1. For a guided wave between two infinite conducting  planes separated by a distance of 0.2m.  If the operating frequency is 3.3 GHz, find the number of distinct modes that can travel in the guide.

The propagation constant is given by

For propagation to take place , so that n<5.  This implies 4 TE modes, 4 TM modes and one TEM mode, giving a total of 9 modes.

2. A TE₂₀ mode is propagating along the z direction between two parallel conducting planes separated by 0.2m  along the x- direction. Find the cutoff frequency. Determine λ_x. If the operating frequency is 2.5 GHz, determine λ_z and the non-vanishing components of the electric and the magnetic field.  If the operating frequency is 1.2 GHz, calculate the distance over which the strength of the  fields reduce to 1/e of their value.

The cutoff frequency is given by GHz. The wavelength in the x direction  for n=2 is  If the operating frequency is Hz., the propagation vector is given by (using n=2)

The fields are as follows :

To determine  λ_z, we use the fact that it is equal to the distance over which the phase of the propagating wave changes by . Thus

so that m.

If the operating frequency  is 1.2 GHz,  the wave attenuates, and we have,

so that the attenuation distance is  m.

3. Calculate the rate at which energy is transmitted in a parallel plane waveguide operating in TE₁₀ mode.

The fields are given by

Power transmitted per unit area is

Power transmitted in z direction through an area of unit width,