tuning tuning technique design multi stage tuned stage tuned slightly different frequency comparison tuning stage tuned produces wider expense reduced gain produces transition tuning tuning circuits easier tune manufacture filter types function tuned circuits expressed rational function designed major filter responses poles circuit easy manipulate achieve desired response stages applications include television 20th century receivers wireless rationale tuning improves multi stage tuned expense overall gain tuning increases skirts improves value tuning best explained looking shortcomings tuning stage method called tuning stage reduce multiple identical stages points response stage points second stage successive stage add band edge stage progressively narrower additional stage example stage points points individual stage circuit given formula power ratio power resonance band edge frequency equal point point quality factor reduced factor formula terms number stages formula stage tuned single stage stage reduced original tuning allows widened expense overall gain overall gain reduced stage resonance maximum gain unlike tuning stages maximum gain frequency stage tuned gain tuned design intended tuned tuning effect inevitable practical keeping tuned circuits perfectly step feedback effects problem narrow band applications essentially spot frequency interest local feed wave trap overall gain tuned theoretical maximum tuned tuned schemes number advantages schemes place tuning components single filter circuit separate ladder networks coupled advantage easy tune stages little effect circuits hand interact particularly nearest neighbours advantage components need close ideal directly working losses components absorbed design designs usually require high tuned circuits components values close tuned circuits identical spread component values tuned circuits circuits design tuned illustrated beginning article depicted chain loaded tuned circuit stage tuned circuit tuned circuit sum output input stage gain gain stage given formula complex frequency operator written generic form assuming type following formula frequency formula gain resonance formula stage quality factor resulting formula stage gain expression given function angular frequency making imaginary unit angular frequency formula frequency band edges found expression value gain band edge magnitude expression formula defined equal points desired solving taking difference positive solutions finds formula formula overall response overall response given product individual stages formula desirable able design filter standard low pass prototype filter required specification frequently smooth response chosen functions allow response popular choice response steep skirt purpose transformation stage gain expression rewritten suggestive form formula transformed low pass prototype filter transform formula frequency low pass prototype complete filter case tuned stage tuned simple solution transform tuned designs approached instead calculating poles low pass prototype desired form transforming poles band pass response poles calculated define tuned circuits individual stages poles stage gain rewritten terms poles formula complex pair poles overall response formula band pass low pass transform given expression found poles terms poles low pass prototype formula desired band pass centre frequency effective overall circuit pole prototype transforms complex pair poles band pass corresponds stage expression greatly simplified frequency prototype set final filter formula case design formula poles inserted stage gain expression terms poles comparing stage gain expression terms component values component values calculated applications tuning benefit applications commonly television receiver saw filters likely role tuning advantages radio applications wireless low spread component values easier implement integrated circuits traditional ladder networks
Staggered tuning