6.002 Fall 2000 Lecture 1 3 6.002 CIRCUITS AND ELECTRONICS Superposition, Thévenin and Norton 6.002 Fall 2000 Lecture 2 3 0= ∑ loop i V Review Circuit Analysis Methods z Circuit composition rules z Node method – the workhorse of 6.002 KCL at nodes using V ’s referenced from ground (KVL implicit in “ ”) ( ) ji ee − G z KVL: KCL: 0= ∑ node i I VI 6.002 Fall 2000 Lecture 3 3 Consider Linearity Write node equations – V I 1 R 2 R + – J 0 21 =−+ − I R e R Ve Notice: linear in IVe ,, VI,eV No terms e 6.002 Fall 2000 Lecture 4 3 Consider Linearity Write node equations -- Rearrange -- V I 1 R 2 R + – J 0 21 =−+ − I R e R Ve I R V e RR +=       + 121 11 G e S = conductance matrix node voltages linear sum of sources linear in IVe ,, 6.002 Fall 2000 Lecture 5 3 Linearity or I RR RR V RR R e 21 21 21 2 + + + = …… +++++= 22112211 IbIbVaVae Write node equations -- Rearrange -- 0 21 =−+ − I R e R Ve I R V e RR +=       + 121 11 G e S = conductance matrix node voltages linear sum of sources linear in IVe ,, Linear! 6.002 Fall 2000 Lecture 6 3 Linearity Homogeneity Superposition ⇒ 6.002 Fall 2000 Lecture 7 3 Linearity Homogeneity Superposition Homogeneity 1 x 2 x y . . . 1 x α 2 x α y α . . . ⇓ ⇒ 6.002 Fall 2000 Lecture 8 3 Linearity Homogeneity Superposition Superposition a x 1 a x 2 a y . . . . . . b x 1 b x 2 b y ⇒ ba xx 11 + ba xx 22 + ba yy + ⇓ . . . 6.002 Fall 2000 Lecture 9 3 Linearity Homogeneity Superposition Specific superposition example: 1 V 0 1 y 0 2 V 2 y 0 1 + V 2 0 V + 21 yy + ⇓ ⇒ 6.002 Fall 2000 Lecture 10 3 Method 4: Superposition method The output of a circuit is determined by summing the responses to each source acting alone. in de p e n de n t s o u r c e s o n l y [...]... etwork N Arb resistors Vm In + – By superposition v = ∑ α mVm + ∑ β n I n + Ri m n no resistance units units By setting ∀n I n = 0, ∀mVm = 0, i = 0 i = 0 i + v - i also independent of external excitement & behaves like a resistor All ∀n I n = 0, ∀mVm = 0 independent of external excitation and behaves like a voltage “ vTH ” 6.002 Fall 2000 Lecture 3 15 Or v = vTH + RTH i As far as the external world is . 6.002 Fall 2000 Lecture 1 3 6.002 CIRCUITS AND ELECTRONICS Superposition, Thévenin and Norton 6.002 Fall 2000 Lecture. and behaves like a voltage “ ” TH v also independent of external excitement & behaves like a resistor 6.002 Fall 2000 Lecture 16 3 Or iRvv THTH +=