1. INEL 5606 Dr. Sandra Cruz-Pol ECE, UPRM
Circular Waveguides
INEL 5606
Dr. Sandra Cruz-Pol
ECE, UPRM

2. Circular Waveguides
In 1897 Lord Rayleigh performed the first theoretical analysis of a wave in a circular waveguide
By Vanessaezekowitz - SVG version by Vanessa Ezekowitz, based on this PNG, CC BY-SA 3.0,

3. Use Cylindrical coordinates

4. From Maxwell Eqs. we can derive for Ez and Hz, all other components:
TEM waves
not supported
where
And we have assumed waves travel to +z , so

5. TE Modes: (Ez=0) Solving the wave equation for Hz:
Use Separation of Variables:
In cylindrical coordinates:

6. Since Hz must be periodic:
Since they are both equal to a constant Kc, we can separate by variables:
Since Hz must be periodic:
kf must be an integer

7. Jn=Bessel function of the 1st kind Yn=Bessel function of the 2nd Kind
This is general solution for Bessel’s Equation!
This is Bessel’s Equation!
Jn=Bessel function of the 1st kind
Yn=Bessel function of the 2nd Kind
n is the order

8. Bessel’s Functions Jn Yn
Similar to Sine and Cosine but amplitude goes down w/argument
Bessel functions are the radial part of the modes of vibration of a circular drum and circular antennas!
Jn Yn
n is the order

9. Bessel Function of the 1st Kind

10. So we are left with: We need to satisfy: Therefore, we need:
derivative
Therefore, we need:

11. Substituting The Cutoff frequency is:
Note we have A and B, which depend on excited power.

12. TE11 is the dominant mode
Due to symmetry of guide, we can rotate the axis of the coordinate system so that either A or B are zero:

13. TM Modes: (Hz=0) Solving the wave equation for Ez:
Use Separation of Variables:
In cylindrical coordinates:
Following similar procedure as for TE, now for TM we obtain:

14. Bessel

15. The Propagation Constant
The cutoff frequency:

16. TM fields and impedance

17. Cylindrical Geometry

18. Modes of Propagation

21. Dominant Mode

22. http://www. rfcafe. com/references/electrical/circular-waveguide-modes

23. Conventional sizes
d=2a

24. Advantages
Circular polarization waves and virtually any other type of polarization can be propagated thru it.
Circular waveguides offer implementation advantages over rectangular waveguide in that installation is much simpler when forming runs for turns and offsets.
Manufacturing is generally simpler, too.