Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por eworks experimeally ad verify heir ierrelaio ships. Theory: osider a passive -por (4-ermial) ework as show Fig-. The volage, ad curre, ca be relaed i erms of he -parameers as show below. ------------ ( ) Where 0 0 -------------- ( ) Similarly, oe may express he curres, i erms of he volages usig he parameers as, Y Y ------------------- (3)
Y Y Y Where Y 0 Y ----------- ( 4 ) Lasly, we may represe he volages ad curre of por i erms of hose of por as follows. A B D -- T. ---------------- ( 5 ) Where, he elemes of he rasmissio marix T, are give as, A ----- B ----- 0 --- D ----- 0 -------------- ( 6) 0 0 f wo eworks M ad N are coeced i cascade (as show i Fig. ). The he rasmissio marix of he overall ework is give as. T T T M. N ------------------- ( 7 )
Fig. - Procedure : ( ). Perform he ope circui ad shor circui ess o he wo -por eworks M ad N separaely as give below: ( i ). Apply a volage + D across ermials - of ework ad measure he volage ad curres ad wih ermials - uder ope circui ad shor circui codiios. (Noe he polariies carefully). ( ii Repea he same from he oher ed - wih ermials - kep ope ad shor, respecively. ( iii ) alculae he wo eworks i cascade as show i Fig. ad oce agai deermie he parameers for he combied ework. ( ). oec he wo eworks i cascade as show i Fig. ad oce agai deermie he parameers for he combied ework. ( 3 ). Measure he values of he circui elemes. Repor : ( i ) erify he heoreical relaioships relaios bewee Y, ad ABD parameers. ( ii ) erify equaio ( 7 ) ( iii ) Esablish he relaioship AD B ( iv ) Obai he heoreical values of he parameers from he values of he circui eleme measured experimeally ad compare wih values of he parameers obaied experimeally. ( v ) omme o discrepacies, if ay.
Elecrical Egieerig Deparme Nework Lab. Par:- Deermiaio of rasie respose of a R-L- ework wih iial codiios Objecive: - To deermie he rasie respose of a R-L- ework i erms of he parameers σ, ξ, ω, ω ad iiial codiios i ( 0 ), v (0 ) L 0 mh K NO 00K Ω R L R 86Ω 00K R3 µ 0 F R 4 N K Fig.- 5 ( ). s Relay oil 3 4 Procedure:. Make he coecios as show i he Fig. 5().. wihou eergizig ay oe of he volage sources.. Swich o he volage source. Adjus he resisaces R3 ad R4 ( i he rage of 00K) o se a iiial volage (0) across he capacior 0μF. apure he rasie by coecig a oscilloscope probe across he capacior ad by riggerig a he risig edge of he waveform i sigle sho mode. Noe he ime cosa of he rasie. 3. Swich o he volage source ad adjus he curre i he iducor L 0mH by chagig R o some value less ha 0.75 A. The volage drop across he shu resisace
R Ω ca be used o record he rasie i he iducor curre. apure he rasie i a digial oscilloscope by riggerig i a ideical maer as was doe i sep. Noe he ime cosa of he rasie. 4. Tur o he swich S o eergize he relay. discoecs he coacs K ad coecs K almos simulaeously (circui ime coa is higher ha he ur o/off ime of he relay coacs).the equivale circui is show i Fig. 5( ).. 5. apure he volage across he capacior i he digial oscilloscope usig sigle sho mode. Measure he maximum overshoo, frequecy of oscillaio, ime cosa, iiial ad fial values of he capacior volage ad skech he waveform i a racig shee. 6. Similarly capure ad record he rasie i he iducor curre (measured by he volage drop across he shu). 7. oduc he experime wih differe combiaios of i L (0)( 0.A,0.6 ),. A v ( 0)(.5,5 ) ad ( 0μF,40μF ) ( variaios i each variable). Noe ha Repor: R will chage for each seig of i L (0). (0 ) i L 8. (a) Refer o he equivale circui show i Fig. 5 ().. Use KL ad KL o formulae he differeial equaio ivolvig capacior d v ( ) L dvc ( ) volage as L + + v ( ) d R d Deermie he iiial codiios ( 0 / v ) ad v (0 ) (b) Also do he same for he iducor curre i.
(c) Use Laplace rasformaio o aalyically deermie he complee soluio for he volage v () ad ideify he seady sae SS ad rasie porios of he soluio v cr. he process, he characerisics equaio of he ework i he form: s (σ ) s + ω 0. The roos of he characerisic equaio are s s + σ ± σ ω. The geeral soluio correspodig o hose roos is, v ( σ + σ ω ) v c ( ) K e + K e ( σ σ ω ) σ A ew parameer ξ ca be defied as ξ, ha physically quaifies he ω dampig of he ework. There are hree differe forms for he roos: ase : ξ >, he roos are real ad uequal ase : ξ, he roos are real ad repeaed ase 3 : ξ <, he roos are complex ad cojugaes Noe ha roos o he imagiary axis correspod o oscillaory respose (zero dampig), roos i he complex plae correspod o damped oscillaio ad ha roos o he egaive real axis correspod o he criically damped case (ξ ) or o a over damped form. Whe he roos are complex cojugae he soluio is of he form v ( ) K e ( σ) os ( ω) ( σ ) + Ke Si (ω) K e ( ξω ) os ( ω ( ξω ) ξ ) + Ke Si ( ω ξ ) Where, he physical ierpreaios of he parameers are: ω is aural frequecy, ω is he udamped aural frequecy ad he ime cosa is σ. (d) Fid he parameers ad cosas: σ, ω, ω,, K, K ξ ad v c (max). (e) Also fid he complee soluio for he iducor curre ad ideify he seady sae ad rasie porios of he soluio. Noe ha he characerisic equaio is he same ad herefore fid oly K ad (max). i L 3, K 4 9. From he experimeal resuls obaied i sep 7 ideify he seady sae ad rasie porios of he soluio. Deermie / esimae he parameers σ, ω, ω,, K K ξ ad (max). ompare hese values wih he aalyical, v i L
resuls obaied i sep 9. 0. Fid he rasform domai ework of he circui show i Fig. 5( ). ad deermie ipu impedace (s) ad he oupu impedace i ( s 0 ).. From he rasform domai ework fid he complee soluios by applyig he pricipal of superposiio ha is, you should rea iiial codiios as idepede volage ad curre sources ad fid ou he soluio due o each source separaely ad he add o fid complee soluio.. he rasformer domai ework apply Thevei s heorem o deermie he curre hrough he iducor L. The iiisal values are L ( 0 ) 0. A ad ( 0 ) 5 ad L 0mH ad 0μF. 3. Explai he differeces (if ay) bewee he aalyical ad experimeal resuls.