RE: [SI-LIST] : the old high-frequency return current model

Eric Bogatin ([email protected])
Mon, 4 Oct 1999 09:54:11 -0500


A quick response about your comment on 2D field solvers-

You are correct in that some 2D field solvers just solve the electrostatic
equation (LaPlace's eq), and get the capacitance matrix. From this matrix,
and assuming that the transmission mode is TEM, they will use the fact that
the velocity of propagation is related to the effective dielectric constant
and the speed of light to get the inductance matrix. So, for these solvers,
the assumption is the current is only surface current and it is effectively
skin depth limited. The return currents do what ever they need to achieve
the TEM mode. The boundary element field solver from Hyperlynx, for example,
uses this approach.

Other field solvers, such as the Maxwell 2D Extractor, from Ansoft, will
solve LaPlace's equation to get the capacitance matrix elements, and
separately, Ampere's equation, to get the high frequency current
distribution, and then the magnetic fields, and then the inductance matrix
elements. The boundary condition it uses is that at high frequency, skin
depth is so small, there is no field inside the conductor and it behaves
like a perfect conductor, so the B field is only tangential at the surface,
no normal component. I have compared the two results- Hyperlynx's and
Ansoft's tool- and the agreement is within 2% across a wide range of aspect

In addition, the Ansoft tool, for example, will separately, if requested,
solve the Helmholtz equation (frequency domain solution for J and B) and
extract the current distribution inside the conductor (using FEM), at a
specified frequency. This will allow you to see the actual current
distribution inside the conductor, as frequency is varied. The plots I sent
around a few weeks ago were created using this tool. That's why the Ansoft
tool is often referred to as the "Rolls Royce of field solvers".

As with most things in life, not all 2D field solvers are created equal. Not
only that, but in some "extraction tools" on the market, they aren't even
field solvers, they are analytic approximations, with a very limited useful
range, but the vendors don't tell you that. They rely on the notion that if
you see three digits showing on the screen you will think the answer must be
accurate to three digits! In general, its caveat emptor- and I think we as
consumers of these tools, should be demanding of our vendors for full, open
and easily obtained disclosure of what is the engine behind the curtain, and
how have they confirmed the accuracy of their tool. This is one of the
topics I will be covering in my next two "No Myths Allowed" columns on


Eric Bogatin
Training for Signal Integrity and Interconnect Design
26235 W. 110th Terr.
Olathe, KS 66061
v: 913-393-1305
f: 913-393-1306
pager: 888-775-1138
e: [email protected]

> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of [email protected]
> Sent: Monday, October 04, 1999 8:06 AM
> To: [email protected]
> Subject: RE: [SI-LIST] : the old high-frequency return current model
> Thanks everybody for writing back. I'm hearing some common
> themes about return
> current distribution:
> 1) Inter-plane capacitance is the first source of ac return current.
> 2) "The shorter the rise time, the closer the via or de-cap."
> This suggests to
> me that the return current distribution vs. frequency is really a
> continuum from
> using the whole plane at dc to using a small swath under the
> trace at microwave
> frequencies. If this adage is true, then there still must be a
> significant
> amount of return current at one rise time away from a signal via
> at most of the
> frequencies we're interested in as signal integrity engineers.
> 3) 2D field solvers don't assume anything about return current.
> I guess if I
> had thought long enough, this should have been clear. A 2D field solver
> essentially solves an electrostatic problem for capacitance,
> often assuming an
> infinite plane, and then computes inductance using the
> telegraphers equations.
> The magnetostatic problem is never solved. Nevertheless, they
> still provide
> accurate solutions from a return current perspective.
> Greg Edlund
> Advisory Engineer, Critical Net Analysis
> 3650 Hwy. 52 N, Dept. HDC
> Rochester, MN 55901
> [email protected]
> ---------------------- Forwarded by Gregory R
> Edlund/Rochester/IBM on 10/04/99
> 07:53 AM ---------------------------
> "Ingraham, Andrew" <[email protected]> on 09/30/99 02:02:40 PM
> To: "'[email protected] '"
> <"IMCEAMAILTO-gedlund+40us+2Eibm+2Ecom">
> cc:
> Subject: RE: [SI-LIST] : the old high-frequency return current model
> Greg,
> Maybe the answer is that, even though the current distribution looks a lot
> different when the nearest decoupling cap is more than a few trace widths
> away, its effect on the impedance is just not that much to worry about?
> Kind of like the argument about using chamfered corners on trace bends.
> Yes, in theory you get an impedance discontinuity if you don't,
> but I think
> Ed Sayre says you'll never see it unless you operate well above 1GHz.
> If the cap is half an inch away from the via, that's around 80ps away. So
> unless the risetimes are of that order of magnitude or faster, then the
> discontinuity might be insignificant.
> But then at those kinds of speeds, our discrete capacitors are pretty much
> ineffective anyway. By that point we are relying on the intrinsic
> capacitance between layers. The higher you go in frequency, the
> better that
> intrinsic capacitance looks (and works).
> Regards,
> Andy Ingraham
> -----Original Message-----
> From: [email protected] [mailto:[email protected]]
> Sent: Thursday, 30 September, 1999 14:12
> To: [email protected]
> Subject: [SI-LIST] : the old high-frequency return current model
> Shoot! I was out of town and missed one of the most interesting
> discussions
> of
> the year! (Plane-jumping return currents) So at the risk of
> re-opening this
> thread, filling all your mailboxes again, and being branded an
> outcast, here
> goes. (Remember, that delete button is only a few inches away...)
> You're all familiar with this picture of high-frequency return current
> bunching
> up under the signal trace, right? According to the picture, it dies off
> pretty
> quickly as you move along the x-axis away from the trace. Well, I've been
> considering rules for the area density of ground vias and decoupling
> capacitors,
> and it occurs to me that if this picture were true, then the only
> place for
> a
> ground via or capacitor is within 2-3 trace widths of the signal via in
> question. (Which is, for most of our applications, absurd.)
> Otherwise I'd
> be
> forcing the return current out of that very tight loop, increasing the
> inductance, adding a discontinuity, generating plane noise, emissions, and
> all
> those nasty things. Now, I know that boards work quite well up to a few
> hundred
> MHz with considerably less than 100 de-caps per square inch! So
> where's the
> discrepancy? Is there a hole in my fairly simplistic,
> qualitative analysis?
> Or
> is this just like everything else: knowing how some parameter varies
> between
> the end cases is much harder than analyzing the end cases?
> On another tangent, I believe 2-D field solvers make the
> assumption that the
> return current is evenly distributed across the surface of a
> plane when you
> ask
> them to compute C, L and Z for a given cross-section. Doesn't this also
> conflict with the high-frequency current distribution picture?
> Eagerly awaiting your answers and hoping I have time to read them,
> Greg Edlund
> Advisory Engineer, Critical Net Analysis
> 3650 Hwy. 52 N, Dept. HDC
> Rochester, MN 55901
> [email protected]
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