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

• ${\displaystyle \mu _{0}}$the magnetic field constant
• ${\displaystyle c}$the speed of light
• ${\displaystyle \varepsilon _{0}}$the electric field constant
• ${\displaystyle h}$the Planck constant
• ${\displaystyle \alpha }$the fine structure constant
• ${\displaystyle e}$the elementary charge .

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 . ${\displaystyle \varepsilon _{\mathrm {r} }}$ ${\displaystyle \varepsilon _{\mathrm {r} }\approx 1{,}00059}$ ${\displaystyle \mu _{\mathrm {r} }}$ ${\displaystyle 376{,}62\;\Omega }$ ${\displaystyle 0{,}1\;\Omega }$

literature

• Gerthsen physics . , Dieter Meschede , 23rd edition, Springer-Verlag, Berlin / Heidelberg / New York 2006, ISBN 978-3-540-25421-8 , p. 427.

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