ANSYS Module on Circular Waveguides

Overview

• Focus on governing equations of circular waveguides.
• Review of previous module: rectangular waveguide using AEDT HFSS simulation.

Circular Waveguide Definition

• Circular cross-section, generally in the xy-plane, uniform along the z-axis.
• Radius defined as A.
• Can be empty or filled with dielectric material (lossless with relative permittivity ε and permeability μ).
• Walls made of PEC (Perfect Electroconductor) or metal.
• Modes: Only TE (Transverse Electric) and TM (Transverse Magnetic) modes exist; no TEM mode.

Maxwell's Equations

1. Represented in phasor format for a source-free region.
2. Fields have components along x, y, and z axes in Cartesian coordinates.
3. Use cylindrical coordinates (ρ, φ):
   • ρ ranges from 0 to A
   • φ ranges from 0 to 2π
4. Transverse components: Eρ, Eφ, Hρ, Hφ; longitudinal components: EZ, HZ.
5. Propagation along the z-axis: variation expressed as e^(jβz), where β is the propagation constant (lossless dielectric).

Expansion of Maxwell's Equations

• Express transverse components in terms of longitudinal components.
• kc: Cut-off wave number defined; k: wave number in the medium, given by
  • k = ω√(με) = 2π/λ.

Wave Equation Derivation

• General longitudinal function φ derived for solutions.
• TE case: E = 0; TM case: H = 0.
• Wave equation expressed in cylindrical coordinates.
• Using separation of variables, terms grouped into equations dependent on one variable.
• Separation constant defined as kρ and kφ.

Bessel's Differential Equation

• Reduced to Bessel's differential equation; general solutions involve Bessel functions (first and second kind).
• C5 must be zero for cylindrical waveguides.
• General function solution: includes constants A and B.

Boundary Conditions and Cut-off Wave Number

• For TE case: tangential electric field must be zero at conductor surface.
• Cut-off wave number derived using boundary conditions:
  • Jn(Kc * A) = 0.
• TM case similar with E and H components.*

Mode Definitions

• Modes categorized using indices TE_n,m and TM_n,m.
• m: number of half-cycles along radial direction, always >= 1.
• n: number of full cycle variations along circumference, can be 0.
• TE11 mode has the lowest cutoff frequency (dominant mode), followed by TM01 and TE21 modes.

Conclusion

• Understanding governing equations is crucial for designing waveguides.
• Upcoming module: Simulating a circular waveguide in ANSYS Electronic Desktop HFSS using physical model geometry.
• Additional resources: ANSYS Course.