# Characteristic impedance of the vacuum

Physical constant
Surname Characteristic impedance of the vacuum
Formula symbol ${\ displaystyle Z_ {0} \,}$
Size type Electrical resistance
value
SI 3.767 303 136 67 (57)e2 ${\ displaystyle \ Omega}$
Uncertainty  (rel.) 1.5e-10
Planck units ${\ displaystyle 4 \ pi \! \,}$
Relation to other constants
${\ displaystyle Z_ {0} = \ mu _ {0} c}$
Magnetic field constant speed of light${\ displaystyle \ mu _ {0}}$
${\ displaystyle c}$

The wave resistance of the vacuum , also free space wave resistance , field wave resistance of the vacuum or wave impedance of the vacuum , is a physical constant with the unit ohm . The free space wave resistance indicates the relationship between the amounts of the electric field strength and the magnetic field strength of an electromagnetic wave that propagates in a vacuum , i.e.: ${\ displaystyle {\ vec {E}}}$ ${\ displaystyle {\ vec {H}}}$

${\ displaystyle Z_ {0} = {\ frac {| {\ vec {E}} |} {| {\ vec {H}} |}}}$

In the International System of Units (SI) the value is

${\ displaystyle Z_ {0} = \ mu _ {0} \, c = 376 {,} 730 \, 313 \, 667 (57) \, \ Omega}$.

## Relationship with other fundamental constants

The wave resistance of the vacuum can be calculated from other natural constants:

${\ displaystyle Z_ {0} = {\ sqrt {\ frac {\ mu _ {0}} {\ varepsilon _ {0}}}} = \ mu _ {0} \, c = {\ frac {2 \, h \, \ alpha} {e ^ {2}}}}$

Are in it

Until the redefinition of the SI units in 2019 , the numerical values ​​of the constants and the definition of the units “meter” and “ampere” were precisely defined. This had the exact value of . Since May 20, 2019, the numerical value is still exact, but no longer. The numerical value of the product is therefore subject to the same relative measurement uncertainty (1.5 × 10 −10 ) as that of . ${\ displaystyle c}$${\ displaystyle \ mu _ {0}}$${\ displaystyle Z_ {0}}$${\ displaystyle Z_ {0} = 4 \ pi \ cdot 29 {,} 979 \, 245 \, 8 ~ \ Omega}$${\ displaystyle c}$${\ displaystyle \ mu _ {0}}$${\ displaystyle Z_ {0} = \ mu _ {0} \, c}$${\ displaystyle \ mu _ {0}}$

## Characteristic impedance in a medium

When electromagnetic waves propagate in a dielectric medium , the wave resistance depends on the permeability and permittivity of the medium: ${\ displaystyle Z_ {F}}$ ${\ displaystyle \ mu}$ ${\ displaystyle \ varepsilon}$

${\ displaystyle Z_ {F} = {\ sqrt {\ frac {\ mu} {\ varepsilon}}} = {\ sqrt {\ frac {\ mu _ {0} \ mu _ {\ mathrm {r}}} { \ varepsilon _ {0} \ varepsilon _ {\ mathrm {r}}}}} = Z_ {0} {\ sqrt {\ frac {\ mu _ {\ mathrm {r}}} {\ varepsilon _ {\ mathrm { r}}}}}}$

The relative permittivity of air under normal conditions is approximately , its permeability number is only slightly higher than 1. The wave resistance of the atmosphere is approximately well reduced compared to the wave resistance of the vacuum . ${\ displaystyle \ varepsilon _ {\ mathrm {r}}}$${\ displaystyle \ varepsilon _ {\ mathrm {r}} \ approx 1 {,} 00059}$${\ displaystyle \ mu _ {\ mathrm {r}}}$${\ displaystyle 376 {,} 62 \; \ Omega}$${\ displaystyle 0 {,} 1 \; \ Omega}$

## Individual evidence

1. CODATA Recommended Values. NIST , accessed July 7, 2019 (value for the magnetic field constant).
2. CODATA Recommended Values. NIST , accessed July 7, 2019 (value for the speed of light).
3. Otto Zinke, Heinrich Brunswig, Anton Vlcek: High frequency technology: high frequency filters, lines, antennas, Volume 1