EC-2.5 Waveguides
You can explain why a hollow guide has a lowest usable frequency, identify the dominant mode of a rectangular guide, and compute cutoff frequency and guide wavelength.
A hollow metal pipe carries a wave that a pair of conductors could not, and the price is that it refuses to carry anything below a cutoff frequency set by its own dimensions. The reason is worth understanding rather than memorising: the wave travels by bouncing between the walls, and below cutoff the bouncing cannot satisfy the boundary conditions at any angle. Everything else in the topic follows from that picture, including why the guide wavelength is longer than the free-space one, which otherwise looks like an error.
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Why a hollow guide cannot carry the simplest wave, and what it carries instead
A wave with both fields across the direction of travel needs two conductors, which a single pipe does not have. What propagates instead has a component along the direction of travel, in one of two families.
NPTEL: Transmission Lines and EM Waves · CourseModes in a rectangular guide, and the two integers that label them
Each mode is a standing pattern across the guide, labelled by how many half-cycles fit along each of the two cross-section dimensions. The dimensions therefore decide which modes exist at a given frequency.
MIT OpenCourseWare 6.013: Electromagnetics and Applications · CourseCutoff frequency, and the dominant mode as the one with the lowest
Every mode has a frequency below which it will not propagate, and the mode with the lowest is the one a guide is normally operated in. Working between that cutoff and the next keeps the guide carrying one mode only.
Guide wavelength, phase and group velocity in a guide
The wavelength measured along the guide is longer than in free space, and the phase velocity is correspondingly faster than light while the energy is not. The bouncing picture from the notes above is what makes that unsurprising.
NPTEL: Electromagnetic Theory · CourseCircular guides, and where each cross-section is preferred
A circular guide has the same physics with different mode labels, and its symmetry suits rotating joints and some low-loss runs. Rectangular guides are preferred where a fixed polarization must be maintained.
Power handling and attenuation, and why guides are used at all
A guide has no centre conductor to heat and no dielectric to lose energy in, so it carries far more power with less attenuation than a cable at the same frequency. That advantage is what pays for its bulk and its cutoff.
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