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Lecture 14 Metallic waveguides

# Lecture 14 Metallic waveguides - Lecture Lecture14 Hayt...

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Lecture 14 Metallic walled waveguides Hayt CH 14 1 McGill ECSE 352, Fall 2011, D. Davis

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Waveguides 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
Waveguides The analysis of waveguides will require starting with Maxwell’s Equations and developing waveguide relationships developing waveguide relationships. The initial assumptions will be: the waveguide dielectrics are lossless the walls are perfectly dielectrics are lossless, the walls are perfectly conducting and flat, there are no other sources 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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Maxwell’s Equations Maxwell s Equations Using Maxwell’s Equations in phasor form the Using Maxwell s Equations in phasor form, the Helmholtz Vector Wave Equation was developed developed. This equation described wave motion of electromagnetic fields in various environments. Th b i l i h l The most basic solution was the plane wave. This was used for transmission lines. McGill ECSE 352, Fall 2011, D. Davis 4
Maxwell’s Equations Maxwell s Equations 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 f i ) h l ibl l i frequencies), where only one possible solution of the wave equation could exist. McGill ECSE 352, Fall 2011, D. Davis 5

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Maxwell’s Equations Maxwell s Equations 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 di i d h h li d b direction and that the amplitudes can be functions of the x and y axes. McGill ECSE 352, Fall 2011, D. Davis 6
Maxwell’s Equations Maxwell s Equations 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 7

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Maxwell’s Equations Maxwell s Equations We will make the assumption that the region is source free and that the region is loss less (zero conductivity) In this case we can write: (zero conductivity). In this case we can write: and Whi h F d d A ’ L i Which are Faraday’s and Ampere’s Laws in phasor form for loss less materials.
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