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Benutzer:Debenben/Parametrischer Oszillator
{{Importartikel}}
Ein '''parametrischer Oszillator''' ist ein [[harmonischer Oszillator]], dessen Parameter (die Frequenz <math>\omega</math> sowie die Dämpfungskonstante <math>\beta</math>) eine zeitabhängige Funktion sind. 

:<math>
\frac{d^{2}x}{dt^{2}} + \beta(t) \frac{dx}{dt} + \omega^{2}(t) x = 0
</math>

(contracted; show full)ommon use is frequency conversion, e.g., conversion from audio to radio frequencies.  Parametric amplifiers ('''paramps''') were first used in 1913-1915 for radio telephony from Berlin to Vienna and Moscow, and were predicted to have a useful future (Alexanderson, 1916).  The early paramps varied inductances, but other methods have been developed since, e.g., the varactor diodes, [[klystron tube]]s, Josephson junctions and [[optical parametric oscillator|optical methods]].

==
ReferencesLiteratur==

Faraday M. (1831) "On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces", 
''Phil. Trans. Roy. Soc. (London)'', '''121''', 299-318.

Melde F. (1859) "Über Erregung stehender Wellen eines fadenförmigen Körpers", 
''Ann. Phys. Chem.'' (ser. 2), '''109''', 193-215.

Strutt JW (Lord Rayleigh). (1883) "On Maintained Vibrations", ''Phil. Mag.'', '''15''', 229-235.

Strutt JW (Lord Rayleigh). (1887) "On the maintenance of vibrations by forces of 
double frequency, and on the propagation of waves through a medium endowed with 
periodic structure", ''Phil. Mag.'', '''24''', 145-159.

Strutt JW (Lord Rayleigh). (1945) ''The Theory of Sound'', 2nd. ed., Dover.

Kühn L. (1914) ''Elektrotech. Z.'', '''35''', 816-819.

Pungs L. DRGM Nr. 588 822 (24 October 1913); DRP Nr. 281440 (1913); 
''Elektrotech. Z.'', '''44''', 78-81 (1923?); ''Proc. IRE'', '''49''', 378 (1961).

Mumford WW. (1961) "Some Notes on the History of Parametric Transducers", 
''Proc. IRE'', '''48''', 848-853.

==Siehe auch==
* [[Harmonischer Oszillator]]
* [[Optisch parametrischer Oszillator]]
* [[Mathieusche Differentialgleichung]]⏎
⏎
<pre>
==See also==

* [[Harmonic oscillator]]
* [[Optical parametric oscillator]]
* [[Optical parametric amplifier]]

[[Category:Oscillators]]
[[Category:Amplifiers]]
[[Category:Dynamical systems]]
[[Category:Ordinary differential equations]]

</pre>