Question

e0-0s0t jno EE4101/EE4101E RF Communications/ Page 5 Section B A uniform plane wave in a lossless dielectric, in general, includes four wave solutions propagating along +z and-z directions as follows: Q.5 TEM Eo = e le EEe н; -E E Ee H yo e le E e н; E Ee E 0 E, Ee н; ele A plane wave can be considered as the combination of all possible solutions. Assume the plane wave is polarized along-direction, it could be generally written as the sum of the waves propagating along both +z and-z directions. En'-Eme Eng-Em Find the amplitude E (as EE) and phase a of the x-direction polarized plane wave E, Ee"l ExEe a. d octon E E (5 marks) Find the magnetic field of the x-direction polarized plane wave E, -Ege + Ee PeCewaleJ-Einest-12+4)16meut er) b. zoe H (5 marks) Find the x-direction polarized plane wave when E-E= jE /2 and their instantaneous electric and magnetic fields. C. (10 marks) Find the power density (Poynting vector) and its time-average. Is this a traveling wave or a standing wave? (5 marks) (c) 3 Exo ejt - Page

Answer 1

E-field wave: E = Ex & Ex. Ezt - KZ + Eno eikz Reflection coefficient sa Eur Exet & E= Ext {e ik z nek z a Exot ejk 21+ reizke

& Ext ejk 2 {1+ IM elekz+Pr)) complex quantity: Meer I Ex = Goh En fine + Exin eipz je ta - G+ e-zxx) AG Pjlp2-4) Let 242 +0 pzv. => 151 = |ext lekz || 1 +17) dosy +j/11smyl Exot / 1 + 1 19 +2 1 ry cosy » TE] - Ezot li+1)*+2111cos (2x2+$) = 560 phase & LExt a K2 & tant (irl siny tricos LExt = phase of East (6) hy = Hy tot Hy in e Ex Sul sutstilulé - , sut stilla Ex in ea to get Hy .

( when Exo = - bu = J Exo E = (x + + 6x) - eikz + Eni eikz Ext[ejk 2 _ ei kz] - JEI ( - 2j Sinkz) JO e e -JO - 2 sine E(2) E = Exo sink2 x 2 & Exo Cos(KZ - A) = -1 E-field wave E (2, t) = RelE e int] - Exo sink coswt 2 H (Zt) Ecet) g n (d) poyuting vector & & EXH*. & & & & Exo sin kz Time average poynting rector - ResEXH*} 2 Exo sinkz 2n. k2 component since no en & standing wave