Lect33TransLines - T ra n s m is s io n L in e s L e c tu r...

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Cunningham ECE329 Lecture 33-34 Transmission Lines Lectures 33 & 34
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Cunningham ECE329 Lecture 33-34 Starting Point: Uniform Plane Wave http://www.phy.ntnu.edu.tw/java/emWave/emWave.html
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Cunningham ECE329 Lecture 33-34 Starting Point: Uniform Plane Waves Consider E and H that are Perpendicular to each other Perpendicular to the direction of propagation Magnitude is constant (“uniform”) in the plane perpendicular to the propagation direction And for perfect dielectric media: E and H are in phase No attenuation in z-direction E = E x ( z , t ) a x H = H y ( z , t ) a y x y z E H propagation
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Cunningham ECE329 Lecture 33-34 Parallel Plate Transmission Line If we place the conducting sheets in the uniform plane wave, some of the wave enters the box and is guided by it z x y Imagine a rectangular box made of perfect conductors on the upper and lower surfaces, filled by perfect dielectric medium x,y=0 x=d y=w z=0 z=l E x H y
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Cunningham ECE329 Lecture 33-34 Parallel Plate Transmission Line x,y=0 x=d y=w z=0 z=l E x H y E x H y x=0 x=d y=w y=0 ε Cross section of the transmission line so wave is propagating into the page
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Cunningham ECE329 Lecture 33-34 Take a look at boundary conditions E x H y x=0 x=d y=w y=0 ε Perfect conductor Perfect dielectric E y =0, D x =0, H y =0, B x =0 E y =0, D x =- ρ s , H y =-J s a z , B x =0 The E and H fields inside the transmission line result in the formation of charge and current on the upper and lower surfaces ++++++++++ - - - - - - - - - - - −ρ s ρ s J s a z -J s a z " s = # E x J s = H y r a z
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Cunningham ECE329 Lecture 33-34 TL Voltage x=d y=w E x H y −ρ s + ρ s V ( z , t ) = ( d ) E x ( z , t )
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Cunningham ECE329 Lecture 33-34 TL Current x=d y=w E x H y -J s a z J s a z I ( z , t ) = wH y ( z , t )
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