# TE Modes in Rectangular and Circular Waveguides

### Key Takeaways

•  In TE mode, Hz≠0, Ez=0.

• The TE10 mode is the dominant TE mode in rectangular waveguides.

• The TE11 mode is the dominant TE mode in circular waveguides. For the propagation of high-frequency waves such as radiofrequency waves, microwaves, or infrared waves, waveguides are commonly used. Waveguides are structures that are used to guide electromagnetic waves to a targeted destination. They transmit energy in one direction (towards the destination) with minimum loss.

The propagation of electromagnetic waves through a waveguide depends on the type of electromagnetic wave and the medium inside it. Wave propagation takes different modes depending on the distribution of the electric and magnetic field with respect to the direction of propagation. Each mode is different; transverse electric mode (TE mode) is one such mode in waveguide propagation that is seen in rectangular waveguides and circular waveguides.

## Electromagnetic Wave Propagation in Waveguides

Waveguide structures transmit electromagnetic energy within a certain frequency range from source to destination. The propagation of waves can be either transverse electric (TE) mode or transverse magnetic (TM) mode. As a waveguide structure is made of a single conductor, transverse electromagnetic mode (TEM) is not supported by them.

In both the TE and TM modes of propagation, the electric fields and magnetic fields oscillate. Depending on the mode, the axis of oscillation changes its orientation with respect to the direction of propagation.

## TE Mode in Waveguides

In the TE mode of electromagnetic wave propagation, the electric field is transverse to the direction of propagation (z-axis), but the magnetic field is not only transverse. The magnetic field has both transverse and longitudinal components. Only magnetic fields exist in the direction of propagation.

In TE, Hz≠0, Ez=0

For each waveguide, the wave equation can be written on the condition prevailing for TE mode and the solution corresponds to magnetic fields. The solutions are distinguished from each other using mode indexes and are represented as TEmn or Hmn

### TE Modes in Rectangular Waveguides

In radars, couplers, isolators, and attenuators, rectangular waveguides are used for signal transmission. The longitudinal transmission of electromagnetic waves through a rectangular waveguide leads to waves reflecting from the conducting walls. The total reflection inside the rectangular waveguide results in either an electric field or magnetic field component in the direction of propagation. When the electric fields are normal to the direction of propagation, they form the TE modes in a rectangular waveguide.

By solving the wave equation in a rectangular waveguide, with length and breadth given by ‘a’ and ‘b’ respectively, the solution is obtained as the equation below, where m=0, 1, 2 and n=0, 1, 2, but m≠n. kzis the z component of the wave vector.

The magnetic fields corresponding to (m, n) in the equation above causes the  TEmn mode in rectangular waveguides. The TE10 mode is the dominant mode in the rectangular waveguide.

### TE Modes in Circular Waveguides

The longitudinal and transverse magnetic and electric fields inside circular waveguides are distributed in different ways for each given wave. Under TE modes in a circular waveguide, there are no longitudinal components of electric fields; only magnetic fields are present. In a circular waveguide, the TE modes are represented as TEmn modes, where m and n give the radial and axial field variations in the internal waveguide structure.

TE11 mode is the dominant TE mode in circular waveguides. It establishes wave propagation with minimum attenuation of signals. The other active TE modes in circular waveguides are TE01, TE02, TE11, and TE12.

The dominant TE modes in rectangular and circular waveguides are determined by the geometric dimension of the waveguide and the cut-off frequency. Cadence software offers tools to design waveguides that support the different TE modes.  