Mjerenje snage. Na kraju sata student treba biti u stanju: Spojevi za jednofazno izmjenično mjerenje snage. Ak. god. 2008/2009
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1 Mjerenje snae Ak. od. 008/009 1 Na kraju sata student treba biti u stanju: Opisati i analizirati metode mjerenja snae na niskim i visokim frekvencijama Odabrati optimalnu metodu mjerenja snae Analizirati uzroke porešaka prilikom mjerenja snae Spojevi za jednofazno izmjenično mjerenje snae Naponska rana spojena na teret t ( Ut / V Ut W P = / U t It = PW P = I = P I ( U t t W Naponska rana spojena na izvor P = U I = P U / U / W P t = U t It = PW It ( A W A i V kontrola preopterećenja Vatmetar ulazne stezaljke označene s * Izbor spoja: t >> A? ili t << V? A W ( V W 3
2 Mjerenje snae kod malih faktora snae Kod malih faktora snae kut poreške δ značajno utječe na porešku Umjesto P=U I cosϕ mjeri P=U I cos(ϕδ Poreška: PW P UI cos( ϕ δ UI cosϕ pδ = 100 = 100 P UI cosϕ = 100 δ tanϕ... raste s smanjenjem faktora snae! vatmetri za male fazne pomake (0,; 0,1; 0,05: puni otklon pri U N, I N i pri cosϕ N 4 Metoda 3 ampermetra Paralelno s teretom se spaja poznati otpor I 0 u fazi s naponom, I pomknuta za ϕ Kosinusov poučak: I = I I I cos( π ϕ 1 0 I0 P=U I cosϕ Koristi se: Na višim frekvencijama Kad je A <<Z T I P = adi točnosti treba biti: Z T 1 I0 I 5 Mjerenje snae u trofaznom sustavu Simetričan sustav Nesimetričan sustav Ako nema nulvodiča umjetna nultočka Aronov spoj (dva vatmetra Simetrično ili nesimetrično Bez nulvodiča Trenutna snaa trošila: p tr = u1i 1 ui u3i3 Sustav bez nulvodiča: i 3 = i1 i p tr = i1 ( e1 e3 i( e e3 Srednja vrijednost: P = P 1 P 6
3 P = U I cos 30 Aronov spoj vektorski dijaram Primjer simetrično trošila o ( ϕ o 1 P = U I cos( 30 ϕ P1 P = U I sinϕ P1 P = 3 U I cosϕ P 7 Mjerenje jalove snae Varmetri direktno mjerenje jalove snae Vatmetri naponska rana spojena na napon pomaknut za 90 o : Q=1/ 3 I U ST 8 Poluizravno i neizravno mjerenje snae Poluizravno: veća snaa (struja na niskom naponu Neizravno mjerenje snae: na višim naponima (izolacija, siurnost 9
4 Mjerenje snae na višim frekvencijama termopretvornici S << T1 ; T I većim djelom kroz S Struja kroz termopretvornike: T1: I t I u T: I t I u [ t u t u ] t u θ = θ 1 θ = k ( I I ( I I = 4 k I I Ako je I t =I teret a I u = U teret U = k U I cosϕ = k P Osjetljivi vatmetri (1µW 10 Mjerenje snae na vrlo visokim frekvencijama (>100 MHz Bolometarske metode: promjena otpora zbo promjene temperature Bareter (izlaze iz uporabe Termistori b / T poluvodiči s NTC: ρ = a e Kulica metalno oksida promjera 0,4 mm Mjerenja pomoću termopara Diodna mjerenja Koristi se nelinearno kvadradično područje Schottky diode nisko praa Mjeri pravu srednju vrijednost Mjeri snae do 0,1 nw, 10 MHz do 0 GHz 11 Bolometarska metoda neuravnotežen most C sprječava dc komponentu L sprječava ac komponentu Most u ravnoteži bez F sinala Dovođenjem F sinala dolazi do zarijavanja otpora b instrument umjeren u snazi 1
5 Bolometarska metoda samouravnotežujući most a P F b U rf s Bez F sinala napon napajanja U FO Dovođenjem F sinala: mijenja se b Javlja se napon na dijaonali mosta Pojačalo pojačava U dia i smanjuje napon napajanja Napon na b : U b =U F / U U P FO F F = 4 Oraničen opse zbo temp. Klizanja (30 µw 13 Dvostruki kompenzirani most b P b F b U c U rf U rf U c U rf U c Drui most za kompenzaciju utjecaja temperature ambijenta S promjenom temperature mijenja se napon napajanja obaju mosta Mjerni opse do 1 µw Frekvencijski opse: 10 khz 100 GHz 14 Mjerenje snae (F termoparom P F TP CHOPPE A ~ SIN. DET. A = 0 Hz MULTIVIBATO Mjerenja snae do 40 GHz Osjetljivost 160 µv/mw za snae 1 µw 15
6 Literatura V. Beo:, 9. izdanje, Graphis, Zareb, 003. D. Vujević, B. Ferković: Osnove elektrotehničkih mjerenja I. i II. Dio, Školska knjia Zareb, D. Ilić, I. Kunšt:, Prilo predavanjima, Zareb 003. Ailent, Fundamentals of F and Microwave Power Measurements, Application Note 641C, 16
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