Short note: Dominant mode in waveguide

The dominant mode of a waveguide is the propagating mode with the lowest cut-off frequency (longest cut-off wavelength). Below its cut-off no energy propagates; between its cut-off and that of the next higher mode, only the dominant mode can travel, which gives clean single-mode operation.

Rectangular waveguide (a > b):

 fc,mn = (c/2) √((m/a)² + (n/b)²)
 TE10: fc = c/(2a),  λc = 2a   (dominant)

TE10 has only Ey, Hx and Hz components; E is maximum at the centre of the broad wall and zero at the side walls. TM modes start at TM11, which is always higher.

Circular waveguide (radius r): dominant mode TE11 (p'11 = 1.841), fc = 1.841c/(2πr), λc = 3.41r. The lowest TM mode is TM01 (λc = 2.61r).

Why the dominant mode is used:

• Single-mode operation avoids mode conversion and distortion.
• Lowest attenuation for a given size (in rectangular guides) and simple field pattern for coupling with probes.
• Easy design of components (tees, couplers) for one known field pattern.

Example: WR-90 guide (a = 2.286 cm, b = 1.016 cm): fc(TE10) = 6.56 GHz, next mode TE20 at 13.12 GHz. It is used in the X-band (8.2–12.4 GHz), where only TE10 propagates.