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The **impedance of free space**, *Z*_{0}, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, *Z*_{0} = |**E**|/|**H**|, 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.

- Terminology
- Relation to other constants
- Exact value
- Approximation as 120π ohms
- See also
- References and notes
- Further reading

The impedance of free space (more correctly, the wave impedance of a plane wave *in* free space) equals the product of the vacuum permeability *μ*_{0} and the speed of light in vacuum *c*_{0}. 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 *μ*_{0},, 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,

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 *Z*_{0} is sometimes referred to as the *intrinsic impedance of free space *,^{ [1] } and given the symbol *η*_{0}.^{ [2] } 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.

*wave impedance of free space*,^{ [3] }*the vacuum impedance*,^{ [4] }*intrinsic impedance of vacuum*,^{ [5] }*characteristic impedance of vacuum*,^{ [6] }*wave resistance of free space*.^{ [7] }

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.

where

*μ*_{0}is the magnetic constant,*ε*_{0}is the electric constant,*c*_{0}is the speed of light in free space.^{ [8] }^{ [9] }

The reciprocal of *Z*_{0} is sometimes referred to as the *admittance of free space* and represented by the symbol *Y*_{0}.

Since 1948, the definition of the SI unit ampere has relied upon *choosing* the numerical value of *μ*_{0} to be exactly 4π × ^{−7} H/m 10. Similarly, since 1983 the SI metre has been defined relative to the second by *choosing* the value of *c*_{0} 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.

*exactly*,

or

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 *Z*_{0}. This is equivalent to taking the speed of light *c*_{0} to be precisely ×10^{8} m/s in conjunction with the current definition of 3*μ*_{0}. For example, Cheng 1989 states^{ [2] } that the radiation resistance of a Hertzian dipole is

- (
*not exact*).

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

- ↑ Haslett, Christopher J. (2008).
*Essentials of radio wave propagation*. The Cambridge wireless essentials series. Cambridge University Press. p. 29. ISBN 978-0-521-87565-3. - 1 2 David K Cheng (1989).
*Field and wave electromagnetics*(Second ed.). New York: Addison-Wesley. ISBN 0-201-12819-5. - ↑ Guran, Ardéshir; Mittra, Raj; Moser, Philip J. (1996).
*Electromagnetic wave interactions*. Series on stability, vibration, and control of systems. World Scientific. p. 41. ISBN 978-981-02-2629-9. - ↑ Clemmow, P. C. (1973).
*An introduction to electromagnetic theory*. University Press. p. 183. ISBN 978-0-521-09815-1. - ↑ Kraus, John Daniel (1984).
*Electromagnetics*. McGraw-Hill series in electrical engineering. McGraw-Hill. p. 396. ISBN 978-0-07-035423-4. - ↑ Cardarelli, François (2003).
*Encyclopaedia of scientific units, weights, and measures: their SI equivalences and origins*. Springer. p. 49. ISBN 978-1-85233-682-0. - ↑ Ishii, Thomas Koryu (1995).
*Handbook of Microwave Technology: Applications*. Academic Press. p. 315. ISBN 978-0-12-374697-9. - ↑ With ISO 31-5, NIST and the BIPM have adopted the notation
*c*_{0}for the speed of light in free space. - ↑ "Current practice is to use
*c*_{0}to denote the speed of light in vacuum according to ISO 31. In the original Recommendation of 1983, the symbol*c*was used for this purpose." Quote from NIST*Special Publication 330*, Appendix 2, p. 45.

- John David Jackson (1998).
*Classical electrodynamics*(Third ed.). New York: Wiley. ISBN 0-471-30932-X.

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 ** ε_{0}**, commonly called the

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.

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