1. Notes 5 ECE 5317-6351 Microwave Engineering Waveguides Part 2:
Fall 2015
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.
(k can be complex)
(kc is always real)

3. Parallel-Plate Waveguidey z w d x
, m, s
Both plates assumed PEC
w >> d
(neglect edge effects)
The parallel-plate structure is a good 1ST order model for a microstrip line. h , w
, m

4. TEM Mode Parallel-plate waveguide 2 conductors  1 TEM mode yz w d x
, m, s
To solve for TEM mode:
Boundary conditions:

5. TEM Mode (cont.)
where

6. TEM Mode (cont.) y Recall d x w z For a wave prop. in + z direction E
, m, s
Recall y x V0 E H
, m,
For a wave prop. in + z direction
Time-ave power flow in + z direction:

7. TEM Mode (cont.) y Transmission line voltage I + V d C - x w z
, m, s C + - V I
Transmission line voltage
Transmission line current
Characteristic Impedance
(Assume + z wave)
Note:
Phase Velocity (lossless case)
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 rectangular “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:
TMz mode
No x variation

12. TMz Modes (cont.) Summary TMn mode Note:
Each value of n corresponds to a unique TM field solution or “mode” in the waveguide.
TMn mode
Note:

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

14. TMz Modes (cont.)
Cutoff frequency: the frequency that defines border between cutoff and propagation
fc  cutoff frequency
cutoff frequency for TMn mode
Note: for a lossy waveguide, there is no sharp definition of cutoff frequency.

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
TEz mode

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

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

20. All Modes For all the modes of a parallel-plate waveguide, we have
Prop .
Cuttoff
TEM TM 1 2 3
Single
mode
prop
modes 5 f …
fc1 TE
fc2
fc3
The mode with lowest cutoff frequency is called the
“dominant” mode of the wave guide.
Important conclusion: If we want to use the structure as a transmission line, we need to operate in the region f < fc1.

21. Field Plots
TEM
TM1
TE1 y x
(from Pozar book)

22. Plane Wave Interpretation
TMz waveguide mode propagating in +z direction:
Relabel this as ky

23. Plane Wave Interpretation (cont.)
The TMz waveguide mode is a sum of two plane waves:
TMz  z y E  H

24. Plane Wave Interpretation (cont.)
The TEz waveguide mode is a sum of two plane waves: z y E  H
TEz 