Neha Patil (Editor)

Impedance of free space

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

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 | / | H |, where | E | is the electric field strength and | H | is the magnetic field strength. It has an exactly defined value

Contents

Z 0 = 119.9169832 π   Ω 376.730   313   461   77 Ω .

The impedance of free space (more correctly, the wave-impedance of a plane wave in free space) equals the product of the vacuum permeability or magnetic constant 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.

Terminology

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:

  • wave impedance of free space,
  • the vacuum impedance,
  • intrinsic impedance of vacuum,
  • characteristic impedance of vacuum,
  • wave resistance of free space.
  • Relation to other constants

    From the above definition, and the plane wave solution to Maxwell's equations,

    Z 0 = E H = μ 0 c 0 = μ 0 ε 0 = 1 ε 0 c 0

    where

    μ 0 = the magnetic constant ε 0 = the electric constant and c 0 = the speed of light in free space.

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

    Exact value

    Since 1948, the definition of the SI unit ampere has relied upon choosing the numerical value of μ0 to be exactly 4π × 10−7 H/m. Similarly, since 1983 the SI metre has been defined relative to the second by choosing the value of c0 to be 7008299792458000000♠299792458 m/s. Consequently,

    Z 0 = μ 0 c 0 = 119.9169832 π   Ω exactly,

    or

    Z 0 376.730   313   461   77 Ω .

    This chain of dependencies will change if the ampere is redefined in 2018. See New SI definitions.

    Approximation as 120π ohms

    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 7008300000000000000♠3×108 m/s in conjunction with the current definition of μ 0 . For example, Cheng 1989 states that the radiation resistance of a Hertzian dipole is

    R r 80 π 2 ( λ ) 2 . [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

    R r = 2 π 3 Z 0 ( λ ) 2 .

    References

    Impedance of free space Wikipedia


    Similar Topics