Skin effect of transmission line

[yungman]

I have to thinking about how the skin effect come into play in transmission lines with two conductors and dielectric in the middle.

For normal skin effect, we consider a potential across a conductor as shown:

Where the tangential E right above and right below the surface at z=0, are equal. The E will cause J0 to flow as show in orange arrows. The J decrease as it goes deeper into the +z direction as E attenuates with depth.

But for a parallel plate transmission line as shown:

As TEM wave travel from left to right, E is in y direction and H in x direction. Boundary condition produce Js as shown in purple color at the surface of the conductors by H, and ρ in red from E.

We know we need to consider skin effect in the two plates. How do I calculate the skin effect? The E is normal to the surface of the conductor, but current flow is parallel to the conductor plates. I have no question the E attenuate as it penetrates normal to the conductor plates, BUT the current flow is parallel to the plates.

Please help me understand this.

Thanks

 

[yungman]

Also I don't understand all the Maxwell's eq talked about surface current and surface charge. But we know that there is skin effect that current do penetrates into the metal, not just on the surface.

 

[yungman]

The diagram of the parallel plate transmission line is a more detail drawing from Field and Wave Electromagnetics by David Cheng. The charge is from boundary condition $\nabla \cdot \vec D = \rho_v$ and surface current from $\nabla X\vec H=\vec J$. But when comes to current derivation, the book only use the J component, there is no mention the contribution of the ρ from the E! How is the ρ plays in the transmission line that transform from EM wave to V and I?

 

[yungman]

Anyone please?

 

[PJC01]

for your question about the skin effect in transmission lines with two conductors and a dielectric in the middle. The skin effect is a phenomenon that occurs in conductors carrying alternating currents, where the current tends to flow more towards the surface of the conductor rather than through the entire cross-section. This is due to the interaction between the changing magnetic field and the conductive material, which causes the current to be concentrated closer to the surface.

In a parallel plate transmission line, as you mentioned, the electric and magnetic fields are perpendicular to each other and to the direction of current flow. This can make it a bit more challenging to understand the skin effect in this type of transmission line. However, the same principles still apply.

The skin effect can be calculated using the skin depth, which is a measure of how deeply the current penetrates into the conductor. This skin depth is dependent on the frequency of the alternating current and the material properties of the conductor.

In a parallel plate transmission line, the electric field is normal to the surface of the conductor, but the current flow is parallel to the plates. This means that the skin depth will be different for the two plates, as the electric field will be stronger on one plate compared to the other. This can lead to unequal distribution of current on the two plates, which can affect the overall performance of the transmission line.

To better understand this, it may be helpful to think of the two plates as two separate conductors, each with its own skin depth. The skin depth for each plate will depend on the frequency and material properties, but they may not be equal due to the difference in electric field strength.

In summary, the skin effect in a parallel plate transmission line can be calculated using the skin depth for each plate, taking into account the frequency and material properties. It is important to consider the unequal distribution of current on the two plates and how it may impact the overall performance of the transmission line. I hope this helps clarify the concept of skin effect in this type of transmission line.