ECE 563 / TCOM 590 Microwave Engineering

1
ECE 563 / TCOM 590 Microwave Engineering

• Guided Waves
• September 23 30, 2004

2
Wave Equation
3
Solution of Fields for General Cross-Section Guide
4
Solution of Fields for General Cross-Section Guide
5
Solution of Fields for General Cross-Section Guide
6
General Procedure to Find Fields in a Guided
Structure

• Use wave equations to find the z component of Ez
  and/or Hz
• note classifications
• TEM Ez Hz 0
• TE Ez 0, Hz ? 0
• TM Hz 0, Ez ? 0
• HE or Hybrid Ez ? 0, Hz ? 0

7
Special Case TE Mode
8
Special Case TE Mode
9
Special Case TM Mode
10
Special Case TEM Mode
11
Special Case TEM Mode
12
Special Case TEM Mode
13
Special Case TEM Mode

• Therefore ? satisfies 2 dimensional version of
  Laplaces equation in electrostatics
• Electrostatic fields are possible
• Must have at least 2 conductors, single conductor
  is electrostatically at an equipotential
• Cant excite TEM mode in waveguides that have
  just one conductor.

14
Rectangular Waveguides
b
1) Wave Equation for Ez, Hz 2) Boundary
conditions for constants 3) Maxwells
equations for other components
y
z
x
a
15
Rect. Waveguide TE modes
16
Boundary conditions
17
Boundary conditions
18
Cutoff conditions
19
TE Modes
20
Dispersion relationship
?
?c1,0
?c
21
Phase velocity
22
Group Velocity
23
Losses
24
Power Flow
25
Power Flow
26
Solution of Transverse Fields for TE Mode
27
Transverse Fields
28
Losses
29
Skin Depth
30
Dielectric Losses
31
Rect. Waveguide TM mode
32
Degenerate Modes