EEE445_Lectr07_PPWG

EEE445_Lectr07_PPWG - Electric and Magnetic Fields Assuming...

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Unformatted text preview: Electric and Magnetic Fields Assuming time convention and propagation in z-direction EEE 591/445 Lecture 07 1 j t e ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 o r , , , , , , j z z j z z j z z j z z E r e z e e H r h z h e E x y z e x y z e x y e H r h x y z h x y e ---- = + = + = + = + (3.1a) (3.1b) Maxwells curl Eqs with z-dependence the component forms From a, d (read line) by eliminating E y , we get H x as EEE 591/445 Lecture 07 2 E j H H j E = - = (3.2a) z y x z x y y x z E j E j H y E j E j H x E E j H x y + = - -- = - - = - z y x z x y y x z H j H j E y H j H j E x H H j E x y + = - - = - = a. b. a. d. a. f. (3.2b) , j z e - (3.3) (3.4) We may present the transverse components in terms is longitudinal fields where EEE 591/445 Lecture 07 3 2 2 2 2 z z x c z z y c z z x c z z y c E H j H k y x E H j H k x y E H j E k x y E H j E k y x = - - = + - = + = - + 2 2 2 c k k = - (3.5a) (3.5b) (3.5c) (3.5d) (3.6) TEM Waves EEE 591/445 Lecture 07 4 ( 29 ( 29 z z z z j z j z E H e h E e e H h e -- = = = = = = c k k = = = (3.8) Zero cutoff Wave (Helmholtz) eq Eq (3.9) becomes or Because of (3.9) and (3.11) TEM is also referred to as Qua si-static EEE 591/445 Lecture 07 5 (3.9) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ( ) ( , ) 0 x x t k E x y z j k z E x y e x y + + + = - = - = - + = = (3.9) (3.11) TEM Waves EEE 591/445 Lecture 07 6 2 2 12 1 ( , ) ( , ) 1 , t t TEM TEM x y e x y h z e Z Z V E d I H d = = - = = = = - = = l l (3.13) (3.14) (3.18/17) (3.15) (3.16) Procedure for Analyzing TEM Waveguides (p. 95) Derive the BCs that apply to . Solve Laplaces equation (3.14) subject to BCs for . Evaluate the transverse fields. Compute voltage and current via (3.15/16) Calculate propagation constant (3.8) and wave impedance. EEE 591/445 Lecture 07 7 TE Waves Substitution into equations (3.5) yields eq (3.19)....
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This note was uploaded on 12/14/2010 for the course EEE 445 taught by Professor Georgepan during the Fall '10 term at ASU.

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EEE445_Lectr07_PPWG - Electric and Magnetic Fields Assuming...

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