## [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
>
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