Magnetic/Electrical Equivalent Circuits and Inductive Matrices
Magnetic/Electrical Equivalent Circuits and Inductive Matrices ECE 4363
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This 5 page Class Notes was uploaded by Bradley Bounds on Tuesday October 13, 2015. The Class Notes belongs to ECE 4363 at University of Houston taught by Dr. Masoud Barati in Fall 2015. Since its upload, it has received 33 views. For similar materials see Electromechanical Energy Conversion in Electrical Engineering at University of Houston.
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Date Created: 10/13/15
1 3 Equiv Circuits and Induc Matrix Thursday September 3 2015 1159 AM Electromechanical Energy Conversion Page 1 Lecture TB Equivalent Circuits and Inductance Matrix There is a perfect equivalence between magnetic and electric circuits Recalling gures iirern previens leetnres let rite be the eresseseetienai area atquot the iren care An the crease seetienal area if the air can an that AEAG The steps in GONEquotEFT the magnetic circuit in its electric equivaient are as fellews 1 Identify seurees cf magnete rnextitr39e Ferec Emmi which are the ceils The eqniealents tier these are eellage senrces with magnitude Ni as T H1 r Figure 1 mrnf tn veltage snur39ce Note the pelarity er the veltagc source it has te be consistent with the dircctien cf the ilua ii and the current i 2 identify anti label naes ID in branches and equivalent currents it 3 identify branch rcluctanecs and their equivalent resistances Thus the equivalent circuit hear an iren care with an air gap and a single eeii week he in H In Re Fig Figure 2quot Earrieel39enr cirenir Electromechanical Energy Conversion Page 2 4 Selre the eirettit by the usual eirertit analysis metherle Per the example abetquote1 we earl eelee the eirettit by tteiag KWL a l at a3 l r 2 at 2 Site 92 lib ia l eattd etapirieally it earn he eetiaidered aa Ag 2 l 53 A6 Certaider the helleteittg example e Jiviarrrre 3 3 hr 39 f 39 ragarelic etirerrir Nete that the elireetieha et the ettrrettta all the eeila were arbitrarily aet There are 3 hraltehee in the eirettit The lengths are de ned by the peiate a he e1 and cl attelt that lam and 13hC are the lettgthe elquot the hrarteheai The relttetatteea are heneej lt zimz rte quotJ rrrri39c39 1 ELItag 2 HA rm Hr39li39E39 E The ereeeeeetiertal area A the aatrte threttgh the entire eere The equivalent eleetrie eirettit is It la in II quot a v 39 it are agate Hit it Rae 27f N3l3 a la Nair Figure 4 Eqrrimferrr eirerrh Electromechanical Energy Conversion Page 3 By KCL at liedue a sinee this yields a gingle equation Q gen um eyumzn Len Fa be the equivaleni weltng in ground at node 1 Then R a I 5 D rri39r m In Snbstiiuiing EiN an Ema mm mm V emit RI Kirk CD ih lzfji Note that E and therefore 131 133 and CD3 are linear fiiiieiieiis ef the iiimf sourees and hienee iinear Wilih respeei ie l39he eeii eiirrenis Wi iere rm em example N R fulle 1 R R nmf if m5 gm39e J N m Jay I Rr c39 Iliad N 1M2 39 m 1330 min The ux linkage ii of coil i i5 defined ago Electromechanical Energy Conversion Page 4 ilr 3 re rahKR i mic lair firm Hrm39e Therefere And L is eahed the i dLlCl CC matrix I w may S I 4 Then i a time E E FBI our example ERIE II RM Rn quotle NTIZ39 Rite391 fe Rm 1th1 Jag 39Rr 39inzquot Rake Reffire 39ATE Rude quot vvl Pf Rm JMTE iwr Rude Rm thajc quot r39r39 will mil m L H 1h generula when there are n mutually eeupled eeile they are eharaelerixed by an ii I ldUCl nEC1111le L of d imeusieu u u h Electromechanical Energy Conversion Page 5
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