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Electromagnetic Field Theory: A Problem Solving Approach Part 68

Electromagnetic Field Theory: A Problem Solving Approach Part 68. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Dielectric Waveguide 645 Figure 8-30 TE and TM modes can also propagate along dielectric structures. The fields can be essentially confined to the dielectric over a frequency range if the speed of the wave in the dielectric is less than that outside. It is convenient to separate the solutions into even and odd modes. where we choose to write the solution outside the dielectric in the decaying wave form so that the fields are predominantly localized around the dielectric. The wavenumbers and decay rate obey the relations k2 A o 2eii 2 2 2 _ 2 V a Kz w e0 j.n The z component of the wavenumber must be the same in all regions so that the boundary conditions can be met at each interface. For propagation in the dielectric and evanescence in free space we must have that a 2 O jLo kz i 2ep 3 All the other electric and magnetic field components can be found from 1 in the same fashion as for metal waveguides in Section 8-6-2. However it is convenient to separately consider each of the solutions for Ez within the dielectric. a Odd Solutions If Ez in each half-plane above and below the centerline are oppositely directed the field within the dielectric must vary solely as sin kxx i a2 Ul I a3 sin kxx ea x d x d x d x d 4 646 Guided. Electromagnetic Waves Then because in the absence of volume charge the electric field has no divergence - A2e a x d x d a A1COskxX lxl- 5 A3ea x d x -d . a while from Faraday s law the magnetic field I kzEx I JtiifJL dx _J O 0A2 g-a x-d x d a Hy COS x d eoA3 x -d is 6 At the boundaries where x d the tangential electric and magnetic fields are continuous z x d- Ez x d A sin kxd A2 -A j sin kxd As i j eoA2 7 H x d- Hy x d ---cos k d ------ -jcoeAj Jcoe A3 --- cos kxd k ------------------a which when simultaneously solved yields A2 1 3 Ai sin kxd cos kxd eo x sin kxd ----- cos kxd Eokx a kx tan k l e 8 The allowed values of a and A are obtained by self-consis-tently solving 8 and 2 which in general requires a numerical method. The critical condition .