[SI-LIST] Re: Via stub math help needed....
- From: "Lambert Simonovich" <bertsimonovich@xxxxxxxxxx>
- To: "'Scott McMorrow'" <scott@xxxxxxxxxxxxx>, "'Eric Bogatin'" <eric@xxxxxxxxxxxxxxx>
- Date: Fri, 13 Jan 2012 22:27:55 -0500
Scott,
According to Wadell -Ref.[1], effective Dk is the ratio of the actual
structure's capacitance to the capacitance when the dielectric is replaced
by air.
Dk_eff = C_actual/C_air.
It is used whenever there are several dielectrics or when Dk varies with
position within the dielectric.
In the three cases you identified below, the capacitance per unit length is
determined by two different dielectric constants. What ever the capacitance
per unit length turns out to be, when you divide by capacitance per unit
length, as if the surrounding material was air, you get Dk_eff.
I see no difference in our definition. The distributed excess capacitance
due to the non TEM fields to the planes as the vias pass through the
anti-pads results in an increase of capacitance per unit length, C_actual,
which by definition above, means an increase in Dk_eff.
Regards,
-Bert
Reference:
[1] Brian C Wadell, Transmission Line Design Handbook, Artech House, Inc.,
ISBN 0-89006-436-9, 1991.
-------------------------------------------------------
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LAMSIM Enterprises Inc.
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-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Scott McMorrow
Sent: January-13-12 9:47 AM
To: Eric Bogatin
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Via stub math help needed....
Eric
I do not like the term "effective Dk" in this context.
Effective dielectric constant is generally used to describe quasi-TEM
layered dielectrics.
- Microstrip
- inhomogeneous stripline
- coplanar waveguide
Effective Dk is a rather imprecise term for loaded interconnect. For
example, a multidrop bus is often described as having an "effective Dk".
It doesn't. Dk does not change anywhere in the interconnect. Neither the
through traces, or the stub traces, or receiver capacitance does anything to
alter dielectric constant of the underlying material or the instantaneous
wave propagation through those sections. We can speak of "loaded delay" of
"loaded impedance", but as I look in Pozar I see no reference to Effective
Dk when he discusses periodic structures.
Call the phenomena "correction factor for physical stuff that happens around
a via", but not Effective Dk.
Scott
On Fri, Jan 13, 2012 at 7:13 AM, Eric Bogatin <eric@xxxxxxxxxxxxxxx> wrote:
> Scott-
>
>
> I thought I would chime in on the question of the higher Dk for vias.
> I learned a lot about vias working on a project with Bert a few years
> back and continue to learn more every time I look at them, so I always
> appreciate your comments and others on this topic.
>
>
>
> I think the first question is, is there a higher propagation delay
> through a via, if you take as its start and finish the top and bottom
> pad region where the transmission line feed hits the annulus clearance
> hole?
>
>
>
> It's really hard to measure directly, but easy to simulate in many 3D
> tools. I find that when you keep the stack height fixed, by just
> changing the clearance holes, NFPs and other physical features inside
> the via pad stack, you can get a variety of propagation delays, as
> extracted from the phase of S21.
>
>
>
> I have to say that I did not use generalized modal S-parameters,
> however, this higher delay is seen even when the return loss is less
> than -25 dB, where you would not expect a phase distortion from
> reflections.
>
>
>
> I interpret this higher delay as a higher "effective Dk". I don't
> think the intrinsic material properties have changed, nor is there an
> issue of the anisotropic effects of the Dk from glass weave. I think
> this has been shown to be only on the order of ~ 20% at most.
>
>
>
> As an aid in describing the via propagation delay, I interpret the
> extra delay as a higher Dk. In some multi layer via structures, I
> extract a Dk_eff as high as 16, if there are NFPs.
> You see this clearly in the lower stub resonance frequencies.
>
>
>
> Why does the prop delay increase thru a via? I think it is due to the
> non TEM fields. In a TEM propagation, I think we all agree that the
> delay is due to the physical length and the bulk Dk.
>
>
>
> In a non TEM propagation, I think all bets are off. The speed of the
> signal will depend a lot on the shape of the fringe fields.
> The more non-TEM, as you get with all those fringe fields from the
> barrel and pads to the planes, the more different the speed is from
> the bulk Dk.
>
>
>
> I think the confusion is over the use of the term Dk. It may be less
> confusing thinking of this as an effective Dk, useful to predict the
> prop delay based on the physical length.
>
>
>
> I can model many complex via structures as uniform transmission lines
> up to the 10 GHz range, using a Z0, the physical length and the
> Dk_eff. This helps in estimating the stub resonances.
>
>
>
> What do you all think?
>
>
>
> --eric
>
>
>
>
>
>
>
> *******************************************************
> Dr. Eric Bogatin, Signal Integrity Evangelist Bogatin Enterprises
> Setting the Standard for Signal Integrity Training web site:
> www.beTheSignal.com <http://www.bethesignal.com/>
>
> beTheSignal Blog: www.beTheSignal.com/blog
> 26235 W 110th Terr
> Olathe, KS 66061
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>
> for class information: email to beTheSignal@xxxxxxxxxx
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> ***********************************************
>
>
>
> Msg: #1 in digest
>
> Date: Thu, 12 Jan 2012 16:41:44 -0500
>
> Subject: [SI-LIST] Re: Via stub math help needed....
>
> From: Scott McMorrow <scott@xxxxxxxxxxxxx>
>
>
>
> Bert and Ralph
>
> There are layered-anisotropic variations in Er for many materials,
>
> especially those that include fiberglass weave. However, Er does not
>
> change with non-TEM modes or different TEM modes (stripline,
> via-coaxial,
>
> circular cavity ... etc). Different propagation modes merely
> concentrate
>
> the field in different directions and select a different set of
> localized
>
> material characteristics.
>
>
>
> I've read the papers and seen the claim that the dielectric constant
> of
>
> layered fiberglass material is higher for propagation through a via,
> due to
>
> the direction of the field, however, I've not seen a systematic study
> of
>
> this. (Adjustment of material Er(effective) to obtain a match to
> modeling
>
> does not constitute proof.) My experience for launch vias with
> coaxial
>
> ground rings has been that the resonance computed by full wave solvers
>
> matches measurements quite well in a multitude of materials, if the
>
> dielectric has been characterized correctly. I find that most of the
>
> mis-correlations that I've seen are due to improper material
>
> characterization. I do not discount the possibility of a higher
> localized
>
> Er region around a via in some measurements, its just that I find
> little
>
> evidence for fiberglass being the sole culprit. In many cases I've
> found
>
> that mismatch in stub resonance could be easily accounted for by
> adding the
>
> correct amount of soldermask to the bottom pad in modeling. In other
> cases
>
> I've found that material variations between layers were not correctly
>
> modeled.
>
>
>
> As a thought experiment, take a section of a PCB with a via along the
>
> z-axis that is fully surrounded by a coaxial metal wall.
> Calculate the
>
> average Er from top to bottom, and then calculate it radially out.
> The
>
> volume of material is the same. The composition of the material is
> the
>
> same. Thus the average Er is the same. The only way to come up with
> a
>
> higher Er for the radial direction is to conclude that somehow the
>
> drilling process selectively removes more epoxy than fiberglass from
> the
>
> mixture. There are layered variations as we travel down the via
> passing
>
> through fiberglass rich, and then epoxy rich layers. But I see no
> reason
>
> why they would not average out. I can make a case that individual
> pairs of
>
> signal and ground vias can have Er variation, just as I can for
> traces, but
>
> I cannot come up with any reason why the Er would not average out in
> the
>
> limit.
>
>
>
> There is one other potential reason why a via could have a higher
> localized
>
> average Er. But it has nothing to do with the fiberglass itself.
> I will
>
> probably use it as a topic for next year's DesignCon paper, as a
> follow up
>
> to the paper I'm involved with this year.
>
>
>
>
>
> regards,
>
>
>
> Scott
>
>
>
>
>
>
>
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--
Scott McMorrow
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