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Finding attenuation, phase constant, and velocity 
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#1
Oct2513, 07:48 PM

P: 663

1. The problem statement, all variables and given/known data
Find the attenuation constant alpha, phase constant β, and phase velocity v if the conductivity of the material is σ=ωε the material parameters are μr=1, εr =2.5, and the wavelength in free space is λ naught = 30cm 2. Relevant equations 3. The attempt at a solution So using some big hairy equations I found alpha to be equal to 9.53 nepers/m. The part I am having trouble with is the beta part? I start out using this equation β=sqrt((με/2)(1+sqrt(1+(σ/ωε)^2))). I have tried a ton of different ways to arrive at this equation β=(ω/c)(sqrt(εr))(sqrt((1+sqrt(2))/(2))) what do I do? 


#2
Oct2613, 02:46 AM

HW Helper
Thanks
PF Gold
P: 4,914

I can't reproduce your equations, sorry.
If we assume an E wave polarized in the y direction (propagation along x direction), the y component of E is E_{y} = E_{m}exp(jωt +/Γx) where E_{m} = constant and Γ is a (very!) complex number including ω, μ, ε, and σ. I leave it to you to obtain or derive this relationship. It will be in your textbook somewhere I'm sure. Then, Γ = α + jβ so the answer to your problem is the imaginary part of Γ. 


#3
Oct2613, 10:46 AM

P: 663

I went through it using the gamma equation I found in my book gamma= alpha+jbeta and then jomega(sqrt(mu(epsilon)))(1j(sigma/((omega)(epsilon)))) once I had gamma I uses gamm=alpha+jbeta and found for beta using alpha I got 22.976



#4
Oct2613, 10:46 AM

P: 663

Finding attenuation, phase constant, and velocity
I used mu=4pix10^7 and epsilon=8.85e12



#5
Oct2613, 02:30 PM

HW Helper
Thanks
PF Gold
P: 4,914

You don't need alpha to get beta. Alpha is the real part of Gamma and beta is the imaginary part. I did not check your numbers. What did you wind up with for alpha and beta in terms of omega, epsion, mu, sigma? 


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