TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 67

Electromagnetic Field Theory: A Problem Solving Approach Part 67. 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. | The Rectangular Waveguide 635 Similarly the surface currents are found by the discontinuity in the tangential components of H to be purely z directed - kJi2E0 sin kjc Kz x y 0 Hx x y 0 2 2 j ap. kx ky k E Kz x y b Hx x y b -7-J 2 2x sin fcpc cos rnr ia u kx 25 k E Kz x 0 y Hy x 0 y --- 2 sin k y o n kx ky . y kxk2E0cos mir sin ky Kz x a y Hy x a y -------------------- j Ufl k2x ky We see that if m or n are even the surface charges and surface currents on opposite walls are of opposite sign while if m or n are odd they are of the same sign. This helps us in plotting the field lines for the various TMmn modes shown in Figure 8-28. The electric field is always normal and the magnetic field tangential to the waveguide walls. Where the surface charge is positive the electric field points out of the wall while it points in where the surface charge is negative. For higher order modes the field patterns shown in Figure 8-28 repeat within the waveguide. Slots are often cut in waveguide walls to allow the insertion of a small sliding probe that measures the electric field. These slots must be placed at positions of zero surface current so that the field distributions of a particular mode are only negligibly disturbed. If a slot is cut along the z direction on the y b surface at x a 2 the surface current given in 25 is zero for TM modes if sin xa 2 0 which is true for the m even modes. 8-6-3 Transverse Electric TE Modes When the electric field lies entirely in the xy plane it is most convenient to first solve 4 for Hz. Then as for TM modes we assume a solution of the form Hz Re Hz x y 26 which when substituted into 4 yields d2 Hz d2 Hz dx2 dy2 2 j2- hz 0 27 TM21 Electric field --- a jk k Eo Ex j -5- cos kjc sin k y k - -J A o . y 72-72 s n x COS z Eo sin kjc sin k y dy Ey ky tan Ape dx Ex kx tan kyy cos Akx - 2 ------------------ const cos kyy Magnetic field ----- j i eky Hx 2 2 0 sin kxx cos kyy x y a j OEkx Hy 72 72 0 COS kxx sin kyy kX ky dy _H _ -kx cot k x dx Hx k cot k

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