4. Transform of active single-port network *KaR Q5:Vs=8(),Vo2=? beorem and Nortons theorem Nor(s Isc(SkZeqis) Vor(t) 23( y )u(0=s(n Description: a()=hMO=i2()=b(e-4-c+-ymr For any linear operational network with two terminals which has sources, if the open-circuit voltage Vod(s). (e,By-c4)6()+(-,万 -2 short-circuit Current Isc(s), equivalent resistant zea(s) are known, this network can be equivalent to: Also another way: which has a voltage souree (Vods). series by a resistant ((s)).(Thevenin's theorem h(t)=H(s)=1/(4+S+S) Inverse transform And we have Vod(s)= lsd(s)zeas 4. Transform of active single-port network aK 4. Transform of active single-port network N voc(s)is the computed value when the Isc(s) independent source and initial value zea(s)is the equivalent operational impedance when the independent sources and initial values in the network are set to zero I(s) 4. Transform of active single-port network a 4. Transform of active single-port network m and Norton's theorem /od S, sc(SheaRs) e.g.It what are the s-field equivalent souree circuits for the following circuits? direction: Is v.(0)=1v g Vods) 2.Then solve Voc(s)[10 Isc(s)100 voc(s)上va(s)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 ) ( ) 2 3 2 3 2 3 2 3 ( ) ( ) ( 2 3 1 ( ) ( )]' 2 3 1 ( ) ( ) ( ) [ ( 2 3) ( 2 3) ( 2 3) ( 2 3) ' ( 2 3) ( 2 3) 02 01 e e t e e u t v t h t v t e e u t t t t t t t − + − − − + − − − + − − − − − − + = − + = = = − δ ( ) ( ) ( ) 2 3 1 ( ) ( 2 3) ( 2 3) 01 v t e e u t S t t t = − = − + − − Q5：Vs=δ(t)，Vo2=？ Also another way: h(t) =H(s) =1/(4+S+S-1 . ) . Inverse transform Chapter2：Solving the linear circuits using Laplace Transform—example 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 Description: For any linear operational network with two terminals which has sources, if the open-circuit voltage VOC(s), short-circuit Current ISC(s) , equivalent resistant Zeq(s) are known, this network can be equivalent to: ▲ a network which has a voltage source (VOC(s),) series by a resistant (Zeq(s) ). (Thévenin's theorem) ▲ a network which has a current source (ISC(s) ) paralleled by a resistant (Zeq(s) ). (Norton's theorem) ▲ And we have VOC(s)=ISC(s) Zeq(s) 4. Transform of active single-port network -- operational form of Thevenin's theorem and Norton’s theorem /Voc(S),Isc(S),Zeq(S) *** 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 Ns Ns Ns Ns V(s)=0 ISC(s) + - Ns Ns I(s)=0 VOC(s) + - *** Set the independent source and the initial state to zero 4. Transform of active single-port network -- operational form of Thevenin's theorem and Norton’s theorem /Voc(S),Isc(S),Zeq(S) Networks with null state and no independent source N0 Networks with null state and no independent source N0 I(s) V (s) + - ( ) I( ) s V s Zeq = 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 VOC(s) ISC(s) Zeq(s) is the equivalent operational impedance when the independent sources and initial values in the network are set to zero. is the computed value when the independent source and initial value both affect. 4. Transform of active single-port network *** -- operational form of Thevenin's theorem and Norton’s theorem /Voc(S), Isc(S), Zeq(S) 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 Ns Ns V=0 ISC + - Ns Ns I=0 VOC + - reference direction: Ns Ns Zeq VOC + - Norton’s source circuits ISC Zeq Thévenin's source circuits 4. Transform of active single-port network *** -- operational form of Thevenin's theorem and Norton’s theorem /Voc(S),Isc(S),Zeq(S) 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 e.g.1：what are the s-field equivalent source circuits for the following circuits? 2.Then solve ISC(s) VOC(s) Zeq(s) 1.Find the operational circuits － 10 s ＋ 100 s 1 5 － ＋ s 1 transform － 10Ω 100V ＋ 1F 5Ω VC (0− ) = 1V － ＋ Solving VOC(s) : － 10 s ＋ 100 s 1 － ＋ s 1 VOC(s) + - + - = VR(s) 4. Transform of active single-port network -- operational form of Thevenin's theorem and Norton’s theorem /Voc(S),Isc(S),Zeq(S)