Notation and dimensions: In rectangular waveguides, which labeling convention is normally used for the cross-sectional dimensions?

Introduction / Context:
Clear notation avoids confusion when computing cutoff frequencies and designing waveguide components. The microwave community follows a common convention for rectangular waveguides that ties directly to mode naming and cutoff expressions.

Given Data / Assumptions:

• Rectangular, hollow guide with internal dimensions a (broad) and b (narrow).
• Dominant mode TE10 uses the broad dimension in its index.
• Analysis focuses on single-conductor metallic guides.

Concept / Approach:

By convention, the larger interior dimension is labelled a (the broad wall), and the smaller dimension is b (the narrow wall). This aligns with TE10 having one half-wave variation across a and none across b at cutoff, yielding fc = c / (2a) in air. Using the standard labels prevents mix-ups when reading charts and selecting commercial WR sizes.

Step-by-Step Solution:

Verification / Alternative check:

Standard waveguide tables (e.g., WR90, WR62) publish a and b explicitly in this convention, and textbooks derive mode charts accordingly.

Why Other Options Are Wrong:

• Swapping a and b contradicts industry practice and many published formulas.
• Claiming no convention risks errors in cutoff and component dimensions.
• Length is not denoted by a in waveguide practice.

Common Pitfalls:

Mixing mechanical external sizes with internal a and b; always reference internal aperture for electromagnetic calculations.

Final Answer:

The broad width is generally labelled 'a' and the height 'b'