§16-5 Tellegen's(特勒根) theorem Tellegen’ s theore1: Consider a lumped network n consisting of N+l nodes and B branches, let Dn=ob1b2ObBI, b=1b1 b2"IbBl Where Dbk and ibk denote the voltage across and current through branch b for k=1.2...B. Then i=0 or bkbk =0 roo U=4 ∴Dnin=0or>U bkbk =0 k=1 The sum of the powers delivered to or absorbed by all the ranches of a given lumped network is equal to zero.§16-5 Tellegen’s(特勒根) theorem Tellegen’s theorem 1: Consider a lumped network n consisting of N+1 nodes and B branches, let . Where T b b b bB T b b b bB [ ] ,i [i i i ] = 1 2 = 1 2 • •     denote the voltage across and current through branch bk for k = 1,2…B. Then bk bk  and i 0 0 1 =  = = • • • b k B k b b k T b  i or  i Proof: • • • = n T  b A  • • •  = A T n T b  • • • • •  = b T b n T b  i  Ai i or b T b • • •   = 0 0 1  = = bk B k bk  i The sum of the powers delivered to or absorbed by all the branches of a given lumped network is equal to zero. • 0