Periodic Boundary Conditions Unit Cell vs Transmission Line Model

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The discussion revolves around the challenge of establishing an analytical relationship between a dielectric-filled unit cell with periodic boundary conditions and a transmission line model. The user has attempted to analyze this using HFSS, finding that the two models do not correlate, particularly for complex dielectric constants. The need arises from modeling a stack of unit cells to study transmission loss in a plasma sheath. Participants are encouraged to share their findings and screenshots to clarify their reasoning for the negative outcome. The inquiry highlights the complexities of modeling advanced dielectric materials in electromagnetic simulations.
katto01
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The problem is:
1. Assume ONE BOX W*W*H1 filled with a dielectric material with dielectric constant eprs. The vertical walls are assigned periodic boundary conditions and the other two faces are Floquet Ports (One TE mode and one TM mode).
2. Assume a transmission line that is L1 long with a characteristic impedance of Z1, and a propagation constant beta.

Q: Is there an analytical relationship between the two? I.e. can one represent the unit cell by a transmission line?

I tried to check this in HFSS, (FEM for the box and Circuit for the TL) and it looks like the answer is NO.
I hope I'm wrong because I need to do the analysis of a stack of 161 unit cells each having crazy dielectric constant (negative, less than 1 etc.). It's my modeling of a plasma sheath for which I need to find the transmission loss.
 
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Can you post some screenshots of your work so far, and say why you think the answer is "No"? Thanks.
 
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