7.11.1 Radial Parallel Plate Waveguide

In a radial waveguide electromagnetic waves propagate in ?-direction. Figure 7.29 shows a radial parallel plate waveguide formed by two circular disks with inner diameter ? ₁ and outer diameter ? ₂. The disks are in distance h. In Section 3.9 we have calculated the circular cylindric TE ^z modes and TE ^z that are transverse electric and transverse magnetic with respect to the z-direction. We will obtain the modal field functions of the radial parallel plate waveguide by matching these solutions to the boundary conditions of this waveguide. In this way we will obtain two sets of solutions that are transverse electric or transverse magnetic with respect to the z-direction.

Figure 7.29: Radial parallel plate waveguide.

The TE ^z modes we obtain from (3.221a) to (3.221f) considering also the waves propagating in negative z-direction. Deriving the wave components for the wave propagating in negative z-direction k _z must be substituted by - k _z, In this case (3.221a) and (3.221b) change the sign and we obtain

(7.332a)

(7.332b)

(7.332c)

(7.332d)

(7.332e)

(7.332f)

With we denote the derivative of the Bessel function C _n with respect to the argument. To satisfy the boundary conditions at the metallic plates E _? and E _? must vanish at z = 0 and at z = h. The first condition yields A ^{(- z}