161_1_Lecture_8

161_1_Lecture_8 - EE161 El EE161 Electromagnetic Waves...

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EE161 Electromagnetic Waves all 2010 Fall, 2010 Instructor: Dr. Shenheng Xu Electrical Engineering Dept., UCLA gg p , © Prof. Y. Ethan Wang
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ecture 8 Lecture 8 • Striplines & Microstrip Lines • General Waveguide Solutions • Longitudinal-Transverse Relationship ave Equations for z nd Hz • Wave Equations for Ez and Hz
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ummary of Solutions for TEM Waves Summary of Solutions for TEM Waves 0 ) , ( 2 v u t 1. Use Laplace’s equation to determine the potential function ubject to boundary conditions (require two or more conductors) subject to boundary conditions (require two or more conductors). ) , ( v u   z j t z j t t e v u e v u z v u  ) , ( ) , ( , , e E 2. Solve for E-field using  z v u z Z z v u t TEM t , , ˆ 1 , , E H 3. Solve for H-field using 4. In the above use  k TEM Z 0 r 5. The phase velocity and guided wavelength are r p c v 1 r g 0 2
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triplines Striplines •“Sandwich” of two wide thin conducting plates, bonded to a dielectric slab in which is buried a narrow thin conducting late “a flatten coax”) plate (a flatten coax ). •The first type of “planar” transmission line •It can support a pure TEM wave, also igher order TM and TE modes ry to higher order TM and TE modes (try to avoid in practice most of the time) If the inner strip is wide enough, the fringing field can be ignored and it can be approximated by two arallel late waveguides stacked back to back How to analyze? parallel-plate waveguides stacked back to back
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Stripline – Parallel Plate Waveguide Model y Two parallel late waveguides x x z plate waveguides back to back a W d jkz t e d V y 0 2 ˆ E z V 2 1 ˆ Upper half jkz t e d V y 0 2 ˆ E jkz V 0 2 1 ˆ Bottom half jk TEM t e d Z x 0 H TEM t e d Z x H kz jkz W V 0 4 We then have voltage and , ) ( 0 j e V z V TEM e d Z z I ) ( current given by, d d z V ) ( he characteristic impedance is thus given by r TEM W Z W z I Z 0 0 4 4 ) ( The characteristic impedance is thus given by,
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Stripline Circuit Assembly Example A Stripline Circuit Assembly Example (courtesy of M/A-COM Inc)
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Fringing Effects - Striplines Ideally Reality •In reality, the fields spread out from the area bound by the center strip and W W eff •The fringing effects cause the strip width “virtually increase” the upper and bottom plates, this is so-called fringing effects.
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161_1_Lecture_8 - EE161 El EE161 Electromagnetic Waves...

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