《电路》（英文版）16-3 Loop matrix and KVL

8 16-3 Loop matrix and KVL Augmented loop matrix +1 when branch b is in loop lk and has the same orientation 1 when branch b; is in loop lk and has the opposite orientation, o when branch b is not in loop lk

§16-3 Loop matrix and KVL Augmented loop matrix   Ba = bkj • and has the same orientation; when branch b i s i n loop l j k when branch b i s not i n loop l . j k          − + = 0 1 1 bkj and has the opposite orientation; when branch b i s i n loop l j k

100-1-1 3 Bn=011-10 2 0-O-O 0 KVL: I202+U3 1 00-1 0 or B 0 ,=0

          − − − − − − = • 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 Ba      − − − = + − = − − = 0 0 0 3 1 2 3 5 2 2 3 4 1 1 4 5           l l l KVL:           =                           − − − − − − 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 5 4 3 2 1      • • • or Ba  b = 0 1 2 4 3 5 3 l 2 l 1 l

Fundamental loop matrix 1.2 and 3--tree branches and 3 orientation of l be the same as the chords 2/5 KVL D=U2+04=0 -U,+U 1-10:10 or BU=0 B 0-1-1:0 D matrix which corresponds to the chords of t' FI--matrix which corresponds to the tree branches

Fundamental loop matrix 1, 2 and 3 -- tree branches, and orientation of lk be the same as the chords.       − − − = • 0 1 1 0 1 1 1 0 1 0 Bf    − − + = − + = 0 0 2 2 3 5 1 1 2 4       l l KVL: • • • or Bf b = 0       =                       − − − 0 0 0 1 1 0 1 1 1 0 1 0 5 4 3 2 1        • • • = − 1 T Bf F F matrix which corresponds t o the tree branches. T − − − • 1− −matrix whichcorresponds t o the chords of T. • 1 2 3 4 5 1 l 2 l

Mesh matrix(planar network) +1 when branch b; is in mesh mk and their orientations coincides M=mkj k 1 when branch b is in mesh mk and their orientations do not coincide. 0 when branch bi is not in mesh mk

Mesh matrix(planar network)   M = mkj • . j mesh mk when branch b is not in          − + = 0 1 1 mkj and their orientations coincide; when branch bj i s i n mesh mk and their orientations do not coincide; when branch b j i s i n mesh mk

0101-10 10100 2 U4+U=0 KVL: m2 U2+D4-D5=0 m3U1+D3+D=0 1000-1 or MD,=0

          − − = • 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 M      + + = + − = − + = 0 0 0 : 3 1 3 6 2 2 4 5 1 1 5 6          m m m KVL           =                             − − 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 6 5 4 3 2 1       • • • or Mb = 0 1 2 3 4 5 6 m1 m2 m3