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Prof. David R. Jackson Dept. of ECE

ECE 5317-6351 Microwave Engineering. Fall 2011. Prof. David R. Jackson Dept. of ECE. Notes 5. Waveguides Part 2: Parallel Plate Waveguide . Field Equations (from Notes 4). Summary. These equations will be useful to us in the present discussion. . Parallel-Plate Waveguide.

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Prof. David R. Jackson Dept. of ECE

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  1. ECE 5317-6351 Microwave Engineering Fall 2011 Prof. David R. Jackson Dept. of ECE Notes 5 Waveguides Part 2: Parallel Plate Waveguide

  2. Field Equations (from Notes 4) Summary These equations will be useful to us in the present discussion.

  3. Parallel-Plate Waveguide • Both plates assumed PEC • w >> d,  Neglect x variation,edge effects The parallel-plate stricture is a good 1ST order model for a microstrip line.

  4. TEM Mode Parallel-plate waveguide2 conductors  1 TEM mode To solve for TEM mode: for Boundary conditions:

  5. TEM Mode (cont.) where

  6. TEM Mode (cont.) Recall For a wave prop. in +z direction Time-ave. power flow in +z direction:

  7. TEM Mode (cont.) Transmission line voltage Transmission line current Characteristic Impedance (Assume + z wave) Phase Velocity (lossless case) Note: c = 2.99792458 108 m/s

  8. TEM Mode (cont.) For wave propagating in + z direction Time-ave. power flow in +z direction: (calculated using the voltage and current) Recall that we found from the fields that: same This is expected, since a TEM mode is a transmission-line type of mode, which is described by voltage and current.

  9. TEM Mode (cont.) We can view the TEM mode in a parallel-plate waveguide as a “piece” of a plane wave. y E H PEC PMC PMC x PEC The PEC and PMS walls do not disturb the fields of the plane wave.

  10. TMz Modes (Hz = 0) Recall where subject to B.C.’s Ez = 0 @ y = 0, d

  11. TMz Modes (cont.) Recall: No x variation

  12. TMz Modes (cont.) Summary Each value of n corresponds to a unique TM field solution or “mode.” TMn mode Note: (In this case, we absorb the An coefficient with the kcterm.)

  13. TMz Modes (cont.) Lossless Case Fields decay exponentially evanescent fields “cutoff” mode

  14. TMz Modes (cont.) Frequency that defines border between cutoff and propagation (lossless case): fc cutoff frequency cutoff frequency for TMn mode

  15. TMz Modes (cont.) Time average power flow in z direction (lossless case): Real for f > fc Imaginary for f < fc

  16. TEz Modes Recall where subject to B.C.’s Ex = 0 @ y=0, d

  17. TEz Modes (cont.) Recall: No x variation

  18. TEz Modes (cont.) Summary Each value of n corresponds to a unique TE field solution or “mode.” TEn mode Cutoff frequency

  19. All Modes For all the modes of a parallel-plate waveguide, we have The mode with lowest cutoff frequency is called the “dominant” mode of the wave guide.

  20. Power in TEzMode Time average power flow in z direction (lossless case): n = 1,2,….. Real for f > fc Imaginary for f < fc

  21. Field Plots y TEM x y x TM1 y TE1 x

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