Question

A coaxial transmission line consists of a long straight wire and a surrounding conducting sheath. Both the wire and the conducting sheath have square cross sections, with side length a and b, respectively. (a)Can the TE or the TM modes of EM waves propagate in the transmission line ? If yes, find all the allowable modes. If no,give your reasons. (b)Find the supported TEM wave for the transmission line.

Problem 2A coaxial transmission line consists of a long straight wire and a surrounding conducting sheath. Both the wire and the conducting sheath have square cross sections, with side length a and b, respectively. (a)Can the TE or the TM modes of EM waves propagate in the transmission line? If yes, find all the allowable modes. If no, give your reasons. (b) Find the supported TEM wave for the transmission line. b

Answer 1

(a) yes, the co-axial transmission line does admit modes with Ezzo and Bz=0 int. TE and the TM modes bet, k = w/e , eBy= Ex ans e B x=-Ey So, E, B² are mutually perpendicular and together with J.E=0 , B=0 For TE moses: Fox = - Juno Ho (1) cos ma sinny Foy = Juho Ho (m) Sintra cos y Hox= - dkg Ho (MT) sim mikrosny Hoy = -tky Ho (MT) cos mix sinn mans n is equal to 0, 1, 2, 3, . . . kg = imaginary For TM modes; Fox= kg to m) cos mir SIM NITY Foy = kg to mr sin mox cosiny Ho Hor= - TW& Fo (MI) sin mix cost Hoy - Je to to (MI) cosmin SinnTy In TM moder all the fleet components vanish for both mans n oro zero or any one of them zero. Thus, Mo., (TM)0 or los modes are not possible. 22