Lecture 14 Metallic waveguides

Lecture 14 Metallic waveguides - Lecture Lecture14...

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cture 4 Lecture 14 Metallic walled waveguides ayt H 14 Hayt CH 14 1 McGill ECSE 352, Fall 2011, D. Davis
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aveguides Waveguides waveguide is a guiding structure that has A waveguide is a guiding structure that has transverse (cross section) dimensions on the order of a wavelength (or larger). Since the cross section is relatively large when compared to a transmission line, the electric and magnetic fields can have transverse standing waves. These standing waves create modes (frequency dependant wave structures). McGill ECSE 352, Fall 2011, D. Davis 2
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aveguides Waveguides e analysis of waveguides will require The analysis of waveguides will require starting with Maxwell’s Equations and eveloping waveguide relationships developing waveguide relationships. The initial assumptions will be: the waveguide ielectrics are lossless the walls are perfectly dielectrics are lossless, the walls are perfectly conducting and flat, there are no other urces within the waveguide sources within the waveguide. The waveguide analysis will then begin. McGill ECSE 352, Fall 2011, D. Davis 3
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axwell’s Equations Maxwell s Equations sing Maxwell’s Equations in hasor rm the Using Maxwell s Equations in phasor form, the Helmholtz Vector Wave Equation was eveloped developed. This equation described wave motion of lectromagnetic fields in various electromagnetic fields in various environments. The most basic solution was the plane wave. This was used for transmission lines. McGill ECSE 352, Fall 2011, D. Davis 4
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axwell’s Equations Maxwell s Equations p to this point we have been using a one Up to this point we have been using a one dimensional wave relationship with constant coefficient amplitudes for the forward and backward travelling waves. This has been enforced by choosing a propagation medium, (i.e. the two conductor transmission line operated at relatively low frequencies), where only one possible solution of the wave equation could exist. McGill ECSE 352, Fall 2011, D. Davis 5
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axwell’s Equations Maxwell s Equations this section we will relax some of the In this section we will relax some of the conditions for the propagation medium and start with the basic equations and boundary conditions. In this case we will assume that the time harmonic electric and magnetic fields are propagating within a given medium in the z direction and that the amplitudes can be functions of the x and y axes. McGill ECSE 352, Fall 2011, D. Davis 6
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Maxwell s Equations e electric and magnetic fields will have The electric and magnetic fields will have solutions of the form: െ݆ߚݖ For the electric field and: ݔݕ ݖ ݖ For the magnetic field. Both of these ݔݕ ݖ ݖ െ݆ߚݖ relationships have wave propagation in the z direction. McGill ECSE 352, Fall 2011, D. Davis
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This note was uploaded on 12/03/2011 for the course ECSE 352 taught by Professor Mi during the Fall '10 term at McGill.

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Lecture 14 Metallic waveguides - Lecture Lecture14...

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