1. Notes 5 ECE 5317-6351 Microwave Engineering Waveguides Part 2:
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 To solve for TEM mode:
Parallel-plate waveguide 2 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 = 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
PEC
PMC x E H
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 TMn mode Note:
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 kc term.)

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

14. Frequency that defines border between cutoff and propagation
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.) TEn mode Cutoff frequency
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 TEz Mode
Time average power flow in z direction (lossless case):
n = 1,2,…..
Real for f > fc
Imaginary for f < fc

21. Field Plots
TEM
TM1
TE1 y x