[SI-LIST] Re: what is the conductivity of a dielectric?
- From: "Knighten, Jim L" <JK100005@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- To: RayCaliendo@xxxxxxxxxx, rob@xxxxxxxxxx
- Date: Wed, 10 Apr 2002 20:02:59 -0400
Ray,
I agree with you that the term "conductivity" is generally accepted to
describe conduction, i.e., the flow of electrons in a metal, or in any
material. When you have conductivity, DC current can flow. Displacement
current is the current that flows in a capacitor, when no DC current can
flow.
Usually, dielectric materials have zero, or very low conductivity. That's
why we call them dielectrics, instead of conductors. As we know, there is a
phase difference between conduction current and displacement current. Yet,
the dielectric can exhibit a loss when used in a capacitor, or some similar
application. This "dielectric loss" is due to material properties, i.e.,
polarization damping forces in the electric polarization of the molecules.
This dielectric loss appears much as a conduction current and is in phase
with any conduction current that flows.
Strictly speaking, loss tangent includes conduction current and dielectric
loss effects. Some texts use an e'' for the dielectric loss term and a
j(sigma)/w for the conduction loss.
Loss tangent has no dimensions. All of your examples below have no
dimensions.
Jim
Jim Knighten, Ph.D.
Teradata, a Division of NCR http://www.ncr.com
17095 Via Del Campo
San Diego, CA 92127
USA
Tel: 858-485-2537
Fax: 858-485-3788
jim.knighten@xxxxxxx
-----Original Message-----
From: RayCaliendo@xxxxxxxxxx [mailto:RayCaliendo@xxxxxxxxxx]
Sent: Wednesday, April 10, 2002 4:24 PM
To: rob@xxxxxxxxxx
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: what is the conductivity of a dielectric?
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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