Why Is There a Negative Sign in the Modal Impedance of TEn Mode?

[Brianrofl]

Hi, I'm working on a parallel plate wave guide for wave propagation and had a question about it. Here's a quick diagram:

While analyzing an EM field polarized in the y-direction, the modal impedance of the TEn mode comes out to be:

Why is that negative sign there? If someone could just explain where that negative sign comes from I'd appreciate it greatly. Does it have to do with the reflection coefficient?

 

[ehild]

Hi, I'm working on a parallel plate wave guide for wave propagation and had a question about it. Here's a quick diagram:

View attachment 97051

While analyzing an EM field polarized in the y-direction, the modal impedance of the TEn mode comes out to be:

View attachment 97052

Why is that negative sign there? If someone could just explain where that negative sign comes from I'd appreciate it greatly. Does it have to do with the reflection coefficient?

You have to go back to Maxwell's equations to get the relation between components of the electric and magnetic fields. In order to get the wave impedance positive the minus sign has to be used.