Characteristic impedance
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In radio communications, characteristic impedance (acoustic impedance or sound impedance) <math>Z_0 \ </math> of a uniform transmission line is the impedance of a circuit that, when connected to the output terminals of a line of arbitrary length, causes the line to appear infinitely long. This is sometimes called surge impedance. The SI unit of characteristic impedance is the ohm.
Description
A uniform line terminated in its characteristic impedance will have no standing waves, no reflections from the end, and a constant ratio of voltage to current at a given frequency at every point on the line. The characteristic impedance of a linear, homogeneous, isotropic, dielectric propagation medium free of electric charge is given by the relation
- <math>Z_0 = \sqrt{\mu \over \epsilon} = {1 \over {c \ \epsilon}} = c \mu </math>
where
- <math>Z_0 \ </math>is the characteristic impedance
- <math>\epsilon \ </math>is the electric permittivity of the medium (in farads per meter)
- <math>\mu \ </math>is the magnetic permeability of the medium (in henries per meter)
- <math>c = \frac{1}{\sqrt{ \mu \epsilon}} \ </math> is the speed of propagation in the medium
When the medium is free space, the magnetic permeability <math>\mu_0 \ </math> and electric permittivity <math>\epsilon_0 \ </math> of free space are used and this defines the universal physical constant, the characteristic impedance of free space:
- <math>Z_0 = \sqrt{\mu_0 \over \epsilon_0} = {1 \over {c \ \epsilon_0}} = c \mu_0 = 376.73 \ \Omega</math>
where
- <math>c = {1 \over \sqrt{ \mu_0 \epsilon_0}} \ = 2.998 \times 10^8 \ \mbox{m/s}</math> is the speed of light in free space,
- <math>\epsilon_0 = 8.854 \times 10^{-12} \ \mbox{F/m} </math> is the permittivity of free space, and
- <math>\mu_0 = 4 \pi \times 10^{-7} \ \mbox{H/m} </math> is the permeability of free space.
See also
Source
Adapted from