▁ampl ifier ▁was ▁the ▁first ▁sem icon duct or ▁ampl ifier ▁at ▁mic row ave ▁frequencies . ▁It ▁was ▁applied ▁to ▁low ▁noise ▁radio ▁rece ivers ▁in ▁many ▁areas , ▁and ▁has ▁been ▁widely ▁used ▁in ▁radio ▁teles cop es , ▁satellite ▁ground ▁stations , ▁and ▁long - range ▁rad ar . ▁It ▁is ▁the ▁main ▁type ▁of ▁paramet ric ▁ampl ifier ▁used ▁today . ▁Since ▁that ▁time ▁paramet ric ▁ampl ifiers ▁have ▁been ▁built ▁with ▁other ▁non linear ▁active ▁devices ▁such ▁as ▁Joseph son ▁j unction s . ▁ ▁The ▁technique ▁has ▁been ▁extended ▁to ▁optical ▁frequencies ▁in ▁optical ▁paramet ric ▁oscill ators ▁and ▁ampl ifiers ▁which ▁use ▁non linear ▁cry st als ▁as ▁the ▁active ▁element . ▁ ▁Mathemat ical ▁analysis ▁A ▁paramet ric ▁oscill ator ▁is ▁a ▁harm onic ▁oscill ator ▁whose ▁physical ▁properties ▁vary ▁with ▁time . ▁The ▁equation ▁of ▁such ▁an ▁oscill ator ▁is ▁ ▁This ▁equation ▁is ▁linear ▁in ▁. ▁By ▁assumption , ▁the ▁parameters ▁ ▁and ▁ ▁depend ▁only ▁on ▁time ▁and ▁do ▁not ▁depend ▁on ▁the ▁state ▁of ▁the ▁oscill ator . ▁In ▁general , ▁ ▁and / or ▁ ▁are ▁assumed ▁to ▁vary ▁period ically , ▁with ▁the ▁same ▁period ▁. ▁ ▁If ▁the ▁parameters ▁vary ▁at ▁roughly ▁twice ▁the ▁natural ▁frequency ▁of ▁the ▁oscill ator ▁( defined ▁below ), ▁the ▁oscill ator ▁phase - lock s ▁to ▁the ▁paramet ric ▁variation ▁and ▁absor bs ▁energy ▁at ▁a ▁rate ▁proportional ▁to ▁the ▁energy ▁it ▁already ▁has . ▁Without ▁a ▁compens ating ▁energy - loss