipads, but are shorted to the rest of the vias on the
> bottom of the board to make the inductance measurement.
>
> g g g
> g s g
> g s g
> g g g
>
> I am not sure what to make of the data that I am getting in
> the measurements, as far as being the correct technique. A more
> accurate assumption may clear my mind.
>
> Regards,
> Merrick
>
> -----------------------------------------------------------------
>
>
> Dear Itzhak Hirshtal and Brian Young,
>
>
> The difficulties with approximating the inductance
> of a via are even worse than you
> may have suspected. Both approximations are flawed whether
> you use +1 or -3/4, (or, as I have also seen, -1).
>
>
> The issue of the exact constant (1, -3/4, or something
> else) depends critically on your assumption about
> the path of returning signal current. (Current always
> makes a loop; when signal current traverses the via,
> a returning signal current flows SOMEWHERE in
> the opposite direction.). It is a principle
> of Maxwell's equations that high-speed returning signal
> current will flow in whatever path produces the
> least overall inductance.
>
>
> Let's do an example involving a signal via that
> dives down through a thick, multi-layer board.
> If the signal in question changes reference
> planes as it traverses the via,
> then the returning signal current will also have to
> change planes, meaning that the returning signal
> current will flow through one or more vias (often
> leading to bypass capacitors) as it moves from
> plane to plane. For example, if the signal starts
> out on the top layer, the returning signal current
> is flowing on the nearest reference plane (call it
> layer 2). If the via conducts the signal current
> down to the bottom layer (16), then the returning
> signal current at that point must be flowing on
> the nearest (bottom-most) reference plane, call it 15.
> Somehow the returning signal current has to hop from
> reference plane 2 to reference plane 15 in the
> vicinity of the via.
>
>
> If you examine the space between the planes, the
> magnetic fields within are created partly by
> the signal current, and in equal measure (but in
> differnt locations) by the returniing signal
> current, which flows on different vias. The
> total magnetic flux between the outgoing and
> returning vias defines the inductance.
> Specifically, to calculate the effective
> inductance of via (A), you must first specify the
> location of the return path, via (B), and then
> calculate the total magnetic flux in the area
> between the two vias. The total magnetic flux
> generated by a signal current of one amp, in units
> of webers, equals the inductance.
> In the case of more complex return-path
> configurations, other considerations apply.
> I think at this point that the following
> formulii for the effective series inductance
> of a via are pretty good:
>
>
> For a signal which pops from one side of the
> plane, through a via, to the opposite side
> of the same plane (i.e., the return current
> doesn't have to jump planes), the via
> inductance is very, very low. This is a best-case
> scenario. I don't know a good way to make this
> calculation except with a true 3-D E&M field solver.
>
>
> For a signal which first uses reference-plane A,
> and then changes (through a via) to use
> reference-plane B, I'll do several examples. In
> all cases the separation between reference planes
> is H. (It doesn't matter if there are other
> unused reference planes in the way, only the
> spacing between the two reference planes A and B
> matter).
>
>
> If the return current is carried mainly on one nearby
> via, where the spacing from signal via to return via
> is S and the via diameter is D:
>
>
> L = 5.08*H*(2*ln(2*S/D)) [1]
>
>
> If the return current is carried mainly on two vias
> equally spaced on either side of the signal via,
> where the spacing from signal via to either return via
> is S and the via diameter is D:
>
>
> L = 5.08*H*(1.5*ln(2*S/D) + 0.5*ln(2)) [2]
>
>
>
> If the return current is carried mainly on four vias
> equally spaced in a square pattern on four sides
> of the signal via, where the spacing from signal via
> to any return via is S and the via diameter is D:
>
>
> L = 5.08*H*(1.25*ln(2*S/D) + 0.25*ln(2)) [3]
>
>
> If the return current is carried mainly on a
> coaxial return path completely encircling the signal
> via, where the spacing from signal via
> to the return path is S and the via diameter is D:
>
>
> L = 5.08*H*(ln(2*S/D)) [4]
>
>
> The last formula I hope you will recognize as the
> inductance of a short section of coaxial cable with
> length H and outer diameter 2*S. I hope this
> recognition will lend credence to the idea that
> the position of the returning current path is
> an important variable in the problem.
>
>
> My earlier formula was a gross approximation which
> ignored the position of the returning current path,
> and omission which I greatly regret. It made the
> crude assumption that the return path was approximately
> coaxial and located at a distance S=5.43*H. As you
> note, when the inductance really matters a
> more accurate approximation is needed.
>
>
> To obtain a result as low as 5.08*H*(ln(2*S/D)-1)
> you would have to assume the return path were coaxial
> and located at a ridiculously small separation of
> S=.735*H, or that the return path were a single via
> located at some even closer distance.
>
>
> On my web site http://signalintegrity.com under "articles"
> there is a write-up about calculating the inductance of
> a bypass capacitor that includes the above formulas for
> vias, as well as some handy ways to estimate the
> inductance of the capacitor body.
>
>
> By the way, if you find a flaw in THIS write-up,
> please let me know.
>
>
> Best regards,
> Dr. Howard Johnson
> -----------------------------------------------------------------
>
>
> -----Original Message-----
> From: Mike Degerstrom [mailto:degers@xxxxxxxxxxxxxxxxxxxx]
> Sent: Thursday, August 28, 2003 9:05 AM
> To: Moeller, Merrick
> Subject: Re: [SI-LIST] Via Inductance Formula Assumptions
>
>
> Merrick,
>
> Try,
>
> http://www.qsl.net/wb6tpu/si-list/index.html
>
> and look for the thread on 'partial inductances'.
>
> It will take you a while to read and sort out all the related posts but as
> I recall it was quite informational.
>
> Mike
>
> On Thu August 28 2003 8:52 am, you wrote:
> > Do you have a link for the archives?
> >
> > -----Original Message-----
> > From: Mike Degerstrom [mailto:degers@xxxxxxxxxxxxxxxxxxxx]
> > Sent: Wednesday, August 27, 2003 4:50 PM
> > To: Moeller, Merrick; Si-List (E-mail)
> > Subject: Re: [SI-LIST] Via Inductance Formula Assumptions
> >
> >
> > Merrick,
> >
> > This topic was covered quite extensively - I think about 2 years ago. I
> > believe that Dr. Johnson also replied and cleared things up quite well.
> > Possibly I'm thinking of via capacitance instead of inductance - but
> > perhaps you should visit the archives.
> >
> > Mike
> >
> > On Wed August 27 2003 3:47 pm, Moeller, Merrick wrote:
> > > What assumptions are made with Dr. Howard Johnson's via
> > > inductance approximaiton:
> > > L=5.08h (ln(4h/d) + 1)
> > >
> > > Where is the return path located? Does this apply to an
> > > an array of vias?
> > >
> > > Merrick M. Moeller
> > >
> > >
> > >
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--
Mike Degerstrom email: degers@xxxxxxxxxxxxxxxxxxxx
Advanced Signal Integrity Design, LLC http://www.advancedsidesign.com
Phone: 507-289-2900 Fax: 507-280-0052 Cell Phone: 507-254-4448
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