Question

5.3. Although the waveguide modes form a complete set so that their combination can represent any field in the waveguide, their formulation is not unique. For example, for the rectangular waveguide shown in Figure 5.2, we can also formulate a complete set of waveguide modes that consist of transverse electric to x (TE) and transverse magnetic to x (TM) modes Formulate the modal fields of these modes and find their cutoff wavenumbers, propagation constants, and wave impedances. Figure 5.2 Uniformly filled rectangular waveguide. equation V E,+ kE, = 0, based on the solution by separation of variables, it has the general form (5.1.76) E.(x. y.z)= (Acosk,x+Bsin k, x) (C cos k,y+ Dsin k, y) e

Answer 1

Hove gui el e 1Pe 10ele CE FO) TE SH2 C CACOSCK)+ B sin CEz) Cecos Cr1 1) t hy y Ckz2) tB sin A oS Bou Condiions and a x 0 and O 16 EX CA COSTRZ t BsinkzCesin jw CAinknat Rcos a Cesos mA D -1) Fy

) H2ca c CoS A Co S H2C2, A Cos mn COS Con A25 H 41 E = Jwun mn OS Eet b wainn mAX Amn sin COS kea mAa JpmA Cos Hx Ama sin ke a jp sin Amn CoS E -

+ kke Cup 2 +t eal k kc offecorcr mn emn fo cup-off fae 0ニ L 2NE 07

TM moe (RSt A Cos Ckrx) +B sin Cr) Cx) Dsin Cty C CoS CH3) L. Fiar Bounelam conaito af and *Ez aund mA A=o, = CD nT mA B sin Dsin sin Bmn Sin Ha Aint Can Sobrdtron Cmeo, n 0) TMoo

Wove impeta dance TE Mode TE P - tet ke l NFTW[ND 23 KILI TE = 1 urs /CEE

Wave impeAen ce TM mode FT 2 크티9 e EOD