▁modification ▁on ▁a ▁system ▁parameter . ▁The ▁classical ▁example ▁of ▁paramet ric ▁reson ance ▁is ▁that ▁of ▁the ▁vert ically ▁forced ▁p end ul um . ▁ ▁For ▁small ▁amplit udes ▁and ▁by ▁linear ising , ▁the ▁stability ▁of ▁the ▁periodic ▁solution ▁is ▁given ▁by ▁Math ieu ' s ▁equation : ▁ ▁where ▁ ▁is ▁some ▁perturb ation ▁from ▁the ▁periodic ▁solution . ▁Here ▁the ▁ ▁term ▁acts ▁as ▁an ▁‘ energy ’ ▁source ▁and ▁is ▁said ▁to ▁param etr ically ▁ex cite ▁the ▁system . ▁The ▁Math ieu ▁equation ▁describes ▁many ▁other ▁physical ▁systems ▁to ▁a ▁sin us oid al ▁paramet ric ▁exc itation ▁such ▁as ▁an ▁L C ▁Circ uit ▁where ▁the ▁capac itor ▁pl ates ▁move ▁sin us oid ally . ▁ ▁Param et ric ▁ampl ifiers ▁ ▁Introduction ▁A ▁paramet ric ▁ampl ifier ▁is ▁implemented ▁as ▁a ▁mix er . ▁The ▁mix er ' s ▁gain ▁shows ▁up ▁in ▁the ▁output ▁as ▁ampl ifier ▁gain . ▁The ▁input ▁weak ▁signal ▁is ▁mixed ▁with ▁a ▁strong ▁local ▁oscill ator ▁signal , ▁and ▁the ▁result ant ▁strong ▁output ▁is ▁used ▁in ▁the ▁en su ing ▁receiver ▁stages . ▁ ▁Param et ric ▁ampl ifiers ▁also ▁operate ▁by ▁changing ▁a ▁parameter ▁of ▁the ▁ampl ifier . ▁Int uit ively , ▁this ▁can ▁be ▁understood ▁as ▁follows , ▁for ▁a ▁variable ▁capac itor - based ▁ampl ifier . ▁Char ge ▁ ▁in ▁a ▁capac itor ▁ob e ys : ▁ ▁therefore ▁the ▁voltage ▁across ▁is ▁ ▁Know ing ▁the ▁above , ▁if ▁a