# [SI-LIST] Re: Loss tangent calculation

*From*: "Jian X. Zheng" <jian@xxxxxxxxxx>*To*: <rplantsprint@xxxxxxxxxxxxx>, <ashamim@xxxxxxxxxxxxxxx>,<si-list@xxxxxxxxxxxxx>*Date*: Thu, 3 Apr 2003 17:09:23 -0800

Hi: I think everything is from the Maxwell's equation: VxH = j*omega*epsilon*E + J, where "V" means the differential operator here. J = sigma*E Therefore, we have VxH = j*omega*epsilon*E+sigma*E = j*omega*epsilon_eff*E where epsilon_eff = epsilon ( 1 - j * sigma / ( omega * epsilon ) ) = epsilon * ( 1 - j * tanDelta ) Therefore, the loss tangent or tanDelta = sigma / ( omega * epsilon ) If sigma is a constant of frequency, then tanDelta is inverse proprotional to f. Thanks! ----------------------------------------------------------------------- Jian-X. Zheng, Ph.D Zeland Software, Inc., 48890 Milmont Drive, 105D, Fremont, CA 94538, U.S.A. Tel: 510-623-7162, Fax: 510-623-7135, Web: http://www.zeland.com --------------------------------------------------------------------- > -----Original Message----- > From: si-list-bounce@xxxxxxxxxxxxx > [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Robert Plant > 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 == (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 = [pi * f * qtand * tand * sqrt(eeff)] > ------------------------------------ > co > > where ad == dielectric loss constant (proportional to f ==> important!) > qtand == "filling factor" approximately 1 but different fo > non-homogenous materials > tand == loss tangent > eeff = effective relative permittivity. > co = 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 = [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 > > > -----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 = 300 ohm-cm (for silicon substrate ) > > I calculate it as follows: conductivity = 1/ resitivity > > Also loss tangent (Tan d)= conductivity / (epsilon * 2 *pi * f ) > where Epsilon (r) for silicon is 12 and f is 24 GHz.In this way I get > > Tan d = 0.25 > > 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 > 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: > http://www.freelists.org/webpage/si-list > > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > List archives are viewable at: > http://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: > http://www.freelists.org/webpage/si-list > > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > List archives are viewable at: > http://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: http://www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: http://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

**References**:**[SI-LIST] Re: Loss tangent calculation***From:*Robert Plant

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