The Rectangular Waveguide Cut-Off Frequency

Key Takeaways

• The cut-off frequency is the frequency above which the waveguide offers minimum attenuation to the propagation of the signal. 

• Frequencies below the cut-off frequency are attenuated by the waveguide.  

• The dominant mode in a waveguide is the propagation mode with the lowest cut-off frequency. 

When selecting an electrical component, designers should focus on the component’s specification or rating. While there are many specifications to consider, there are a few key ones to focus on in each component being used in a circuit. 

In RF and microwave circuits, the cut-off frequency is a significant specification for waveguides. In a rectangular waveguide being used to transfer energy, the rectangular waveguide cut-off frequency determines when the waveguide becomes obsolete, which is whenever it reaches below the cut-off frequency. A similar condition applies to circular waveguides, however, in this article, we will focus on the rectangular waveguide cut-off frequency.

Waveguide Cut-Off Frequency

Waveguides are hollow metallic structures that carry signals from one end to another. All the signals that propagate through a waveguide are above a certain frequency, called the cut-off frequency. Below the cut-off frequency, waveguides fail to transfer wave energy or propagate waves.

Cut-off frequency can also be described as the frequency above which the waveguide offers minimum attenuation to the propagation of the signal. Frequencies below the cut-off frequency are attenuated by the waveguide. The signal propagation through a waveguide is dependent on the signal wavelength as well. When a wavelength is too long, the waveguide stops carrying signals and becomes inoperative. 

The Geometry of Waveguides

The geometry of a waveguide is an important factor in determining the cut-off frequency.  There can be various modes in a waveguide, such as TE₁₀, TE₂₀, TE₃₀, or TM modes. However, if all modes are active in a waveguide, it results in attenuation of the signal. Only one mode should be active and waveguide dimensions should be selected so that the waveguide only supports one active mode. 

How to Avoid Signal Attenuation and Power Loss

To avoid signal attenuation and power loss from multiple active modes, waveguides should be constructed with their cut-off frequency in mind. When trying to pass signals of lower frequency than the cut-off frequency, the waveguide develops mechanical constraints. During waveguide construction, it is recommended to keep the width of a waveguide in the same order of magnitude as the wavelength of the signal being transmitted. As the waveguide gets larger, it lowers its cut-off frequency. 

In the electronics market, waveguides are available in standard sizes; however, if you wish to use waveguides for specific applications, they should be custom made.

The Equation for Rectangular Waveguide Cut-Off Frequency

Consider a rectangular waveguide with width ‘a’ and thickness ‘b’. Let TE_mn be the mode active in the waveguide. To calculate the cut-off frequency f_c of the rectangular waveguide, use the following equation, where c is the speed of the light inside the waveguide and m and n are the numbers that define the mode of propagation.

Dominant and Degenerate Modes

Dominant Mode

The dominant mode in a waveguide is the propagation mode with the lowest cut-off frequency. The criterion for wave propagation through the waveguide is that the operating frequency should be greater than the dominant mode cut-off frequency. There will be minimum degradation of the signal in the dominant mode. 

Degenerate Mode

We know that the rectangular waveguide does not support TEM mode. It allows either TE mode or TM mode. If any two modes of propagation share the same cut-off frequency, such modes are called degenerate modes. The modes TE_mn and TM_mn are degenerate modes in a rectangular waveguide. 

The rectangular waveguide cut-off frequency is a critical specification associated with rectangular waveguides, below which there is no signal propagation. If you are trying to design a waveguide, Cadence’s software helps you to design waveguides that support wave propagation in a given band of frequencies. 

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