TABLE OF CONTENTS Lossless Rectangular Guides: the Wave Equation/TE and TM Solutions/Cutoff Frequencies/Field Lines/Dominant Mode/Average Power Flow/Lossy Guides: Core and Wall Losses/Cylindrical Waveguides: Maxwell's Equations/Bessel Function Solutions for TM and TE Modes/Dielectric-Slab Waveguides/Optical Fibers
Note: Where confusion is unlikely, problems of Chapters 7, 8, and 9 employ the same symbols for time-sinusoidal vectors and their phasor representations.
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| 7.1 Figure 7-1 represents a rectangular waveguide, in the lossless interior of which the fields are governed by
Assuming the field components E x( x, y, z), , H z( x, y, z) all to be of the form F( x, y) e - ?z, obtain a partial differential equation for the functions F.  Figure 7-1 |
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| 7.2 Defining the transverse vector operator  replace equations ( 3) of Problem 7.1 by a pair of vector equations. |
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| 7.3 Apply Faraday's law and Amp re's law to the interior of the waveguide of Fig. 7-1 and obtain coupled partial differential equations governing the components of the E- and H-fields. |
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| 7.4 Combine the three equations ( 1) of Problem 7.3 into a single vector equation; do the same for the three equations (2). |
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| 7.5 Show that all field components may be derived from E z and H z. |
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| 7.6 What conclusion can be drawn from Problems 7.5 and 7.1? |
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| 7.7 Set... |
