D. M. Pozar, Microwave Engineering, 4th ed., Ch. 3
Waveguide field decomposition, TE/TM modes, cutoff, rectangular guides and wave impedance.
RF-02
Course overview
Waveguides, modes, cutoff & resonators
Build guided-wave physics directly from Maxwell boundary-value problems: first establish PEC guide boundaries and the absence of TEM in a hollow single-conductor guide, then construct TE/TM modes, derive cutoff and dispersion, solve the rectangular guide and finally close the guide into resonant cavities.
5/5available
Prerequisites
- EM-04 — electromagnetic waves
- RF-00 — distributed transmission lines
- Vector calculus and boundary conditions
By the end of this course
- Formulate waveguides as Maxwell eigenvalue problems.
- Build TE/TM mode families from longitudinal generating fields.
- Connect transverse eigenvalue, cutoff, dispersion and propagation.
- Solve the rectangular guide and then closed resonant cavities.
Syllabus
Waveguides, modes, cutoff & resonators
Build guided-wave physics directly from Maxwell boundary-value problems: first establish PEC guide boundaries and the absence of TEM in a hollow single-conductor guide, then construct TE/TM modes, derive cutoff and dispersion, solve the rectangular guide and finally close the guide into resonant cavities.
- 01→
Boundary conditions in hollow waveguides
Start from source-free Maxwell equations in a z-invariant PEC guide, derive the wall conditions, separate transverse and longitudinal field content, prove why a simply connected hollow single-conductor guide cannot support a nontrivial TEM mode, and formulate the transverse eigenvalue problem that later generates TE/TM modes and cutoff.
210–270 min · Advanced · available - 02→
TE and TM modes
Use the longitudinal eigenfunctions as generating functions, reconstruct every transverse field from Maxwell, derive TE/TM modal wave impedances, prove scalar modal orthogonality from the self-adjoint transverse problem, and separate field, energy and power normalization before studying cutoff.
200–255 min · Advanced · available - 03→
Cutoff and dispersion
Turn the transverse eigenvalue k_c into longitudinal dynamics: derive cutoff, the decaying below-cutoff branch for exp(+jωt−jβz), guide wavelength, phase/group velocities, v_pv_g=v² in a nondispersive filling, TE/TM impedance trends, energy velocity and numerical propagation audits before specializing the cross-section.
205–260 min · Advanced · available - 04→
Rectangular PEC waveguide
Derive the rectangular TE/TM eigenfunctions from PEC wall data, reconstruct the TE10 fields, identify the strictly single-mode band and calculate guide wavelength, modal impedance and power.
210–270 min · Advanced · available - 05→
Resonant cavities, stored energy and Q
Close the waveguide into a rectangular PEC cavity; derive TM110 and TE101 eigenfields, identify allowed mode triples, calculate resonance, stored energy and conductor/dielectric loss, and distinguish Q0, external Q and loaded Q in VNA measurements.
220–280 min · Advanced · available
Reference backbone
References
The course follows field-based microwave theory and keeps the phasor, propagation and boundary conventions explicit at every derivation.
R. E. Collin, Foundations for Microwave Engineering, 2nd ed., Chs. 3–4
Rigorous modal boundary-value formulation, guide eigenfunctions and propagation.
S. Ramo, J. R. Whinnery & T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed.
Field boundary conditions, transmission structures, waveguide modes and energy flow.
J. D. Jackson, Classical Electrodynamics, 3rd ed., Ch. 8
General waveguide and resonant-cavity boundary-value viewpoint.