Question: The average power density is given by Pav= Re[Es Hs*] . Calculate average power density for TE20 mode.

The average power density is given by Pav= ½ Re[Es × Hs*] . Calculate average power density for TE20 mode.

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To calculate the average power density for the TE20 mode in a rectangular waveguide we need to follow a series of steps involving the field expressions for the TE20 mode Step 1 Expressions for Electric and Magnetic Fields The expressions for the electric and magnetic fields in a rectangular waveguide for a TEmn mode are Electric Field vecE in the xdirection for TE mode Ex 0 Electric Field vecE in the ydirection Ey left j fracbetakc2 fracpartialpartial x Hz ight Electric Field vecE in the zdirection Ez E0 sinleftfracmpiax ight cosleftfracnpiby ight Since for TE20 m 2 and n 0 it simplifies to Ez E0 sinleftfrac2piax ight Magnetic Field vecH in the xdirection for TE mode Hx H0 cosleftfrac2piax ight Step 2 Determine the Cross Product vecEs times vecHs For calculating the average power density we need the cross product vecEs times vecHs Since the z component of E field Ez and y component of H field Hy are predominantly involved the real part ReEs times Hs focuses on these field components Step 3 Simplify and Evaluate Given fields vecEs E0 sinleftfrac2piax ighthatz vecHs H0 cosleftfrac2piax ighthaty Since vecE and vecH are orthogonal the expression ... View full answer

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