Wave guide

History:

J. J. Thomson suggested the first wave-guiding structure in 1893, and Oliver Lodge tested it for
the first time in 1894. Lord Rayleigh produced the first mathematical study of electromagnetic
waves in a metal cylinder in 1897. In his landmark book, "The Theory of Sound," Lord Rayleigh
presented a complete mathematical study of propagation modes for sound waves. Jagadish
Chandra Bose investigated milli metre wavelengths using waveguides, and presented his findings
to the Royal Institution in London in 1897.

A waveguide is a structure that directs waves, such as electromagnetic waves or sound waves,
with minimum energy loss by limiting energy transfer to one direction. Wave intensities fall
according to the inverse square law when they spread into three-dimensional space without the
physical limitation of a waveguide.

Waveguides are a device (or "a guide") that transports electromagnetic energy from one location
to another. Waveguides are typically hollow metal tubes (often rectangular or circular in cross
section). They have the ability to precisely direct power where it is required, can handle
enormous quantities of power, and can also act as a high-pass filter.

The waveguide serves as a high pass filter, allowing most energy above a particular frequency
(the cutoff frequency) to pass through while attenuating radiation below the cutoff frequency. At
microwave frequencies, waveguides are often utilised (greater than 300 MHz, with 8 GHz and
above being more common).

Wideband devices, waveguides may transport (or transmit) both power and communication
signals. The figure below shows an example of a hollow metal rectangular waveguide.
As demonstrated in the accompanying Figure, waveguides may bend if the application needs it.

The waveguides mentioned above can be utilised using waveguide to coaxial cable adapters, as
demonstrated in the following diagram:
We now have a better understanding of what a waveguide is. Let's take a look at metal cavities
with a rectangular cross section, as seen in Figure 1. Assume the waveguide is filled with
vaccuum, air or a dielectric with permeability and permittivity ε of and respectively µ.

The waveguide has an x-direction width of a and a y-direction height of b, with a>b. The z-axis
represents the waveguide's power transmission direction.

Cross section of a waveguide with long dimension a and short dimension b.

The cutoff frequency, fc, is the first and arguably most essential feature of this waveguide. The
cutoff frequency is the frequency at which the waveguide attenuates all lower frequencies and
allows all higher frequencies to travel within the waveguide.
The cutoff frequency determines the waveguide's high-pass filter characteristic: power is sent
through the waveguide above this frequency, while power is attenuated or blocked below this
frequency. The cutoff frequency is determined by the waveguide's cross section form and size.
The waveguide's cutoff frequency decreases as the waveguide becomes bigger. The cutoff
frequency of a rectangular cross sectioned waveguide may be calculated using the following
formula:

The speed of light within the waveguide is c, the permeability of the material that fills the
waveguide is mu, and the permittivity of the material that fills the waveguide is epsilon. It's
worth noting that the cutoff frequency is unaffected by the waveguide's short length b.

For a waveguide with a circular cross section of radius a, the cutoff frequency is given by:

The fields within the waveguide always have a certain "form" or "waveshape" according to
Maxwell's Equations, which are referred to as modes. Assume the waveguide is positioned so
that the energy is transferred along the z-axis, which is the waveguide's axis. TE ('transverse
electric' - denotes that the E-field is orthogonal to the axis of the waveguide, so Ez=0) and TM
('transverse magnetic' - indicates that the H-field is orthogonal to the axis of the waveguide, so
Hz = 0) are the two modes. The modes are further divided into TEij and TEij. The modes are
further categorised as TEij, with I and j denoting the number of wave oscillations for a given
field direction in the long (dimension an in Figure 1) and short (dimension b in Figure 1)
directions, respectively.
Principle:

In free space, spherical waves spread in all directions. The strength of the wave decreases with
the square of the distance R from the source (inverse square law). A waveguide limits the wave
to travel in one dimension, ensuring that the wave loses no power when propagating under ideal
conditions. Waves are restricted to the inside of a waveguide due to complete reflection at the
walls.

Uses

Waveguides were used for transmitting signals long before the word was created. Sound waves
directed by a tight wire, as well as sound through a hollow pipe such as a cave or a medical
stethoscope, have been known for a long time. Waveguides are also used to transport power
between system components such as radio, radar, and optical equipment. The essential premise
of guided wave testing (GWT), one of several non-destructive assessment methods, is
waveguides.

 Optical fibres transport light and data across great distances with low attenuation and a
broad wavelength range.
 A waveguide transmits electricity from the magnetron, where waves are produced, to the
cooking chamber of a microwave oven.
 A waveguide in a radar transmits radio frequency energy to and from the antenna, and the
impedance must be matched for effective power transmission.
 Rectangular and circular waveguides are frequently used to connect parabolic dish feeds
to their electronics, which can be either low-noise receivers or power
amplifier/transmitters.
 In scientific equipment, waveguides are used to measure the optical, acoustic, and elastic
characteristics of materials and objects. The waveguide can be placed in touch with the
specimen (as in medical ultrasonography) to guarantee that the testing wave's power is
conserved, or the specimen can be placed inside the waveguide (as in dielectric constant
measurement) to test smaller objects with greater precision.
 Transmission lines are a form of waveguide that is widely utilised.
Properties:

Propagation modes and cutoff frequencies:

In a waveguide, a propagation mode is one solution of the wave equations, or the shape of the
wave. The wave function can only travel through the waveguide in a restricted number of
frequencies and shapes due to the boundary conditions' limitations. The cutoff frequency of a
certain mode is the lowest frequency at which it may propagate. The basic mode of the
waveguide has the lowest cutoff frequency, and its cutoff frequency is the waveguide cutoff
frequency. The Helmholtz equation is used to calculate propagation modes, coupled with a set of
boundary conditions based on the geometrical form and materials that surround the area. For
indefinitely long uniform waveguides, the common assumption is that the wave has a
propagating form, which states that every field component has a known dependence on the
propagation direction.