[SI-LIST] Re: what is the conductivity of a dielectric?
- From: RayCaliendo@xxxxxxxxxx
- To: rob@xxxxxxxxxx
- Date: Wed, 10 Apr 2002 16:24:18 -0700
Rob et. al.,
I believe the word 'conductivity' (sigma) should be used for a
conductor, while the movement of charge in a dielectric is the 'Displacement
current' (D = eE), which, if I understand it correctly, behaves "like" a
conduction current. Also, It looks to me that the units of some of the
equations' here don't seem to balance. What have I missed? I found some
other explanations for loss tangent :
- Tan(delta) = er'' / er'
- Howard Johnson article "Dielectric Loss Tangents"
Theta = Im(Capacitance) / Re (Capacitance)
- Tan(delta) = Resistance / Reactance (parallel equivalent
circuit)
Regards,
Ray Caliendo
Solectron Corp
(408)956-6294
> ----------
> From: Rob Hinz[SMTP:rob@xxxxxxxxxx]
> Reply To: rob@xxxxxxxxxx
> Sent: Tuesday, April 09, 2002 2:29 PM
> To: Patrick_Carrier@xxxxxxxx
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: what is the conductivity of a dielectric?
>
>
>
> Patrick,
>
> The definition of loss tangent, tan(delta) is:
>
> tan(delta) = (we'' + cond)/(we')
>
> Where:
>
> w = 2*pi*freq
> e' = eo*er (dielectric constant real part) This is the one we are used to
> seeing...
> e'' = imaginary (and therefore loss generating) part of the dielectric
> constant
> cond = electrical conductivity of the material.
>
> Thus, in general, the dielectric constant is expressed as a complex number
> as:
>
> e = e'-je''
>
> Now to your question, if you assume that the dielectric is otherwise
> lossless, that is, e''=0, then conductivity is:
>
> cond = tan(delta)*2*pi*freq*eo*er.
>
> So I would agree with the equation you propose except that it is missing a
>
> key term eo=8.854e-12. The should correct the scale problem you are
> noting...
>
> cond = .02*2*pi*100e6*8.854e-12*4 = 4.5e-4 S/m
>
> On background, the loss tangent equation is easily understood from first
> principles. If you recall the relationship between Electric flux (D) and
> Electric field (E) in free space:
>
> D = eo*E;
>
> the addition of a material to the space causes a polarization of the
> molecules of that material resulting in additional electric flux that can
> be represented as a polarization vector as:
>
> D = eo*E + Pe (the same can be said of the magnetic field, for that, Pm
>
> is used)
>
> Pe is consequence of the applied E field and for linear materials,
> (generally true for the material we use in SI work), Pe = eo*Xe*E. Xe is
> the relative electric susceptibility of the material. In general, it may
> be
> complex resulting in the following:
>
> D = eo*E + Pe = eo*(1+Xe)*E = eo*er*E = e*E
>
> e = eo*(1+Xe) = e'-je''
>
> The complex part accounts for damping effects on the polarizing dipole
> vibrations. Like a finite Q tank circuit or a spring and dash pot, this
> loss is generally in the form of heat. You might ask why -je'' and not
> +je''? This is because choosing +je'' would violate the conservation of
> energy by allowing the dielectric to add energy to the system.
>
> Finally the equation for loss tangent can be arrived at using Maxwell's
> equations for time harmonic fields. I should point out that this is a
> sticky issue for those of us doing SI analysis in the time domain and wish
>
> to use the concept of loss tangent for that analysis. The assumption of
> constant loss tangent, brings with it all sorts of complex and probably
> non-causal time domain behavior. So BE CAREFUL!
>
> curl(H) = jwD + J (J is electric current density, J = cond *E)
> curl(H) = jweE + cond*E
> curl(H) = jwe'E + (we'' + cond)*E
> curl(H) = jw(e'-je''-j(cond/w))*E
>
> As you can see here the e' term is the lossless part and j(e''+cond/w) is
> the "lossy" part and if we think of the lossless part, e', as being on the
>
> real axis and the "lossy" part (e'' + cond/w) as being on the imaginary
> axis and we take the ratio of imaginary and real parts to get a "tangent"
> that gives us a loss perfomance metric:
>
> tan(delta) = (we''+cond)/(we')
>
> for a SINGLE frequency!
>
> I hope this helps your understanding.
>
> Rob Hinz
> Principal Engineer
> SiQual Corporation
> rob@xxxxxxxxxx
> phone (503)885-1231
> fax (503)885-0550
> http://www.siqual.com
>
>
>
>
> At 01:33 PM 4/9/2002 -0500, Patrick_Carrier@xxxxxxxx wrote:
>
> >Transmission line gurus and people who love dielectrics--
> >
> >I am trying to figure out the conductivity of a dielectric.
> >I have an equation that gives me:
> >tanD = 1/(2*pi*Freq*Er*rd) where rd is the resistivity of the dielectric
> >I assume that 1/rd is the conductivity of the dielectric. Is that an
> >erroneous assumption?
> >That gives me the equation:
> >conductivity of dielectric = 2*pi*Freq*Er*tanD
> >
> >This second equation makes sense to me in that increasing your frequency
> >increases the dielectric conductivity, causing more "leakage" of your
> >transmitted energy. However, using this equation, that would indicate
> that
> >the conductivity of a dielectric with Er=4 and tanD=0.02 would have a
> >conductivity approaching that of copper at 100MHz. Now that does not
> make
> >sense.
> >
> >Is there a such thing as non-frequency-dependent conductivity of a
> >dielectric? How would I obtain such a number?
> >Is there something else I am missing?
> >
> >Any guidance would be greatly appreciated. Thanks.
> >--Pat
> >
> >
> >
> >
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>
> Rob Hinz
> Senior Electromagnetics Specialist
> SiQual Corporation
> rob@xxxxxxxxxx
> phone (503)885-1231
> fax (503)885-0550
> http://www.siqual.com
>
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