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Circular Waveguides

Circular Waveguides. INEL 5606 Dr. Sandra Cruz-Pol ECE, UPRM. Circular Waveguides. In 1897 Lord Rayleigh performed the first theoretical analysis of a wave in a circular waveguide. Use Cylindrical coordinates. From Maxwell Eqs. we can derive for E z and H z , all other components:.

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Circular Waveguides

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  1. 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

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

  7. 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 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! JnYn n is the order

  9. Bessel Function of the 1st Kind

  10. So we are left with: We need to satisfy: 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 https://www.youtube.com/watch?v=kp33ZprO0Ck

  19. Dominant Mode

  20. Conventional sizes d=2a

  21. 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.

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