Rectangular waveguide design rule of thumb: What is the typical ratio of the broad dimension (width) to the narrow dimension (height) for a standard rectangular waveguide cross section?

Introduction / Context:
Commercial rectangular waveguides are standardized with a broad wall dimension 'a' and a narrow wall dimension 'b'. A common proportion is a ≈ 2b, which supports the dominant TE10 mode with desirable bandwidth and mechanical practicality.

Given Data / Assumptions:

• Hollow metallic guide with internal dimensions a (width) and b (height).
• Operation in the dominant TE10 mode is desired over a useful frequency band.
• Design targets include manageable cutoff and reasonable higher-mode separation.

Concept / Approach:

For TE10, the cutoff frequency is fc = c / (2a) in an air-filled guide. Choosing a ≈ 2b balances TE10 dominance and mechanical strength while avoiding overly high aspect ratios that may invite unwanted mode behavior or fabrication issues. Industry waveguide families (e.g., WR series) follow this proportion closely.

Step-by-Step Solution:

Verification / Alternative check:

Datasheets for standard guides (e.g., WR90: a = 0.9 in, b = 0.4 in) show a/b ≈ 2.25; other bands are similar, validating the rule of thumb.

Why Other Options Are Wrong:

• 0.5 and 1: would not yield the typical dominant-mode spacing and are uncommon in standards.
• 4 or 10: impractically wide; would encourage higher-mode issues and mechanical problems.

Common Pitfalls:

Assuming exact 2.0 in every standard; actual ratios vary slightly but cluster near 2.

Final Answer:

2 (width is about twice the height)