A schematic coaxial transmission line is depicted below and widely used both commercially and industrially, especially in connectors.

The scheme of a coaxial transmission lines.
The scheme of a coaxial transmission lines.

To obtain the field solution for a coaxial transmission line we have to resolve the Laplace equation for potential with the boundary conditions Ψ(a)=V0,Ψ(b)=0. The easiest way to do this is to use polar coordinates similar to the ones used in a circular waveguide.

The potential function for a given type of coaxial waveguide is Ψ(ρ,φ)=V0lnbρinba. A coaxial line can perform TEM, TE and TM modes. However, in practice the TEM mode is the most common used mode.

Let’s consider the TE mode with EZ=0, HZ0, so we must resolve the Laplace equation for HZ. The solution for HZ will be the following: Hz(ρ,φ)=(Asinnφ+Bcosnφ)(CJn‘ (kcρ)+DYn‘ (kcρ))ejβz, where J and Y are Bessel functions. The type of electric field function can be obtained using the boundary conditions. The cut-off number here will be kc=2a+b, fc=ckc2πε.

The transmission line of parallel planes, stripes and microstripes


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