An Introduction to Circular Waveguide Modes

Key Takeaways

• Circular waveguides are waveguides with a circular cross-section.

• The lowest order propagation mode in a circular waveguide is TE₁₁, which offers minimal degradation of signals.

• The possible TM modes in circular waveguides are TM₀₁ , TM₀₂ , TM₁₁, and TM₁₂. 

Whenever high-frequency electromagnetic wave propagation is present, waveguides are used. Waveguides are useful for directing and propagating electromagnetic waves such as radiofrequency waves, microwaves, and infrared waves from one point to another. There are several types of waveguides used for electromagnetic wave propagation, and some of the parameters for their selection are the waveguide material, mode of propagation, cut-off frequency, and cross-section.

One such waveguide is called a circular waveguide, which is a waveguide with a circular cross-section. Circular waveguide modes are generally variants of the transverse electric (TE) and transverse magnetic (TM) modes. The field distribution of each mode varies with the circumferential and radial variations in the circular waveguide. 

Let’s discuss circular waveguides and their modes of propagation, cut-off frequency, and applications a little further.

Circular Waveguides: Their Advantages and Disadvantages

As the name suggests, circular waveguides have a circular cross-section and support TE as well as TM modes. Compared to rectangular waveguides, circular waveguides are easier to construct. However, circular waveguides are less desirable than rectangular waveguides due to the following reasons:

• In a circular waveguide, the difference between the dominant mode’s lowest frequency and the next mode’s frequency is smaller than in a rectangular waveguide.
• The circular cross-section can limit the polarization of the wave throughout its length. 
• The size of the circular waveguide is larger than the rectangular waveguide for the given operating frequency. 

Despite these disadvantages, engineers still use circular waveguides for a variety of applications due to advantages such as: 

• Easy manufacturability.
• The ability to make easy joins.
• Low attenuation rates for a given cut-off frequency.
• High power handling capacity.
• The presence of  TM₀₁ modes that are rotationally symmetrical, which helps to overcome rotation of polarization.
• The suitability of long-distance waveguide transmission due to the modes with the lowest attenuation per unit length (Example: TE₀₁).

Let’s take a look at the types of circular waveguide modes. 

Circular Waveguide Modes  

The distribution of longitudinal and transverse magnetic and electric fields inside circular waveguides yields different transverse magnetic and transverse electric waveguide modes with index numbers m and n. The letters m and n represent the number of radial, axial, or circumferential field variations in the circular waveguide, respectively. 

TE Modes in Circular Waveguides

In TE modes of the circular waveguide, there is not a longitudinal component of electric fields. Only the longitudinal components of the magnetic field are present in TE modes. Corresponding to the m and n values, there are variants of TE modes present in circular waveguides, such as TE₀₁, TE₀₂ , TE₁₁, and TE₁₂. TE₀₁ is the  TE mode in the circular waveguide that offers low attenuation characteristics with increasing frequency. The TE₁₁ mode is the dominant mode and is the most frequently-used TE mode in circular waveguides. It is the lowest order propagation mode in a circular waveguide and offers minimal degradation of signals.

TM Modes in Circular Waveguides 

In TM modes of the circular waveguide, there is an absence of magnetic fields in the direction of propagation; only electric fields exist. The possible TM modes in a circular waveguide are TM₀₁ , TM₀₂ , TM₁₁, and TM₁₂. TM₀₁   is the dominant TM mode in a circular waveguide.

The Cut-Off Frequency of Circular Waveguides

The cutoff frequency is an important parameter associated with the propagation modes of a circular waveguide. The term “cutoff frequency” of a circular waveguide defines the lowest frequency at which mode propagation exists. 

The cut-off frequency of a circular waveguide is dependent on its geometry and is inversely proportional to the radius of the circle. There are fixed waveguide sizes available for each frequency band in circular waveguides. 

For the transverse electric and transverse magnetic modes in a circular waveguide, the cut-off frequency can be  given by the following formula, where k_c is the cut-off wavenumber and and are the permeability and permittivity of the dielectric used in the circular waveguide, respectively.

https://drive.google.com/file/d/1AxYeCdEqldp3dtsbc2Dtgt3-VK3J7RL2/view     

Where Are Circular Waveguides Used?

Circular waveguides find application in:

• Attenuators 
• Phase-shifters
• Antennas
• Radar systems
• Waveguide transmission above 10GHz 

For each application, different circular waveguide modes and cut-off frequencies are required. The circular waveguide radius is designed according to application specifications. Cadence can help in the designing of not only circular waveguides, but also  the waveguides of any cross-section.  

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