# Modes of Wave Propagation Along Transmission Lines

### Key Takeaways

• In microwave applications, power is stored in electric and magnetic fields, and the transmission lines in such systems are considered rare electromagnetic systems.

• According to the direction of oscillation and propagation, there are different modes of wave propagation on transmission lines.

• When a time-varying signal starts to flow through a transmission line, it aligns the electric and magnetic fields in different directions and establishes various modes of wave propagation.

The way in which electromagnetic waves travel from source to load describes the wave propagation along a transmission line. In microwave applications, electromagnetic wave power is stored in electric and magnetic fields and the transmission lines in such systems are considered rare electromagnetic systems.

According to the direction of oscillation and propagation, there are different modes of wave propagation along transmission lines. Depending on the frequency and type of transmission line or waveguide used, the mode of propagation varies. In this article, we will discuss the various modes of wave propagation along a transmission line.

## The Modes of Wave Propagation Along a Transmission Line

Electromagnetic waves have both electric and magnetic fields that are perpendicular to each other and travel in the same direction. The transverse components of electric and magnetic fields are determined by their components in the z direction. When a time-varying signal starts to flow through a transmission line, it aligns the electric and magnetic fields in different directions and establishes various modes of wave propagation.

The modes of wave propagation can be categorized as the following:

### Transverse Electric and Magnetic (TEM) Mode

TEM, also referred to as transmission line mode, is the principal mode of wave propagation and exists only in transmission lines made of two conductors. This mode becomes dominant in wave propagation where the cross-sectional area of the transmission line is small compared to the signal wavelength. That means the electric and magnetic fields are transverse to the direction of propagation in this mode. The z axis components of electric and magnetic fields are equal to zero. Transmission lines support TEM mode with two conductors and have uniquely defined voltage, current, and characteristic impedance. When the frequency is very small, quasi-TEM modes are used to approximate the TEM modes.

### Transverse Magnetic (TM) Mode

In this mode, the magnetic field is purely transverse to the direction of wave propagation and the electric field does not follow suit. The electric field has both transverse and longitudinal components.

### Transverse Electric (TE) Mode

In this mode, the electric field is transverse to the direction of wave propagation and the magnetic field is not. The magnetic field has both transverse and longitudinal components.

#### In TE, Hz≠0, Ez=0

TE and TM modes are commonly found in enclosed guiding structures and are generally called waveguide modes. Both of these modes are dispersive, where the phase velocity is dependent on frequency. As transmission lines generally operate below this cut-off frequency, they support only TEM mode. TE and TM modes are limited by a cut-off frequency below which there is no wave propagation through it. This cut-off frequency causes limited bandwidth in these modes.

### 4) Hybrid Wave Mode

In this mode, the wave propagates in z direction. None of the fields are purely transverse to the direction of propagation in this mode. Both the magnetic and electric fields have longitudinal components. When the longitudinal electric field is dominant, the hybrid wave mode is called EH mode. When the longitudinal magnetic field is dominant, the hybrid wave mode is called HE mode. This mode is usually observed in waveguides with inhomogeneous dielectric and in optical fibers.

## Types of Transmission Lines

The table below describes the conductors that support various modes of wave propagation.

 Mode of Wave Propagation Type of Transmission Line TEM Co-axial line, two-wire line, parallel-plate line, stripline, microstrip line, multi-conductor lines, and coplanar waveguides TE or TM Metal or optical fiber waveguides, cavity resonators Hybrid wave mode Optical fibers, open conductor guides

The modes of wave propagation along a transmission line depend on the direction of the electric and magnetic field, and this direction changes with the type of transmission line. Wave propagation can be analyzed using either electromagnetic field theory or electric circuit theory. When solving the transmission line problem using circuit theory, designers must mathematically represent the line in circuit parameters such as resistance, inductance, capacitance, and conductance. In field theory analysis, equations should be written in terms of electric and magnetic fields. In both these analyses, we are solving the wave equation for a solution.