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By Cam Nguyen

Assemble the paintings of others within the box, write a booklet approximately it, improve it with a couple of mathematical appendices, ship it to the editor, and you will get two hundred pages+ of thick conception, void of useful curiosity for the layout engineer.

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71b), we can rewrite Eq. 83 S This result indicates that the transverse electric fields of two different TM modes are always orthogonal to each other. Following the same approach, we can also derive the other orthogonality relationships for the transverse electromagnetic fields of TM, TE, and hybrid modes. All the orthogonality relationships are given as follows. 86b S S Hybrid Modes S S Note that Eq. 86) is valid even when m D k and n D l. 87b e h where Cemn , Chmn , Dmn , and Dmn are the orthogonal coefficients.

15) between two different media as shown in Fig. 2. 2 Using the Poynting vector, prove that the average power density of a signal propagating in a waveguide is given by Eq. 20). 3 Show that TE modes can be characterized only by the magnetic scalar potential h x, y . 4 Derive Eqs. 54). 5 Show that TM modes can be characterized only by the electric scalar potential e x, y . 6 Prove that, in any waveguides, both Ez and Hz cannot be even or odd simultaneously. 7 Consider a general waveguide with perfectly conducting walls as shown in Fig.

Note that, in general, different modes have different cutoff frequencies or cutoff wave numbers and hence different propagation constants. A rectangular waveguide is a special waveguide that has the same cutoff frequency for the corresponding TEmn and TMmn modes. When the modes have the same cutoff frequency, they are classified as degenerate modes. Otherwise, they are said to be nondegenerate modes. 48b x, y eš x, y e we can prove easily that the corresponding longitudinal electric and magnetic fields are equal to zero.

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