C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals (One-port Network) (One-port Network Example: C1-3: Equivalent of the Linear Network with Two Terminals( One-port Network ①2A a The concept of equivalent, the transfer of source, Thevenin's theorem. Nortons theorem =+4l1-2a1 e eau nt of source (2)letV=4a=3=4-2/1 L Thevenin nch scientist, he proposed his theorem in 1883(26-year-old) ①2=卩2ammh A engineer from Bell Lab, he proposed his theorem in 1937(39- controlling source. i C1-3: Equivalent of the Linear Network with Two Terminals t C1-3: Equivalent of the Linear Network with Two Terminals tk 3. The equivalent of source: (equivalent of practical source) Thevenin's theorem and Norton's theorem nort-cIrcu Description: R, y(t) For any linear network with two terminals which has v(t)=v-R.i(t sources, if the open-circuit voltage Voc, short-circui tage Thevenin's.国mmy= equivalent resistant R are known, this source circuits network can be equivalent to: P a network which has a voltage source (Voc) series by a resistant(Reg).(Thevenin's theorem 9L,V(t) a network which has a current source (Isc) paralleled v(t)=R l-R.i(t) y a resistant(Ro).(Nortons theorem) source rem B Norton's /And we have Voc=lsR C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals Theorem explanation: Thevenin's source circuits Any linear network with two terminals which has sources equivalent Norton's souree cireuits北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 4Ω 1I + - s 2A V 1 2αI + - + - 2Ω 2Ω 2A 1 αI Vs 1I 1 1 V V 4I 2 I = s + − α + - V I + - V I (2) let = 4 Vs α = 3 1 V = 4−2I 2A + - 4V −2Ω −2Ω The negative resistance reflects the active characteristic of controlled source. Its energy comes from the controlling source. Example: C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network)  The concept of equivalent, the transfer of source, Thévenin's theorem , Norton's theorem (the equivalent of source) L.Thevenin French scientist, he proposed his theorem in 1883 (26-year-old) E.L.Norton A engineer from Bell Lab, he proposed his theorem in 1937 (39- year-old) C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 3.The equivalent of source: (equivalent of practical source) + - vs Rs Is Rs + - + - v(t) i(t) v(t) i(t) 0 I V Vs 0 I V Is Vs/Rs RsIs v(t)=Vs-Rsi(t) v(t)=RsIs-Rsi(t) Thévenin's source circuits Norton’s source circuits open-circuit Short-circuit voltage Current *** Equivalent condition: Vs =RsIs C1-3：Equivalent of the Linear Network with Two Terminals Practical voltage source Practical current source 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 Thévenin's theorem and Norton's theorem *** C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) Description: For any linear network with two terminals which has sources, if the open-circuit voltage VOC, short-circuit Current ISC , equivalent resistant Req are known, this network can be equivalent to: ¾ a network which has a voltage source (VOC) series by a resistant (Req). (Thévenin's theorem) ¾ a network which has a current source (ISC) paralleled by a resistant (Req). (Norton's theorem) ¾And we have VOC=ISCReq 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 Theorem explanation: Thévenin's source circuits equivalent equivalent Req=0 C1-3：Equivalent of the Linear Network with Two Terminals equivalent Norton's source circuits Req VOC I Req SC Ns Ns Ns Ns 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 北京大学 wwhu 北京大学 wwhu 北京大学 wwhu 北京大学 Any linear network with two terminals which has sources 3Ω + - 16V + - 2Ω 2Ω 2A 1 αI Vs 1I Is −2Ω Rs Theorem explanation: Is C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network)