8 16-4 Interrelationship between matrices of a G AB=0 and B2=0 Relationship between branch and node voltages 2 n 3 bI 2 b2 n2 D 3 3 5 Db4 =l Re∫ 10 b2 1-1010 000 0 or D 100 100
§16-4 Interrelationship between matrices of a G • • • • • • = 0 = 0 T f f T ABf and B Q Relationship between branch and node voltages 1 2 3 4 5 Re f . n1 n2 n3 b1 =n1 −n2 b2 = −n2 +n3 b3 = − n3 b4 =n2 b5 = − n1 − − − − = 3 2 1 5 4 3 2 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 0 n n n b b b b b • • • = n T or b A − − − − = • 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 A
Relationship between branch and loop currents bI l1 12 2 La =L-l n n3 b3 b4 12 L 13 5 3 65 12 66 l1 Re∫ 110 b2 0 110001 b3 001 or i,= B 100-110 12 0-11100 b4 65 010 13 00
Relationship between branch and loop currents b1 l1 l 2 i = −i + i b2 l1 l 3 i = i − i b3 l 3 i = i b4 l 2 l 3 i = −i + i b5 l 2 i = i b6 l1 i = i − − − = 3 2 1 6 5 4 3 2 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 l l l b b b b b b i i i i i i i i i • • • = l T b f or i B i − − − = • 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 Bf 1 2 3 4 5 Re f . n1 n2 n3 6 l1 i l 2 i l 3 i
,=Bli Proof: AB=0 BO,=BA D=0 ba=o or AB=0 r00f: B 0 2r in=er bi=0 or b=0 or B of=0
• • • = n T b A • • • = l T b f i B i • • • Pr : = 0 T oof ABf • • • • • • = n = 0 T Bf b Bf A • • • • • • = 0 = 0 T f T Bf A or AB • • • = 0 T Bf Qf Pr oof : • • • • • • = l = 0 T f b f f Q i Q B i • • • • • • = 0 = 0 T f f T Qf Bf or B Q