[SI-LIST] Re: Loss tangent calculation
- From: andrew.c.byers@xxxxxxxxxxxxxx
- To: justin.tabatchnick@xxxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Thu, 3 Apr 2003 16:44:14 -0800
Hello Atif and Justin and SIers,
Justin's equation below points out the fact that tand is separated
into two terms - one that deals with the conductivity of the material and
one that deals with another lossy dielectric property.
When I originally saw Atif's email and his question about tand
increasing proportional to frequency, I was a bit surprised. I had always
seen tand for dielectrics as relatively stable with frequency. However, in
silicon you will have a non-zero conductivity of the material (ie free
charge carriers), and there will be this steadily increasing portion of the
tand = sigma/(eps*omega).
For most classic dielectric materials, ranging from FR4 to SiO2,
sigma is essentially ZERO and you will usually only consider the second term
in the equation below, which has to do with a different dielectric material
loss property. (see Robert Plant's email). This term of tand tends to remain
more constant within frequency ranges of interest (as seen in
measurements). In reality it does begin to increase a bit as frequency
increases, due to changes in permittivity, but that is a different thread. I
believe that the "dielectric loss constant" referred to below has to do with
the energy dissipated (as heat) due to the vibrations/rotations of the
dipoles in the material - the bound charges. Waxing material physics here -
will have to dust off that textbook or look at material charts.
Back to Atif's narrow band case, it may turn out that the
conductivity term in the tand equation dominates in silicon, especially at
24GHz, and the other term can be ignored. With you calculation of tand=0.25
(gulp), I think this is true. You would have to hunt down equations or
measured data for the second term and see. A relevant point here, though, is
how much of your field is actually located in the silicon? You have your
antenna sitting on another dielectric above the silicon too - the tand here
will most likely be dominated by the second term in the equation (which for
SiO2 is nearly zero).
Great topic though! Hope this helps,
Andy Byers
-----Original Message-----
From: Tabatchnick, Justin [mailto:justin.tabatchnick@xxxxxxxxx]
Sent: Thursday, April 03, 2003 4:38 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Loss tangent calculation
er" is called the dielectric loss constant - not to be confused with
loss tangent which is e"/e'
Justin
-----Original Message-----
From: Robert Plant [mailto:rplantsprint@xxxxxxxxxxxxx]=20
Sent: Thursday, April 03, 2003 4:29 PM
To: ashamim@xxxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Loss tangent calculation
According to Wadell's venerable book "Transmission Line Design Handbook"
(page 21), the precise definition of loss tangent is:
tand =3D=3D (er") / (er')
where er' is the real part of er (relative permittivity) and
er" is the imaginary part of er...normally we just pay attention
to er' because er" is small.
THEN(!): on page 27 the loss factor (what we're all really interested
in anyway!) is given by:
ad =3D [pi * f * qtand * tand * sqrt(eeff)]
------------------------------------
co
where ad =3D=3D dielectric loss constant (proportional to f =3D=3D> =
important!)
qtand =3D=3D "filling factor" approximately 1 but different fo=20
non-homogenous materials
tand =3D=3D loss tangent
eeff =3D effective relative permittivity.
co =3D speed of light in a vacuum.
What Wadell doesn't say but you might be able to approximate is:
qtand ~ 1 (assume the material is approximately homogenous)
eeff ~ er (same assumption)
ad =3D [pi * f * tand * sqrt(er)]
--------------------------
co
I think those are the operative equations you want to use.
As far as determining tand, the only way I know how to do this is to
either
calculate the loss factor and do a reverse calculation of tand
or else look up on the web or in a book for the material in question.
There's no other way I'm aware of.
Good luck,
Drew Plant
=20
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of atifshamimkhan
Sent: Thursday, April 03, 2003 11:58 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Loss tangent calculation
Hi
I am designing an antenna on Si substrate at 24 GHz.I want to
calculate the Loss tangent for this substrate .I have the following
info
Resistivity =3D 300 ohm-cm (for silicon substrate )
I calculate it as follows: conductivity =3D 1/ resitivity
Also loss tangent (Tan d)=3D conductivity / (epsilon * 2 *pi * f )
where Epsilon (r) for silicon is 12 and f is 24 GHz.In this way I get
=20
Tan d =3D 0.25=20
I dont know whether this calculation is right or not.My question is if
this is not the right way then how can I calculate the Loss tangent
from resistivity only and secondly if this is right then why the loss
tangent decreases with the increase in fequency.
Thanks=20
Atif
------------------------------------------------------------------
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 archives are viewable at: =20
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages=20
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
=20
------------------------------------------------------------------
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 archives are viewable at: =20
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages=20
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
=20
------------------------------------------------------------------
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 archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
------------------------------------------------------------------
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 archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
Other related posts:
