Given a rectangular waveguide of dimensions (a,b). Assume a TEno mode is propagating in the waveguide. The total field is the sum of the positively and negatively traveling waves.
Now a metal plate is attached to the waveguide at z=0 as shown in the figure. Since Ey is tangent to this metal at z=0, from the boundary conditions, Ey(z=0)=0
Which is expected. The wave is completely reflected back. Substituting into the total E field, and simplifying the resulting expression
We now attache another metal plate at z=d. Again applying the boundary condition that Ey(z=d)=0,
This can be satisfied if
Here l is an integer. Substituting the value of b into this equation
This can only be satisfied for specific frequencies fc (called resonant frequencies). Solving for fc
Note that there is a specific frequency for each of the integers. Thus the resonant frequencies are labeled as fnol . More general expression for TEnml and TMnml modes is
Last Modified: Tuesday, August 10, 1999