[SI-LIST] Re: (no subject)
- From: "Scott McMorrow" <scott@xxxxxxxxxxxxx>
- Date: Wed, 11 Dec 2002 14:43:33 -0800
Justin,
The article which you reference concerns the issue of anisotropic
materials, that is, materials that have property differences in
different directions, due to non-uniformity of the material
construction. In this particular case, the author from Rogers is
discussing the variation of the material Er vs. the direction in which
the direction is measured. Of course this is the case for FR4, since
there are strong directional components due to the glass fiber bundles.
Rogers materials are designed to minimize these directional components,
and thus have a much flatter response. However, even accounting for
anisotropy, as the Rogers white paper does, we cannot escape the fact
that the Rogers measurements show a variation in Er across frequency,
even in the same direction of measurement. You will also note that they
show a variation in loss tangent across frequency.
It is shown in the paper "Physically Consistent Transmission Line Models
for High-Speed Interconnectos in Lossy Dielectrics", Karen Coperich
Branch, et al, IEEE Transactions on Advanced Packaging, Vol 25, No 2,
May 2002, that in order to guarantee causality of the electric field in
a dielectric across frequency, the modeling of loss tangent and the
dielectric permitivity cannot be constant. They must vary with frequency.
For engineered materials that are near-homogeneous and non-anisotropic,
and have extremely low losses, Er and loss tangent can for all practical
purposes be considered to be constant. Pure air and some PTFE and
ceramic based dielectrics can be reasonably well modeled with this
assumption. However, this is an assumption and results in an
approximation which has some amount of error. For extremely low loss
materials, this assumption is quite acceptable. For materials with
significant loss, like FR4, a more physically consistant model must be
used to insure causality in the response. In Microwave engineering,
models that satisfy the Kramers-Kronig relation are used, such as the
Debye model. The Debye model was originally developed in the area of
studies of the relaxation of crystal lattices. It turns out that the
physical mechanism of loss is quite similar to the mechanics and physics
of these lattice structures. There are also other models of dielectric
permitivity and loss that are also physically consistent. All of them
require what we call loss tangent and permitivity (which gives rise to
Er) to vary somewhat across frequency. The only materials that have
constant Er are ideal materials. Unfortunately, I don't seem many of
those in this line of work.
I must state that I am certainly not an expert in these matters. I am
only quoting what I have learned from the true experts. Others can
expound much more knowledgably than I on the theoretical foundations.
I'm just a practical engineer that has learned a bit through the
experiences of others. In reality, manufacturing tolerances and
non-uniformity of materials causes much larger variations in actual
transmission line performance than the change in Er across frequency.
However, that does not mean that it does not exist.
best regards,
scott
--
Scott McMorrow
Grand Poobah, Waterbuffalo Lodge Chapter
Teraspeed Consulting Group LLC
2926 SE Yamhill St.
Portland, OR 97214
(503) 239-5536
http://www.teraspeed.com
Tabatchnick, Justin wrote:
>Hi Steve and Scott;
>
>Steve - you have to look at the other side of the equation C=3Dlamda =
>times frequency, dividing both sides by the sqrt of the dielectric =
>constant gives reduction in wavelength , which yields are reduction in =
>velocity.
>
>Scott- I will read the article however I have a feeling that dielectric =
>dependance on frequency has more to do with manufacturing flaws in the =
>substrate - if you are talking about pure dielectrics I still maintain =
>that the dielectric constant is not frequency dependent - check out this =
>link http://www.rogerscorporation.com/mwu/pdf/rt2121.pdf
>
>Justin
>
>PS we only use FR4 for power and groud layers , never for HF because of =
>it's high loss
>
>-----Original Message-----
>From: Steve Corey [mailto:steven.corey@xxxxxxxxxxxxxx]
>Sent: Wednesday, December 11, 2002 11:37 AM
>Cc: si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: (no subject)
>
>
>
>Or perhaps take this approach, since as the modeling guy I always resort =
>
>to equations:
>
>v =3D c/sqrt(er)
>
>v is the velocity of the wave, c is the speed of light in a vacuum, and=20
>we assume that the relative permeability is unity for simplicity.
>
>Now, if we have already settled that v can vary with frequency, and=20
>hopefully we can agree that c doesn not vary with frequency, that leaves =
>
>only er to vary with frequency. If er is constant, so is v.
>
>If this doesn't seem authoritative enough, consult any undergraduate=20
>physics book or electromagnetics book published over the past 100 years. =
>
> It will tell you that er varies with frequency. I find it a good=20
>practice to consult such books prior to posting, since half the time the =
>
>person who wrote the book is lurking on this list.
>
> -- Steve
>
>
>Scott McMorrow wrote:
>
>
>
>>Justin,
>>=20
>>You are just plain wrong here about FR4. It is a highly non-linear=20
>>material that does have significant changes in Er across frequency =
>>
>>
>that=20
>
>
>>have been characterized in the peer reviewed engineering literature =
>>
>>
>for=20
>
>
>>at least 20 years. Dielectric losses and changes in Er are linked by=20
>>causality as Steve Corey wrote a few days ago, and has been well=20
>>discussed in the professional and academic journals. The latest issue =
>>
>>
>
>
>
>>of IEEE Transactions on Advanced Packaging, which includes papers from =
>>
>>
>
>
>
>>last years EPEP, has several papers on just this subject.
>>=20
>>For FR-4, non-uniform dielectric properties throughout the material =
>>
>>
>tend=20
>
>
>>mask the effects of frequency dependent Er (or velocity of =
>>
>>
>propagation)=20
>
>
>>changes. (i.e. - you get more impedance variation due to material=20
>>variation than due to Er changes across frequency.) For low loss=20
>>materials, such as Real Air, the dielectric loss and Er does change,=20
>>based upon the relative humidity. Pure air, however, does have a =
>>
>>
>flat=20
>
>
>>frequency response and extremely low losses.
>>=20
>>As for broadband, just launch a gaussian pulse down a microstrip or=20
>>stripline trace on an FR4 substrate and see what you receive at the =
>>
>>
>far=20
>
>
>>end. After you subtract out the effects of variable skin depth=20
>>penetration at different frequency (due to the finite conductivity of=20
>>the conductor) you will find that there is still pulse distortion due =
>>
>>
>to=20
>
>
>>Er variation.
>>=20
>>Finally, I would refer you to the material data sheets for many=20
>>different vendors versions of FR4, where you will find that the =
>>
>>
>measured=20
>
>
>>Er does truly vary with frequncy, tending to lower at the higher=20
>>frequencies. Since the velocity of propagation of an electromagnetic=20
>>wave in a dielectric media is proportional to the square root of the =
>>
>>
>Er,=20
>
>
>>I would expect an accompanying dispersion of any broadband signal =
>>
>>
>across=20
>
>
>>the entire frequency band, with an accompanying change in Impedance.
>>=20
>>regards,
>>=20
>>scott
>>=20
>>=20
>>
>>
>
>
>--=20
>-------------------------------------------
>Steven D. Corey, Ph.D.
>Time Domain Analysis Systems, Inc.
>"The Interconnect Modeling Company."
>http://www.tdasystems.com
>
>email: steven.corey@xxxxxxxxxxxxxx
>phone: (503) 246-2272
>fax: (503) 246-2282
>-------------------------------------------
>
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--
Scott McMorrow
Teraspeed Consulting Group LLC
2926 SE Yamhill St.
Portland, OR 97214
(503) 239-5536
http://www.teraspeed.com
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