Single-Mode Operation in an Air-Filled Rectangular Waveguide (Dominant TE10 Only) To ensure that only the dominant TE10 mode propagates, what practical lower and upper operating frequency limits are chosen relative to the cutoff of TE10 and the next higher mode (TE20)?

Introduction / Context:
Rectangular waveguides are designed to operate in single-mode—typically the dominant TE10 mode—to avoid dispersion jumps, mode conversion, and pattern distortion. This question asks for the practical frequency window that ensures only TE10 propagates in an air-filled guide.

Given Data / Assumptions:

• Air-filled rectangular waveguide.
• Dominant mode is TE10 with cutoff frequency fc(TE10).
• The next higher mode is commonly TE20 with cutoff fc(TE20).
• We seek a practical, not purely theoretical, operating band.

Concept / Approach:

A safe single-mode band avoids the vicinity of fc(TE10) (where attenuation is high and fields are very dispersive) and also stays below fc(TE20) to prevent multimode propagation. A widely used engineering rule is to operate from about 1.25 * fc(TE10) up to about 0.95 * fc(TE20). This builds margin for manufacturing tolerances, temperature/refractive-index variations, and network transitions.

Step-by-Step Solution:

Verification / Alternative check:

Standard waveguide band tables (e.g., WR-series) reflect this single-mode window; connectors and components are specified so normal operation falls within these limits.

Why Other Options Are Wrong:

50% or 25% gaps around both cutoffs are unnecessarily wide or mis-centered. Operating at either cutoff is impractical due to high attenuation or multi-mode onset.

Common Pitfalls:

Confusing cutoff frequency margins with bandwidth of a component; forgetting that higher-order modes start at their own cutoffs, not at harmonics of TE10.

Final Answer:

about 25% above fc for TE10 and 5% below fc for TE20 mode respectively