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If you do some work on metamaterial using HFSS, you don't get the effective dielectric constant directly. εeff can be determined from the transmission coefficient, which need retrieval procedure and is not simple.
A simple way to get it is to simulate the transmission line structure in HFSS(larger than 1 wavelength)at the frequency interested. Then you observe the surface current distribution. You will clearly see the two nulls of one wavelength. You can measure its dimension. That will be wavelength in dilectric rg. then use the relation of rg=r0/sqrt(effitive relative dilectric constant), you will get the effective relative dilectric constant roughly.where r0 is the wavelength in air.
for simple uniform structure, you can use APPCAD to directly get it.
there is a method of finding Z0(impedance) and impedance always related to effective dielectric constant so find Z0 nad look for equations then eff. dilelectric constant
A simple way to calculate the effective dielectric constant of a transmission line is to use the unwrapped phse of the S21. The phase of S21 is electrical length of the transmission line in degree. So, you can plot the effective dielectric constant versus frequencies by adding an expression of the output variable as shown below.
θ=(2*pi/λ)*L where L=physical length of the transmission line, θ=unwrapped phase of S21.
=(2*pi*√(er_eff)/λ0)*L
Er_eff=(θ*c/(2*pi*f*L))^2;
Actually, the expression for the effective dielectric consatnt is more complex, but for general transmission lines such as microstrip lines and CPWs, you can use this express.
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