Characteristic impedance
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The characteristic impedance <math>Z_0</math> of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm. A transmission line terminated at one end with its characteristic impedance will appear infinitely long to a source at the other end.
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[edit] Transmission line model
Applying the transmission line model based on the telegrapher equations, the general expression for the characteristic impedance of a transmission line is:
- <math>Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}</math>
where
- <math>R</math> is the resistance per unit length,
- <math>L</math> is the inductance per unit length,
- <math>G</math> is the conductance per unit length, and
- <math>C</math> is the capacitance per unit length.
The voltage and current phasors on the line are related by the characteristic impedance as:
- <math>\frac{V^+}{I^+} = Z_0 = -\frac{V^-}{I^-}</math>
where the superscripts <math>+</math> and <math>-</math> represent forward- and backward-traveling waves, respectively.
[edit] Lossless line
For a lossless line R and G are zero and the equation for characteristic impedance reduces to
- <math>Z_0 = \sqrt{\frac{L}{C}}</math>.
[edit] See also
[edit] References
- Federal Standard 1037C.
- Ulaby, F. T. (2004). Fundamentals Of Applied Electromagnetics, media edition. ISBN 0-13-185089-X.
- Pozar, D. M. (February 2004). Microwave Engineering, 3rd edition. ISBN 0-471-44878-8.de:Wellenimpedanz
es:Impedancia característica fr:Impédance caractéristique du vide nl:Karakteristieke impedantie
