25-04-2012, 01:09 PM
Waveguide
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A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave. The original and most common[1] meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves.
Waveguides differ in their geometry which can confine energy in one dimension such as in slab waveguides or two dimensions as in fiber or channel waveguides. In addition, different waveguides are needed to guide different frequencies: an optical fiber guiding light (high frequency) will not guide microwaves (which have a much lower frequency). As a rule of thumb, the width of a waveguide needs to be of the same order of magnitude as the wavelength of the guided wave.
There are structures in nature which act as waveguides: for example, the SOFAR channel layer in the ocean can guidewhale song enormous distances
Contents
[hide]
• 1 Principle of operation
• 2 History
• 3 Uses
• 4 A sketch of the theoretical analysis
o 4.1 Propagation modes and cutoff frequencies
o 4.2 Impedance matching
• 5 Electromagnetic waveguides
• 6 Optical waveguides
• 7 Acoustic waveguides
• 8 Sound synthesis
• 9 See also
• 10 References
• 11 External links
Principle of operation
Waves in open space propagate in all directions, as spherical waves. In this way they lose their power proportionally to the square of the distance; that is, at a distance R from the source, the power is the source power divided by R2. The waveguide confines the wave to propagation in one dimension, so that (under ideal conditions) the wave loses no power while propagating.
Waves are confined inside the waveguide due to total reflection from the waveguide wall, so that the propagation inside the waveguide can be described approximately as a "zigzag" between the walls. This description is exact for electromagnetic waves in a hollow metal tube with a rectangular or circular cross section.
[edit]History
The first structure for guiding waves was proposed by J. J. Thomson in 1893, and was first experimentally tested by Oliver Lodge in 1894. The first mathematical analysis of electromagnetic waves in a metal cylinder was performed by Lord Rayleigh in 1897.[3] For sound waves, Lord Rayleigh published a full mathematical analysis of propagation modes in his seminal work, “The Theory of Sound”.[4]
The study of dielectric waveguides (such as optical fibers, see below) began as early as the 1920s, by several people, most famous of which are Rayleigh,Sommerfeld and Debye.[5] Optical fiber began to receive special attention in the 1960s due to its importance to the communications industry.
[edit]Uses
Waveguide supplying power for theArgonne National Laboratory Advanced Photon Source.
The uses of waveguides for transmitting signals were known even before the term was coined. The phenomenon of sound waves guided through a taut wire have been known for a long time, as well as sound through a hollow pipe such as acave or medical stethoscope. Other uses of waveguides are in transmitting power between the components of a system such as radio, radar or optical devices. Waveguides are the fundamental principle of guided wave testing (GWT), one of the many methods of non-destructive evaluation.
Specific examples:
Optical fibers transmit light and signals for long distances and with a high signal rate.
In a microwave oven a waveguide transfers power from the magnetron where waves are formed, to the cooking chamber.
In a radar, a waveguide transfers Radio Frequency energy to and from the antenna, where the impedance needs to be matched for efficient power transmission (see below).
A waveguide called stripline can be created on a printed circuit board, and is used to transmit microwave signals on the board. This type of waveguide is very cheap to manufacture and has small dimensions which fit inside printed circuit boards.
Waveguides are used in scientific instruments to measure optical, acoustic and elastic properties of materials and objects. The waveguide can be put in contact with the specimen (as in a Medical ultrasonography), in which case the waveguide ensures that the power of the testing wave is conserved, or the specimen may be put inside the waveguide (as in a dielectric constant measurement[6]), so that smaller objects can be tested and the accuracy is better.
[edit]A sketch of the theoretical analysis
This article's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced. See the relevant discussion on the talk page. (January 2010)
Electromagnetic wave propagation along the axis of the waveguide is described by the wave equation, which is derived from Maxwell's equations, and where thewavelength depends upon the structure of the waveguide, and the material within it (air, plastic, vacuum, etc.), as well as on the frequency of the wave.
The spatial distribution of the time-varying electric fields and magnetic fields within the waveguide depends on boundary conditions imposed by the shape and materials of the waveguide. Let us assume that the waveguide is made of a metal that is such a good conductor that we can consider it to be a perfect conductor. Nearly all waveguides have copper interiors, but some of them are even plated with silver or gold on the inside - excellent conductors, and also resistant to corrosion. Now, the boundary conditions are these:
1). Electromagnetic waves do not pass through conductors, but rather, they are reflected.
2). Any electric field that touches a conductor must be perpendicular to it.
3). Any magnetic field close to a conductor must be parallel to it.
These boundary conditions eliminate an infinite number of solutions to the wave equation, and the ones that remain are the possible solutions to the wave equation inside the waveguide. The rest of the analysis of the solutions of the electromagnetic waves inside a waveguide gets very mathematical.
All that remains that can be said without getting very mathematical is that commonly-used waveguides are only of a few categories. The most common kind of waveguide is one that has a rectangular cross-section, one that is usually not square. It is common for the long side of this cross-section to be twice as long as its short side. These are useful for carrying electromagnetic waves that have a horizontal or vertical polarization to them.
The second most commonly used kind of waveguide has a circular cross-section. These turn out to be quite useful when carrying electromagnetic waves with a rotating, circular polarization to them. Then, its electrical field traces out a helical pattern as a function of time.
The third kind of a waveguide - actually a seldom-used one - has an elliptical cross-section.