The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.
In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor. In other words, it is the length of the conductor measured in wavelengths. It can alternately be expressed as an angle, in radians or degrees, equal to the phase shift the alternating current experiences traveling through the conductor.
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the dimensionless change in magnitude or phase per unit length. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next.
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances. However, the theory of transmission lines was historically developed to explain phenomena on very long telegraph lines, especially submarine telegraph cables.
Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.
Coaxial cable, or coax, is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ; many coaxial cables also have a protective outer sheath or jacket. The term coaxial refers to the inner conductor and the outer shield sharing a geometric axis.
Line-of-sight propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves can only travel in a direct visual path from the source to the receiver without obstacles. Electromagnetic transmission includes light emissions traveling in a straight line. The rays or waves may be diffracted, refracted, reflected, or absorbed by the atmosphere and obstructions with material and generally cannot travel over the horizon or behind obstacles.
Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.
In the physical sciences, the wavenumber, also known as repetency, is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time or radians per unit time.
In optics and in wave propagation in general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium.
In electromagnetism, skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the conductor. It is caused by opposing eddy currents induced by the changing magnetic field resulting from the alternating current. The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth. Skin depth depends on the frequency of the alternating current; as frequency increases, current flow becomes more concentrated near the surface, resulting in less skin depth. Skin effect reduces the effective cross-section of the conductor and thus increases its effective resistance. At 60 Hz in copper, skin depth is about 8.5 mm. At high frequencies, skin depth becomes much smaller.
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency-dependence of wave propagation and attenuation.
A transmission line which meets the Heaviside condition, named for Oliver Heaviside (1850–1925), and certain other conditions can transmit signals without dispersion and without distortion. The importance of the Heaviside condition is that it showed the possibility of dispersionless transmission of telegraph signals.In some cases, the performance of a transmission line can be improved by adding inductive loading to the cable.
Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as "substrate". Microstrip lines are used to convey microwave-frequency signals.
The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated between two separated parties. No signal velocity can exceed the speed of a light pulse in a vacuum.
The telegrapher's equations are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. The equations and their solutions are applicable from 0 Hz to frequencies at which the transmission line structure can support higher order non-TEM modes. The equations can be expressed in both the time domain and the frequency domain. In the time domain the independent variables are distance and time. The resulting time domain equations are partial differential equations of both time and distance. In the frequency domain the independent variables are distance and either frequency, or complex frequency, The frequency domain variables can be taken as the Laplace transform or Fourier transform of the time domain variables or they can be taken to be phasors. The resulting frequency domain equations are ordinary differential equations of distance. An advantage of the frequency domain approach is that differential operators in the time domain become algebraic operations in frequency domain.
The word electricity refers generally to the movement of electrons, or other charge carriers, through a conductor in the presence of a potential difference or an electric field. The speed of this flow has multiple meanings. In everyday electrical and electronic devices, the signals travel as electromagnetic waves typically at 50%–99% of the speed of light in vacuum. The electrons themselves move much more slowly. See drift velocity and electron mobility.
The primary line constants are parameters that describe the characteristics of conductive transmission lines, such as pairs of copper wires, in terms of the physical electrical properties of the line. The primary line constants are only relevant to transmission lines and are to be contrasted with the secondary line constants, which can be derived from them, and are more generally applicable. The secondary line constants can be used, for instance, to compare the characteristics of a waveguide to a copper line, whereas the primary constants have no meaning for a waveguide.
