The impedance of free space, Z0, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, Z0 = |E|/, where |E| is the electric field strength and |H| is the magnetic field strength. It currently has an exactly defined value
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.
In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.
The impedance of free space (more correctly, the wave impedance of a plane wave in free space) equals the product of the vacuum permeability μ0 and the speed of light in vacuum c0. Since the values of these constants are exact (they are given in the definitions of the ampere and the metre respectively), the value of the impedance of free space is likewise exact. However, with the redefinition of the SI base units which are going into force on May 20, 2019, this value is subject to experimental measurement.
In the physics of wave propagation, a plane wave is a wave whose wavefronts are infinite parallel planes. Mathematically a plane wave takes the form
The physical constant μ0,, commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum.
The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second. It is exact because by international agreement a metre is defined to be the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most commonly associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.
The analogous quantity for a plane wave travelling through a dielectric medium is called the intrinsic impedance of the medium, and designated η (eta). Hence Z0 is sometimes referred to as the intrinsic impedance of free space , and given the symbol η0. It has numerous other synonyms, including:
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.
An optical medium is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by
Eta is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its sound value in the classical Attic dialect of Ancient Greek was a long vowel, raised to [i] in hellenistic Greek, a process known as iotacism.
From the above definition, and the plane wave solution to Maxwell's equations,
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.
The reciprocal of Z0 is sometimes referred to as the admittance of free space and represented by the symbol Y0.
Since 1948, the definition of the SI unit ampere has relied upon choosing the numerical value of μ0 to be exactly 4π × H/m10−7. Similarly, since 1983 the SI metre has been defined relative to the second by choosing the value of c0 to be 792458 m/s. Consequently, 299
The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.
The henry is the SI derived unit of electrical inductance. If a current of 1 ampere flowing through the coil produces flux linkage of 1 weber turn, the coil has a self inductance of 1 henry. The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.
The metre or meter is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second.
This chain of dependencies will change when the ampere is redefined on 20 May 2019. See New SI definitions.
It is very common in textbooks and papers written before about 1990 to substitute the approximate value 120π ohms for Z0. This is equivalent to taking the speed of light c0 to be precisely ×108 m/s in conjunction with the current definition of 3μ0. For example, Cheng 1989 states that the radiation resistance of a Hertzian dipole is
This practice may be recognized from the resulting discrepancy in the units of the given formula. Consideration of the units, or more formally dimensional analysis, may be used to restore the formula to a more exact form, in this case to
The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.
In electromagnetism, there are two kinds of dipoles:
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced rather than passing through.
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 change per unit length, but it is otherwise dimensionless. 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.
The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.
Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be used interchangeably.
In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.
The Smith chart, invented by Phillip H. Smith (1905–1987), is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits. The Smith chart can be used to simultaneously display multiple parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, including mechanical vibrations analysis. The Smith chart is most frequently used at or within the unity radius region. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis.
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave, and its direction is ordinarily the direction of wave propagation.
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter µ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.
The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has an exactly defined value that can be approximated as
In microwave and radio-frequency engineering, a stub or resonant stub is a length of transmission line or waveguide that is connected at one end only. The free end of the stub is either left open-circuit or short-circuited. Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus function as capacitors, inductors and resonant circuits at radio frequencies.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Antenna measurement techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, radiation pattern, beamwidth, polarization, and impedance.
When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:
An LC circuit can be quantized using the same methods as for the quantum harmonic oscillator. An LC circuit is a variety of resonant circuit, and consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C. When connected together, an electric current can alternate between them at the circuit's resonant frequency:
In quantum field theory, and especially in quantum electrodynamics, the interacting theory leads to infinite quantities that have to be absorbed in a renormalization procedure, in order to be able to predict measurable quantities. The renormalization scheme can depend on the type of particles that are being considered. For particles that can travel asymptotically large distances, or for low energy processes, the on-shell scheme, also known as the physical scheme, is appropriate. If these conditions are not fulfilled, one can turn to other schemes, like the Minimal subtraction scheme.