s2-4 Thevenin's and Norton's theorems One of the main uses of Thevenin's and norton's theorems is the replacement of a large part of network very simple equivalent. 7 4A 126 36 R (b) ④8 R 8 (c) (d)
§2-4 Thevenin's and Norton's theorems One of the main uses of Thevenin' s and Norton's theorems is the replacement of a large part of network very simple equivalent. (a) − + 12V 3 6 RL 7 (b) 3 6 RL 7 4A ( c ) − + 8V 2 RL 7 ( d ) − + 8V 9 RL
Thevenin's theorem. Given any linear circuit, rearrange it in the form of two networks A and B that are connected together by two resistance-ess conductors. f either network contains a dependent source, its control variable must be in that same network. Define a voltage v as the open-circuit voltage, which would appear across the terminals of A, if B were disconnected so that no current is drawn from a Then all currents and voltages in B will remain uncharged if A is killed(all independent voltage sources and independent current sources in A replaced by short circuits and open circuits, respectively) and an independent voltage source is connected, with proper polarity, in series with the dead (inactived networ k
Thevenin's theorem: Given any linear circuit, rearrange it in the form of two networks A and B that are connected together by two resistance-less conductors. If either network contains a dependent source, its control variable must be in that same network. Define a voltage voc as the open-circuit voltage, which would appear across the terminals of A, if B were disconnected so that no current is drawn from A. Then all currents and voltages in B will remain uncharged if A is killed (all independent voltage sources and independent current sources in A replaced by short circuits and open circuits, respectively) and an independent voltage source is connected, with proper polarity, in series with t h e d e a d ( i n a c t i v e ) A n e t w o r k
B → B oc voc---open-voltage. Rth---equivalent-resistance Proving: Thevenin th equivalent circuit
A B voc---open-voltage. Rth---equivalent-resistance. Proving: A circuit equivalent Thevenin oc Rth − + B − + oc Rth
B B i=0 R B 十 十 i=i A Thevenin-eguivalent-circuit
i B oc Rth A oc Rth i B A A oc oc + −− + B oc Rth A i'= 0 + − oc B oc Rth A i'' − + oc − + oc Rth Thevenin− equivalent − circuit B i = i
4.000R1 R2 E996 2k 3k R3 2mA 10000k 0 R14000uA600mAR2 3k 1600mA 400.0uA R3 2mA 0.000001 2000mA 0
R 1 2k 4.000V 7.998V 0V 2mA R 2 3k 4V 7.996V R 3 10000k 0 R 3 0.000001 1.600mA R 1 2k 400.0uA 2mA 2.000mA R 2 3k 1.600mA 0 4V 400.0uA