
naikvist sthiratha maanadandam

niyanthrana sidhaanthathilum sthiratha sidhaanthathilum, 1930-ll seamensile jarmman electrical enchineeyarum 1932-ll bell telephone laborattarikalile sweedish-american electrical enchineeyarumaaya haari nikvisttum swathanthramaayi kandethiya naikvist sthiratha maanadandam allengil strecker-naikvist sthiratha maanadandam oru chalanathmaka samvidaanathinte sthiratha nirnnayikkunnathinulla oru graaphikkal saankethikathayaanu. 
ithu ooppan lupe sisttangalude naikvist plott maathram nokkunnathinaal, clossed-lupe allengil ooppan-lupe sisttathinte dhruvangalum poojyangalum vyakthamaayi kanakkakkathe ithu prayogikkaan kazhiyum (ennirunnaalum oro tharatthilulla raitt-haff-playin singulaarittikaludeyum ennam ariyanam). thalphalamaayi, kaalathamasamulla sisttangal polulla yukthirahithamaya pravarthanangalaal nirvachikkapetta sisttangalil ithu prayogikkaan kazhiyum. booad plottukalil ninnu vyathyasthamayi, ithinu sariyaaya haff-playin singulaarittikal upayogichu transfer functionukal kaikaaryam cheyyaan kazhiyum. koodaathe, vimanangalkkulla niyanthrana samvidaanangal polulla onniladhikam inputtukalum onniladhikam aouttputtukalum ulla kooduthal sankeernamaaya samvidaanangalkku swaabhaavikamaaya saamaanyavalkkaranamund.
electronics, kantrol sisttam enchiniyaring, mattu mekhalakal ennivayil feedback upayogichu sisttangal roopakalppana cheiyunnathinum vishakalanam cheiyunnathinum naikvist sthiratha maanadandam vyaapakamaayi upayogikkunnu. ettavum pothuvaaya sthiratha parishodhanakalilonnaan naikvist, ithu ippozhum leanier time-invariyant (ell. tii. aii) samvidaanangalil parimithappedutthiyirikku. ennirunnaalum, noonn-leanier systengalkkaayi sarkkil maanadandavum nonleeniyar oopparettarude skeyil cheytha aapekshika graph polulla naikvist maanadandatthinteyum (plottinteyum) saamaanyavalkkaranangalund. koodaathe, leanier ithara samvidaanangalkku liapunov reethikal polulla mattu sthiratha maanadandangalum prayogikkaam.
naikvist oru graaphikkal saankethikavidyayaanenkilum, oru sisttam enthukondaanu sthirathayullatho asthiramo aayirikkunnath ennathino allengil oru asthiramaaya sisttam engane sthirathayullathaakkaamennu parishkkarikkam ennathino parimithamaaya avabodham maathrame ithu nalkunnulloo. booad plottukal polulla saankethikavidyakal pothuvallengilum chilappol kooduthal upayogapradamaaya design upakaranamaan.
naikvist plott.
automatic niyanthranatthilum signal prosessingilum upayogikkunna freekwansi prathikaranatthinte oru parametric plottaan naikvist plott. feedback upayogichu oru sisttathinte sthiratha vilayiruthuka ennathaanu naikvist plottukalude ettavum saadhaaranamaaya upayogam. cartician kordinettukalil, transfer functionte yadhaartha bhagam "x"-akshatthilum saangalppika bhagam "y"-akshathilumaanu plott cheythirikkunnathu. aavruthi oru paaraameteraayi maarunnu, athinte falamaayi oru aavruthikku oru pooyint labhikkunnu. transfer functionte geyin radial kordinettum transfer functionte ghattam anubandha koneeya kordinettumaanu, dhruva kordinettukal upayogichu athe plott vivarikkaam. bell laborattarikalile muun enchineeyaraayirunna haari naikvisttinte peraanu naikvist plottinu nalkiyirikkunnath.
ooppan-lupe sisttathinte (i.iii. feedback lupe illaathe athe sisttam). kaalathaamasangalum mattu yukthirahithamaya kaimatta pravarthanangalumulla systengalkku polum eee reethi eluppathil baadhakamaan, mattu reethikal upayogichu vishakalanam cheyyaan prayaasamaanennu thonniyekkaam. pooyintinte chuttupaadukalude ennam (−1,0) nokkunnathiloodeyaanu sthiratha nirnnayikkunnath. yadhaartha akshatthinte crossingukal nokkiyaal sisttam sthirathayulla nettangalude paridhi nirnnayikkaan kazhiyum. 
kaimatta pravartthanatthinte aakruthiyekkurichu chila vivarangal nalkaan naikvist plottinu kazhiyum. udaaharanathinu, transfer functionte poojyangaludeyum dhruvangaludeyum ennam thammilulla vyathyasathekkurichulla vivarangal karvu uthbhavasthaanathe sameepikkunna konil plott nalkunnu.
kaikondu varaykkumbol, naikvist plottinte oru cartoon pathipp chilappol upayogikkunnu, ithu vakrathinte rekheeyatha kaanikkunnu, ennaal thaalpparyamulla pradeshangalil kooduthal vishadaamshangal kaanikkunnathin kordinettukal valachodikkunnu. computationalaayi plott cheyyumbol, thaalpparyamulla ellah aavruthikalum ulkkollunnathil oraal shradhikkendathundu. vishalamaaya moolyangal ulkkollunnathinayi paaraameettar logaritmikkalaayi switch cheythirikkunnu ennaanu ithinartham.
pashchaathalam.
ganithashaasthram laplace parivartthanam upayogikkunnu, ithu time domainile integralukaleyum derivetteevukaleyum "s" domainile lalithamaaya gunanathilekkum vibhajanathilekkum parivartthanam cheiyunnu.
formula _ 1 aaya transfer function ulla oru systethe nammal pariganikkunnu; negatteevu feedback formula _ 2 ulla oru clossed looppil sthaapikkumbol, clossed lupe transfer function (cletef) inipparayunna reethiyil maarunnu
desensitivity factor polynomial formula _ 4, e-yude verukal parishodhichu sthiratha nirnnayikkaan kazhiyum.jii. rauthu shreni upayogikkunnu, pakshe eee reethi alppam maduppikkunnathaanu. ooppan lupe transfer function (oltf) formula _ 5 parishodhikkunnathiloodeyum athinte booad plottukal upayogicho allengil ivide ullathupole, naikvist maanadandam upayogichu athinte pollar plott upayogicho inipparayunna nigamanagalil athicheraam.
eathenkilum laplace domaine transfer function formula _ 6 rund polynomialukalude anupaathamaayi prakadippikkaam
formula _ 8-nte verukale formula _ 6-nte "poojyangal" ennum formula _ 10-nte verukale formula _ 6-nte "dhruvangal" ennum vilikkunnu. formula _ 6-nte dhruvangale "swabhaavasavisheshatha samavaakyam" formula _ 13-nte verukalaayum parayappedunnu.
formula _ 6-nte sthiratha nirnnayikkunnath athinte dhruvangalude moolyangalaanu sthirathaykkaayi, oro dhruvathinteyum yadhaartha bhagam negatteevu aayirikkanam. ooppan-lupe transfer functionu chuttumulla oru negatteevu yoonitti feedback lupe adachu formula _ 6 roopappedukayaanenkil,
appol swabhaavasavisheshathakalude samavaakyathinte verukal formula 17-nte poojyangalaanu, allengil formula 18-nte verukalaanu.
kauchiyude vaada thathwam.
sankeernamaaya vishakalanathil ninnu, sankeernamaaya formula _ 20 playinil varacha oru kondoor formula _ 19, oru function formula _ 21-nte poojyangaliloodeyum dhruvangaliloodeyum kadannupokaathe, function formula _ 23 vazhi mattoru plainilekku (formula _ 21 playin ennu perittirikkunnu) mapp cheyyaan kazhiyum. krithyamaayi paranjaal, kondoor formula _ 19-leeii oro complexes pooyint formula _ 20 puthiya formula _ 21 playinile pooyint formula _ 21-lake mapp cheythirikkunnu, ithu oru puthiya kondoor nalkunnu. 
kondoor formulayaya _ 21-nte naikvist plott, formula _ 21 playin formulayude pooyint formula _ 30-neey 32 thavana valayam cheyyum, ivide formula _ 33 ennathu kauchiyude aargyument tatwatal chuttappettirikkunnu. ivide formula 34 umm formula 35 umm yathaakramam kondoor formula 19-nullil formula 36-nte poojyangaludeyum formula 21-nte dhruvangaludeyum ennamaanu. kondoor formula 19-nte athe ardhathil formula 21-leeii enkrikkalmentukal nammal kanakkakkunnuvennum ethir dishayilulla enkrikkalmentukal "negatteevu" enkrikkalmentukalaanennum shradhikkuka. athaayath, gadikaaradishayil chuttupaadukal positteev aayum ethir gadikaaradishayil chuttupaadukal negatteevu aayum njangal kanakkakkunnu.
1932-ll haari naikvisttinte yadhaartha prabandham, kauchiyude vaada thathwathinu pakaram, athra gambheeramallatha sameepanamaan upayogikkunnathu. ivide vishadeekaricha sameepanam leroy macaul (servomechanisangalude adisthaana sidhaantham 1945) allengil hendrick booad (network vishakalanavum feedback amplifier design 1945) upayogicha sameepanathin samaanamaan, iruvarum bell laborattarikalil pravarthichu. niyanthrana sidhaanthathekkurichulla mikka aadhunika paatapusthakangalilum eee sameepanam kaanapedunnu.
nirvachanam.
sankeernamaaya thalatthinte valathuvashathe ulkkollunna oru kondooraaya naikvist kondoor aanu nammal aadyam nirmmikkunnath.
function formula _ 47 vazhi mapp cheytha naikvist kondoor sankeernamaaya thalatthil formula _ 47 nte oru plott nalkunnu. aargyument thathwam anusarichu, uthbhavathinte gadikaaradishayil chuttupaadukalude ennam valath pakuthi sankeernna thalatthile formula _ 47 nte poojyangalude ennam mainus valath pakuthi sankeernna thalatthile formula _ 47 nte dhruvangalude ennam aayirikkanam. pakaram, kondoor ooppan-lupe transfer function formula _ 1 vazhi mapp cheiyukayaanenkil, phalam formula _ 1 nte naikvist plottaan. thathfalamaayundaakunna kondoorinte enkrikkalmentukal −1 ennunnathiloode, formula _ 47 nte valath pakuthi sankeernna thalatthile dhruvangaludeyum poojyangaludeyum ennam thammilulla vyathyasam nammal kandethunnu. formula _ 47 nte poojyangal clossed-lupe sisttathinte dhruvangalaanennu oormmikkukayum formula _ 47 nte dhruvangal formula _ 1 nte dhruvangalkk thulyamaanennu shradhikkukayum cheiyunnu, nammal ippol naikvist maanadandam prasthaavikkunnu "oru naikvist kondoor formula _ 19 nalkiyaal, formula _ 35 formula _ 19 kondu valayam cheytha formula _ 1 nte dhruvangalude ennamaayirikkatte, formula _ 34 formulayude valath nirayil 47 nte poojyangalude ennamaayirikkatte. valath-pakuthi-thalam (arhp) dhruvangal aaa asthirathaye prathinidheekarikkunnu. oru sisttathinte clossed-lupe sthirathaykku, "s"-plaininte valath pakuthiyile clossed-lupe roottukalude ennam poojyamaayirikkanam. athinaal, formula _ 72 nekkurichulla ethir gadikaaradishayil chuttupaadukalude ennam rhp-yile ooppan-lupe dhruvangalude ennathinu thulyamayirikkanam. ooppan-lupe freekwansi prathikaranam (kuranja freekwansiyil ninnu uyarnna freekwansiyilekku vilayiruthumbol) nirnaayaka pooyintinte gadikaaradishayil chuttunna eathenkilum upakaranangal lupe adachaal feedback niyanthrana samvidaanam asthiramaakumennu soochippikkum. (arhp dhruvangal "radhaakkaan" arhp poojyangal upayogikkunnathu asthiratha illaathaakkunnilla, marichu feedbaakkinte saannidhyathil polum sisttam asthiramaayi thudarumennu urappaakkunnu, kaaranam clossed-lupe roottukal feedbaakkinte saannidhyathil ooppan-lupe dhruvangalkkum poojyangalkkum idayil sanjarikkunnu. vaasthavathil, arhp seroic asthiramaaya dhruvathe nireekshikkaanaavaathaakkaanathaam athinaal feedbaakkiloode sthirappeduthaanum kazhiyilla.)
saangalppika achuthandil dhruvangalulla sisttangalude naikvist maanadandam.
ooppan-lupe transfer function formula _ 1 nuu saangalppika achuthandil oru dhruvavum illenna anumaanathodeyaanu melpparanja pariganana nadathiyathu (i.iii. formulayude dhruvangal _ 74). mapping functionte oru dhruvathiloodeyum kondoorinu kadannupokaan kazhiyillenna aargyument thathwathinte aavasyakathayil ninnaan ithu sambhavikkunnath. integrettarukalulla (poojyathilulla dhruvangal) samvidaanangalaanu ettavum saadhaaranamaaya cases.
saangalppika akshatthile dhruvangalulla samvidaanangal vishakalanam cheyyaan, pooyint formula _ 74-loode kadannupokaathirikkaan naikvist kondoor parishkkarikkam. athinulla oru maarggam formula _ 78-ll aarambhich formula _ 79-lake ethir gadikaaradishayil sanjarikkunna formula _ 74-nuu chuttum 76 enna vyaasamulla oru ardhavrithaakrithiyilulla arck nirmmikkuka ennathaanu. atharam oru parishkkaranam soochippikkunnathu facer formula _ 1 ananthamaaya vyaasamulla oru kamaanathiloode formula _ 81 vazhi sanjarikkunnu ennaanu, avide formula _ 82 ennathu saangalppika akshatthile dhruvathinte gunithamaan.
ganithashaasthraparamaaya vyulppannam.
eee prakriyayiloode, nammude yoonitti feedback sisttathinte transfer functionte sthiratha parisodhikkuka ennathaanu njangalude lakshyam, ithu nalkunna geyin "k" aanu.
athaayath, mukalil paranja transfer functionte swabhaavasavisheshatha samavaakyam, nalkiyirikkunnathaano ennu parisodhikkaan njangal aagrahikkunnu
thuranna idathu-pakuthi-thalathinu purathu poojyangalundu (saadhaaranayaayi oolhp ennu aarambikkunnu).
namukk gadikaaradishayil (i.iii. negatteevu ooriyantad) kondoor formula _ 19, valathuvashathe pakuthi thalathe valayam cheiyunnu, function formulayude poojyangaliloodeyo dhruvangaliloodeyo kadannupokunnathu ozhivakkaan aavashyamaaya indentationukal. 
ivide formula 34 ennathu kondoor kondu chuttapetta formula 10-nte poojyangalude ennathe soochippikkunnu, formula 35 ennathu formula 10-nte dhruvangalude ennathe ore kondoor kondu soochippikkunnu. punakrameekarikkuka, njangalkk undu
formula _ 92, athaayath
formula _ 94 nuu formula _ 1-nuu samanamaaya dhruvangalundennu nammal shradhikkunnu. athinaal, kondoorinullil drishyamaakunna formula _ 1-nte dhruvangal ennunnathiloode, athaayath ooppan raitt haff playinil (oorechpi) formula _ 35 kandethaam.
ippol nammal melpparanja integral pakarakkaaraniloode punakrameekarikkum. athaayath, formula _ 98 sajjeekarikkuka, namukk undu
thudarnnu nammal oru adhika pakarakkaaran undaakkunnu, formula _ 100 krameekarikkunnu. ithu namukk nalkunnu.
102 enna soothravaakyam nammude kondoorinte chithram formula 1 nuu keezhil nalkunnuvennu nammal ippol shradhikkunnu, athaayath nammude naikvist plott. namukk integral kurachekkaam
kauchiyude avibhaajya soothravaakyam prayogikkuka. vaasthavathil, mukalil paranja integral, 105 gadikaaradishayil pooyint formula naikvist plott ethra thavana chuttunnu ennathumaayi krithyamaayi yojikkunnuvennu nammal kandethunnu. athinaal, oduvil namukk athu prasthaavikkam
mukalil nirvachicha formula _ 107, mukalil vilayiruthiya formula _ 34,0 nuu thulyamaakumbol sthirathayulla oru yoonitti-feedback sisttavumaayi poruthappedunnuvennu nammal kandethunnu.

