# [SI-LIST] Re: Loss tangent calculation

• From: "Robert Plant" <rplantsprint@xxxxxxxxxxxxx>
• To: <ashamim@xxxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
• Date: Thu, 3 Apr 2003 16:28:41 -0800

```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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