Analysis
Electromagnetic waveguides are analyzed by solving Maxwell's equations, or their reduced form, the electromagnetic wave equation, with boundary conditions determined by the properties of the materials and their interfaces. These equations have multiple solutions, or modes, which are eigenfunctions of the equation system. Each mode is characterized by a cutoff frequency below which the mode cannot exist in the guide.
Waveguide propagation modes depend on the operating wavelength and polarization and the shape and size of the guide. The longitudinal mode of a waveguide is a particular standing wave pattern formed by waves confined in the cavity. The transverse modes are classified into different types:
- TE modes (Transverse Electric) have no electric field in the direction of propagation.
- TM modes (Transverse Magnetic) have no magnetic field in the direction of propagation.
- TEM modes (Transverse ElectroMagnetic) have no electric nor magnetic field in the direction of propagation.
- Hybrid modes have both electric and magnetic field components in the direction of propagation.
In hollow waveguides (single conductor), TEM waves are not possible, since Maxwell's Equations will give that the electric field must then have zero divergence and zero curl and be equal to zero at boundaries, resulting in a zero field. (or, equivalently, with boundary conditions guaranteeing only the trivial solution). However, TEM waves can propagate in coaxial cable because there are two conductors.
The mode with the lowest cutoff frequency is termed the dominant mode of the guide. It is usual to choose the size of the guide such that only this one mode can exist in the frequency band of operation. In rectangular and circular (hollow pipe) waveguides, the dominant modes are designated the TE1,0 mode and TE1,1 modes respectively.
-
TE1,0 mode of a rectangular hollow metallic waveguide.
-
TE1,1 mode of a circular hollow metallic waveguide.
Read more about this topic: Waveguide (electromagnetism)
Famous quotes containing the word analysis:
“The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.”
—Henry Brooks Adams (1838–1918)
“A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.”
—Karl Marx (1818–1883)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)