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characteristic impedance of free space

The characteristic impedance of free space , also called the Z o of free space, is an expression of the relationship between the electric-field and magnetic-field intensities in an electromagnetic field ( EM field ) propagating through a vacuum . The Z o of free space, like characteristic impedance in general, is expressed in ohm s, and is theoretically independent of wavelength . It is considered a physical constant.

Mathematically, the Z o of free space is equal to the square root of the ratio of the permeability of free spaceo ) in henrys per meter ( H/m ) to the permittivity of free space ( o ) in farads per meter ( F/m ):

Z o = (µ o / o ) 1/2

= [(1.257 x 10 -6 H/m)/(8.85 x 10 -12 F/m)] 1/2

= 377 ohms (approximately)

The exact value of the Z o of free space is 120 pi ohms, where pi is the ratio of the circumference of a circle to its diameter.

The Z o of dry air is similar to that of free space, because dry air has little effect on permeability or permittivity. However, in environments where the air contains seawater spray, excessive humidity, heavy precipitation, or high concentrations of particulate matter, the Z o is slightly reduced. Characteristic impedance is important to wireless communications engineers involved in antenna design.

Also see Table of Physical Units and Constants.

This was last updated in September 2005

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120 pi is not exact value of the impedance of free space. It's an approximation that assumes the speed of light is 300,000,000 m/s. The speed of light is in fact 299,792,458 m/s (by definition). In addition, 120 pi looks like unitless number so it's confusing. Zo looks like a quantity with units of ohms.
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