Question

The electromagnetic field propagating in metallic rectangular hollow waveguide of dimensions a and b in the +z direction has an electric field of the form: Ě(x,y,z, t) = [tổox(x,y) + ĢĒoy(x,y)]e'(kz2-wt) Explain what all the terms in above equation represent. What type of electric field is this field? Derive equations for Ēox and Ēoy in terms of the magnetic field. Hence, determine Æox and Ēoy. Determine the cut-off frequencies of the three lowest-order modes for a = 0.1 m and b= 0.05 m. If the angular frequency of the modes is 47 GHz, determine which modes will propagate. Comment on the degeneracy of any of the modes.

Answer 1

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2 (w.)2 22 mye X² B2 be sy Sigling using variation of paraneker, Beluy) = XW Y4y) we get, Yazx + *dly)-22]xy = dyz we get . 612 7,12 2 divide by xy 바 i 21 day I d²x X dic² X ? ay $ with SO So, solu XWU = Asintax) + bcos lai bot_ frien boundary condition Broz de Cat R=0) &u=a. ران a 예 Kuzma & 몹 same An “古 goes bey for y ht So, wie gut Bez bolies(mm) cos( now from manwell's equation , Ex-18 dt. 4 x = Metoda it t. from the we can get elechic field component in terme of b. ics Scanned-with CamScanner

cutoff frequency A b=0.05- Wmn ch is given by 병 a=ool my © first three modes are, (10) Lot) 12.0) (iii) + So wio a a 3x 108 x 3.14 6) Joost 24 x the 9.42 X 109 Hz WALIONYM21:884X160 Hz depenuria Wal = 31/0843_14 mode 3x10 8 x 14 22 work 1.989700Hz 7 Wat 3x10 6 x 3.14 th SAHAH 211 8100 Hz Given w = 4K GHz Ics Scannedything Hz CamScanner į 12.58x10 " He a 1.256x10° the

so, only who made will propagato (only one mode) es Gs Scanned with CamScanner