8.1 A rectangular cavity resonator may be constructed by inserting conducting plates in a rectangular waveguide at z = 0 and z = d, as shown in Fig. 8-1. Write an expression for E _z within the cavity, assuming a TM mode.

Figure 8-1

8.2 Write the forms of field components E _x, E _y, H _x, H _y, and H _z for the TM mode in Problem 8.1.

8.3 Apply the boundary conditions at z = 0 and z = d in the cavity of Fig. 8-1.

8.4 Using Problems 8.1 8.3, write explicit expressions for all the field components in TM _mnp.

8.5 Give the time-domain expressions for the field components of Problem 8.4.

8.6 Referring to Problem 8.5, find the unique (resonance) frequency at which TM _mnp "stands."

8.7 What is the lowest-order (lowest-resonant-frequency) TM mode that can exist in a cavity such as shown in Fig. 8-1?

8.8 Obtain expressions for the field components for the TE modes in the cavity of Fig. 8-1.

8.9 It is obvious that the z-boundary conditions require and ? = jP in Problem 8.8, just as with TM modes. Rewrite the field components for TE