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Waveguides

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Waves in cylinder In a waveguide whose cross-section is uniform along z-axis, variation of E, H is proportional to exp(-j z). In a waveguide, transverse E and H can be obtained from Ez and Hz.

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TM, TE mode TM mode : Electromagnetic wave modes with Hz=0 are called TM modes (Transverse Magnetic). Those modes can be found from Ez. TE mode : Electromagnetic wave modes with Ez=0 are called TE modes (Transverse Electric). Those modes can be found from Hz.

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**Eigen-function expansions in waveguides**

TM modes TE modes TEM modes

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**Rectangular waveguide (TE mode)**

Boundary condition

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Field lines for some of the lower order modes of a rectangular waveguide. Reprinted from Fields and Waves in Communication Electronics, Ramo et al, © Wiley, 1965)

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**Example : WR-90 WR-90 X-band 8.2GHz~12.4GHz (2.286cm × 1.016cm)**

5GHz input signal Attenuation by a 3cm-long evanescent waveguide

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Cavity resonator Minimum frequency

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**Cylindrical waveguide**

By separation of variables

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**Cylindrical waveguide mode**

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Cutoff frequencies of the first few TE and TM modes of a circular waveguide, relative to the cutoff frequency of the dominant TE11 mode.

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