# The Types of Losses in a Rectangular Waveguide

### Key Takeaways

• Rectangular waveguides are widely used in high-power applications due to their low loss propagation.

• The two types of losses in a rectangular waveguide are dielectric losses and conductor (metallic) losses in the walls.

• Total attenuation is the sum of the attenuation caused by conductor and dielectric losses. A rectangular waveguide

Waveguides are ubiquitous in systems requiring electromagnetic wave propagation. Parallel-plate waveguides, circular waveguides, and rectangular waveguides are some of the types of waveguides used. The shape of the waveguide for a given application is determined by considering the mode of propagation, frequency of the signal, cut-off frequency, losses, etc.

In a rectangular waveguide, the cross-section of the waveguide is a rectangle. Rectangular waveguides are extensively used for microwave and millimeter-wave propagation due to their flexibility. The cut-off frequency of a rectangular guide is dependent on the length and breadth of the cross-section. The two types of losses in a rectangular waveguide are dielectric losses and conductor (metallic) losses in the walls. Let’s take a closer look at these two types of losses and how they happen.

## The Types of Losses in Rectangular Waveguides

Rectangular waveguides transmit electromagnetic energy from one location to a destination through a path formed by its four walls. This type of waveguide supports either transverse electric or transverse magnetic modes of wave propagation, however, it does not support the transverse electromagnetic mode of wave propagation.  Rectangular waveguides are known for their low loss propagation.

### Conductor Losses

Conductor losses in rectangular waveguides are found to be lower than co-axial cables. The finite conductivity of the walls of rectangular waveguides are the cause of these conduction losses.

When an electromagnetic wave propagates through the rectangular waveguide, it creates current in the four walls. Due to the symmetry of the rectangular waveguide, the current in the top wall and bottom wall are identical. Similarly, the current in the left side and right side of the rectangular waveguide are equal. These currents are capable of disturbing the field distribution in the waveguide.

The impedance (Zs) offered by the waveguide material to the current flow through the walls causes finite conductor losses. There is a dependency between the conductor losses, frequency of wave propagation, and the dispersion characteristics of the rectangular waveguide. The dispersion characteristics vary with conductor losses at different impedances. The attenuation caused by conductor losses, denoted by c, is one of the factors worth considering when dealing with the total attenuation of the signal.

### Dielectric  Losses

Rectangular waveguides can be either air-filled or dielectric-filled. Typically, homogeneous dielectric materials are filled inside the waveguide. The attenuation caused by the dielectric material in electromagnetic power transmission is called dielectric loss. This type of loss is dependent on the permittivity and permeability of the dielectric material inside the rectangular waveguide. The dielectric losses in a rectangular waveguide are significant in determining the propagation constant. A rise in dielectric losses increases the propagation constant value.

## Dielectric Loss and the Propagation Constant in Rectangular Waveguides

The complex propagation constant of a rectangular waveguide can be written as the following equation, where dis the attenuation due to dielectric loss and is the phase constant: When the rectangular waveguide is filled with a dielectric of small loss tangent, the equation reduces to: Comparing the two equations above, we can say that the attenuation due to dielectric loss is dependent on the wave number (k), loss tangent, and phase constant.

## Total Attenuation in Rectangular Waveguides

The total attenuation of a rectangular waveguide describes the power lost from the transmitted electromagnetic energy. The total attenuation is the sum of the attenuation caused by conductor losses and dielectric losses. The total attenuation of a rectangular waveguide can be given by: When choosing a waveguide for high-power applications, total attenuation is an important parameter to consider, as it affects transmission reliability and waveguide efficiency. The attenuation caused by the two types of losses in a rectangular waveguide can be calculated using methods such as the perturbation method or the wheeler incremental inductance method.