Characteristic impedance
From Academic Kids
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. The SI unit of characteristic impedance is the ohm.
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.
If the line is not uniform, the iterative impedance must be used.
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}} <math>
where
- <math>Z_0 \ <math>is the characteristic impedance
- <math>\mu \ <math>is the magnetic permeability of the medium
- <math>\epsilon \ <math>is the electric permittivity of the medium
- <math>c = {1 \over \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}} = 376.730313461... \ \Omega<math>
- here <math>c = {1 \over \sqrt{ \mu_0 \epsilon_0}} \ <math> is the speed of propagation in vacuum.
See also
Source
Adapted from
