Lecture 13 TE and Tm mode solutions to waveguide equations

# Lecture 13 TE and Tm mode solutions to waveguide equations...

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cture 13 Lecture 13 TE and TM Mode solutions to Wave Equation Waveguide Basics Hayt 7 th ed. Ch 14 1 McGill ECSE 352, Fall 2011, D. Davis

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ansverse Fields Transverse Fields In the case of guiding structures such as te case o gu d g st uctu es suc as transmission lines and waveguides, the direction of propagation is typically defined as the z direction, (the cross section of the guiding structure is parallel to the x y plane). t f fi ld th t ll l t th The components of a field that are parallel to the x y plane are the transverse components of the eld. field. The guiding structure uses a loss less dielectric as the propagation medium. McGill ECSE 352, Fall 2011, D. Davis 2
ansverse Fields Transverse Fields hen solving for the wave equation the When solving for the wave equation, the transverse solution and the propagating lution are both used to construct the full solution are both used to construct the full solution. e general form of the electric field The general form of the electric field propagating in the z direction with transverse mponents on the x plane is given by: components on the x y plane is given by: ܧ ൌܧ ሺݔ,ݕሻ݁ െ݆ߛݖ ݁ ݆߱ݐ McGill ECSE 352, Fall 2011, D. Davis 3

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ansverse Fields Transverse Fields e propagating medium is a loss ss The propagating medium is a loss less dielectric which must satisfy: 2 2 Where the phase coefficient is given by: ׏ ܧ ൅ ߚ ݖ ܧ 0 At the same time the electric field must satisfy ߚ ݖ ൌ߱ ߤ߳ the wave equation: 2 ݕ 2 2 McGill ECSE 352, Fall 2011, D. Davis 4 ׏ ܧ ൫׏ ݔݕ ൅ ׏ ݖ ൯ܧ
ansverse Fields Transverse Fields is will lead to: 2 2 2 This will lead to:

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Lecture 13 TE and Tm mode solutions to waveguide equations...

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