s13_lec - Steps in Solving a Linear Dynamic Network Using...

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Unformatted text preview: Steps in Solving a Linear Dynamic Network Using Eigenvalue Method 1. Identify the states of the circuit (capacitor voltages and inductor currents), cc. 2. Use the node method (or loop method) to solve for unknown node voltages (or loop currents). 3. Voltage across inductors is difference in node potentials. (Current in capacitors is differ- ence in loop currents.) 4. Find current in capacitors using KCL. (Find voltage across inductor using KVL.) 5. Using the Constitutive relations for the ca- pacitors and inductors, find the state equa- tion of the form 2:14; 6. Find the eigenvalues Az- and the eigenvectors v- of the matrix A. —Z 7. The general solution is 8. Solve for the ai that give the correct initial conditions. This may be calculated as —1 g=[yl Q2 Edam) Leg-Lure S I?) FVOVVI [437’- fnmo U. TLn. eijevalues and event/«4o»; am. /\\ = —’J. Ml : I M: -25) 2;: (I) ‘ Th 70mm, Sela-’72»: [S Haem Alf AZ+ 11+) :7 Chi/1e 4' Glaze .{ -2S1‘. "" 0' 4' e +' qL ' e ’ 1 Tim. 1454 5:47: [5 +o (Loose a.) QL 4c Mal-(A Zniha Candi-Hows, C3) 01C Cat—WM) +LV/S )5 +£0— Sqw-L 55/u+}btq as bexcwe. Mar-Q 72w2/‘QH3, SD +Lae Magi comdi-HOL—p (.3 sq-hswcmfl when .9 = ‘73“) Cam /e ‘ nu! a»: ‘ewvechrs 77o qno-qur exqm/D/e; 7J‘.(o)-‘-'IV (“41(6): IV FMAZE: dvl:_i_£1WW+°’§t/\A;I 6H C: if 4 diz:_,_v.;a/" Lise-54+!— mo Lur‘Ham. (Awk- dt L1 needed 0+ 7f: LII"? _—_—> g/z—zr,_gz 723 So 84-44e 25 cm Hqu art—4, a v7): “MC. -'/c.][m] at L2 ' ‘/L—7_ O ‘2. Th. characrLeris-Hc. 25041409 is 8+2. +2 -S’ 5 ¢[$): ’ISI'A/c. :- G+a)(5)— 09(2) :2 51+ 2: +/o :0 U842. Zuadm-H; {smug/A 4‘3 «Cit/1A eijenvcvlues: )i': ’ZjJ ZZ—fi‘I/o Noe Sinol eijewvec-Jorsz ),I_.A : [14355 —-S Rog) reduce. : H—Z' Z c) 1 3 ' _.9 l “'5: —Ea ~s’ —H-3J‘ --—17 O Q So 'T'o ex/oress 2M firm: 0; I‘Ea/ Va/iaL/esj 0&2- falle m: eoHJB —_-, e°<(co¢fl +- (Mace/~13" , --6 v7(£)=(o,5+o.§d')(@s 31E +Jw3+k _ + (o.f’o.fcj)(¢os 3+ 3f)€ —t 2 (C05 31 -S4Lv\5+)e ‘6: L; Kew‘l K D . 45‘ 61h?) : (Cos 34': + 2W3Qe ...
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s13_lec - Steps in Solving a Linear Dynamic Network Using...

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