Complex Permittivity: Solving Debye's Equation

[polarmystery]

Homework Statement

The problem statement is shown on the picture
[PLAIN]http://img252.imageshack.us/img252/1184/graphsq.jpg

Homework Equations

Debye's equation?

The Attempt at a Solution

Hey guys, I am trying to figure out how to obtain the equation for the graphs, but from what I understand, losses start vanishing after the pole seen @ ~17GHz. I say the relevant equation is the Debye equation for complex permittivity, but honestly I'm not sure. Any help as always is appreciated.

 

[rude man]

Start with Maxwell's equation for H for a medium with finite conductivity. I'll help you more after that if necessary.

 

[polarmystery]

I guess I don't understand why we need to use Maxwell's equation to come up with a model for the line. Can you explain why that is necessary? (The chapter in our book doesn't seem to show anywhere in the complex permittivity section that this is necessary, but I wouldn't know either way).

 

[rude man]

Line? Whatb line?

Anyway, you're supposed to derive a model for complex permittivity so the way I look at it you should start with fundamentals.

OK, del x H = σE + ∂D/∂t = (σ + jwε)E transformed for sine waves, right, since ∂D/∂t = wD? And we can rewrite (σ + jwε) = jwε(1 + σ/jwε).

So if we were to substiture a complex εc = ε(1 + σ/jwε) you can see that we would be able to ignore σ from then on & pretend we have a non-conducting dielectric with complex permittivity εc.

So how about the next step?

 

[polarmystery]

Sorry about the line statement, I mistyped.

Give me some time to absorb what you typed, this subject is excruciatingly difficult for me to grasp.

 

[polarmystery]

Okay,

I still don't get why this is:

"So if we were to substitute a complex εc = ε(1 + σ/jwε) you can see that we would be able to ignore σ from then on & pretend we have a non-conducting dielectric with complex permittivity εc."

How does injecting εc = ε(1 + σ/jwε) into del x H = jwε(1 + σ/jwε) eliminate the conductivity? My fundamentals are pretty bad, just for the record.

 

[rude man]

It doesn't eliminate it, it incorporates it into the permittivity coefficient, which is now complex.

This is really on a level beyond elementary physics, how come you're involved in it?
Or has it been 'a while' since you had the fundamentals? Don't feel bad, same here, I have to re-learn a lot of what I post myself on the fly.

 

[polarmystery]

To be honest, this class is supposed to be an "introductory" course in signal integrity in grad school but our professor goes well beyond that when he gives us assignments (And when I signed up for it, I basically had no idea what I was getting into). The last time I had a course in electromagnetic fundamentals was well over 7 years ago, with the intention to NEVER take another Emag course again.

I'm going for a master's in computer engineering, with a focus on embedded systems/computer architecture. In hindsight, I probably should not have taken this course but it's too late to drop it to get any kind of refund. At this point I'm just going to ride it out and hope for the best, because well...there are 7 students (we started with 14, which 7 dropped) in our class and 5 of them failed (myself included) our midterms. I'm sure all of us feel the same way, but I virtually have no say in altering the professors teaching style and I'm just trying to get to the end, which is in 6 weeks time...

So yes, I'm virtually lost on most of it...but I'm trying my damnedest to finish tonight (as it's due tomorrow)

 

[rude man]

I feel for you, this is definitely part of an advanced course in e-m, in the sense of advanced beyond the Resnick & Halliday level (introductory physics for physics and engineering majors).

Define εc = ε0(ε' - jε''). Then loss tangent = ε''/ε' by definition.

Your graph is ε' = ε/ε0 vs. frequency. So you know ε' and you know ε''/ε' so now you know all you need for your modeling of εc or |εc|.

 

[polarmystery]

Yeah I'll see if I can hack at it and try to come up with something. There are still 4 homework assignments left in the semester and I'm sure I'll post questions from them as well. Thanks again for all your help!

I'm probably going to be up all night trying to figure out the rest of my homework...