Chapter 1 1-1: Introduction to Linear Circuit Analysis PLumped Parameter Hypothesis, Basic Approaches Basic Parameters, Basic Terminology, Reference 《 Principles of Circuit Analysis》 direction, Fundamental Law(KVL、KCL、VCR) C1-2: Common circuit elements and Their Constraint Equations Introductory Linear Circuit Analysis ts, resistance element, Lecture 2 ndependent source, controlled source, dynamic element C1-3: Equivalent of the Linear Network with Two 2009.09.17 Terminals(One-port Network) 2 The concept of equivalent, the transfer of source Thevenin's theorem, Nortons theorem Chapter 1 Introductory Linear Circuit Analysis Cl-1: Introduction to Linear Circuit Analysis The electronics signal analySis: E(t, z)&H(t, z) =1A, V=5V Consistent reference direction Electromagnetic field theory, Circuit Analysis lated reference directio ai(t) The electronics signal analysis It is different between L0? Dissipative element o: the actual direction follows the reference (long wavelength (short wavelength (short wavelength) If result<0: the actual direction opposites the reference Parameter cireuit distributed Parameter circuit Aswell,s equations C1-2: Common circuit elements and Their Constraint REvie C1-2: Common circuit elements and Their Constraint equations Independent source V-V. nclusion: Components paralleled with the ideal voltage source have nothing to do with the outer circuits. Conclusion: Components in series with the ideal current source have nothing to do with the outer circuits 10A
第 ？讲： 复习 《Principles of Circuit Analysis》 Introductory Linear Circuit Analysis Lecture 2 2009.09.17 Interest Focus Persistence Originality 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 Chapter 1 C1-1：Introduction to Linear Circuit Analysis Lumped Parameter Hypothesis, Basic Approaches, Basic Parameters, Basic Terminology, Reference direction, Fundamental Law（KVL、KCL、VCR） C1-2：Common circuit elements and Their Constraint Equations Classification of components, resistance element, independent source, controlled source, dynamic element 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) 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 C1-1：Introduction to Linear Circuit Analysis The electronics signal analysis： Electromagnetic field theory、Circuit Analysis E(t, z)&H(t, z) A B C C’ The electronics signal analysis : It is different between L 0 ? 0: the actual direction follows the reference. If result0 ? P0 ？ 0 I V Is / / Is1=10A / Is2=5A R + - Vs1× + - Vs2 Vs1× + - Is2=5A Is1=10A R × × C1-2：Common circuit elements and Their Constraint Equations ***
Chapter 1 Chapter 1 Introductory Linear Circuit Analysis Cl-1: Introduction to Linear Circuit Analysis -From time-domain analysis to frequency-domain analysis CLumped Parameter Hypothesis, Basic Approaches. C1-2: Common circuit elements and Their Constraint Equations Basic Parameters. Basic Terminology. Reference D Classification of components, resistance element, independent direction, Fundamental Law(KVL、KCL、VCR) source, controlled source, dynamic element C1-2: Common circuit elements and Their Constraint Equations operational amplifier, triode, transformer a classification of Independent souree, controlled source, dynamic element coupling inductance, gyrator C1-3: Equivalent of the Linear Network with Two we can explain the physical phenomena bout transfer /amplification of source- 2 The concept of equivalent, the transfer of source, Thevenin's theorem Norton's theorem (the equivalent of source) C1-21 Common cireuit elements and Their Constraint Equations C1-2: Common circuit elements and Their Constraint Equations Controlled source Controlled source symbol:o◇ 1. Explained the active characteristic of the element Feature: the voltage or current of this kind of source which does not have independent source. controlled by the outer branch's voltage or current. Exami -At v。vi"Avi/v C1-2: Common circuit elements and Their Constraint Equations Cl-2: Common circuit elements and Their Constraint Equations d source magician Circuit for further consideration Explained the active characteristic of the element which does not have independent source Unreasonable circuit 2. Explained the conception of impedance conversion ample 2 The conception of negative resistance
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 Chapter 1 C1-1：Introduction to Linear Circuit Analysis Lumped Parameter Hypothesis, Basic Approaches, Basic Parameters, Basic Terminology, Reference direction, Fundamental Law（KVL、KCL、VCR） C1-2：Common circuit elements and Their Constraint Equations Classification of components, resistance element, independent source, controlled source, dynamic element 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) 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 operational amplifier , triode, transformer, coupling inductance, gyrator …… we can explain the physical phenomena about transfer /amplification of source~ Chapter 1 Introductory Linear Circuit Analysis ----From time-domain analysis to frequency-domain analysis C1-2：Common circuit elements and Their Constraint Equations Classification of components, resistance element, independent source, controlled source, dynamic element 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 Controlled source symbol： Feature: the voltage or current of this kind of source is controlled by the outer branch’s voltage or current. - + VCCS VCVS CCCS CCVS - + - + gVi AVi KIi rIi 0 I V I=gVi 0 I V V=rIi *** C1-2：Common circuit elements and Their Constraint Equations 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 Controlled source 1. Explained the active characteristic of the element which does not have independent source. Example 1: Ri + Vi - + Vo - Ro + - AVi Vo/Vi=AVi/Vi=A Circuit model of operational amplifier C1-2：Common circuit elements and Their Constraint Equations 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 Controlled source 1. Explained the active characteristic of the element which does not have independent source. 2. Explained the conception of impedance conversion and negative resistance element Example 2: R1 + Vo - aI1 I1 Io R=Vo/Io=V1/(1-a)I1= R1/(1-a) The conception of negative resistance Magician C1-2：Common circuit elements and Their Constraint Equations 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 Circuit for further consideration: + Vs - R I 3I Unreasonable circuit R R Not in accord with KCL X Impossible circuit C1-2：Common circuit elements and Their Constraint Equations
Content C1-2, Common circuit elements and Their Constraint equattons C1-2: Common circuit elements and D Classification of compo a Linear constant capacitance: C dependent source controlled source, dynamic element Constraint Equation: @(t=Cr(t) C1-3: Equivalent of the Linear Network with Two Symbol: i(t) Terminals(One-port Network 2 The concept of equivalent, the transfer of source p()-/)=a CV curve Thevenin,s theorem Norton's theorem the equivalent of source) b Linear constant inductance: L Constraint Equation: P(t=Li(t) Symbol: I(t) omen=dy(o) y(t L a( WA curve Content C1-3: Equivalent of the Linear Network with Two Terminals C1-2: Common circuit elements and Their Constraint Equations independent source, controlled source, dynamic element If the port characteristic(I-V curve)of an one-port network NI is the C1-3: Equivalent of the Linear Network with Two same as another one-port network N2, these two networks are Terminals(One-port Network) quivalent, which means they can be exchanged equivalently 2 The concept of equivalent, the transfer of source, Thevenin's theorem, Norton's theorem ( the equivalent of source) I-V curve Overlapping completely I-V equations V Completely the same C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals Equivalent Components paralleled with the ideal voltage source have nothing to do with the outer crcuits. omponents in series with the eal current source have nothmg to do with the outer circur
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 Content C1-2：Common circuit elements and Their Constraint Equations Classification of components、 resistance element 、 independent source 、controlled source、 dynamic element 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) restless element 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 0 + v(t) - i(t) Q V CV curve a. Linear constant capacitance: C Constraint Equation: Q(t)=Cv(t) Symbol： dt dv t C dt d t i t ( ) ( ) ( ) = = Q 0 + v(t) - i(t) I WA curve b. Linear constant inductance: L Constraint Equation : Ψ(t)=Li(t) Symbol: dt di t L dt d t v t ( ) ( ) ( ) = = ψ Ψ C1-2：Common circuit elements and Their Constraint Equations *** 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 Content C1-2：Common circuit elements and Their Constraint Equations Classification of components、 resistance element 、 independent source 、controlled source、 dynamic element 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) 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 conception of equivalent: If the port characteristic (I-V curve) of an one-port network N1 is the same as another one-port network N2, these two networks are equivalent, which means they can be exchanged equivalently. V(t) + - N1 I(t) N2 I(t) V(t) + - Outer circuit Any circuit 0 I V I-V curve or I-V equations Overlapping completely or Completely the same *** Any circuit Outer circuit 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 Example 1: N1 1Ω + - 10V 5A 1Ω 1Ω N2 5A 5A 0 I V Equivalent ？ Why? 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 0 I Vs V R + - Vs + - + - Vs 0 I V I0 Is R Is Example: *** C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) Equivalent ？ Why? Components paralleled with the ideal voltage source have nothing to do with the outer circuits. Components in series with the ideal current source have nothing to do with the outer circuits
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) The equivalent of resistance elements 2.The equivalent of dynamic elements 0)=V R=R1+R2+ 0)=c V=R1+R2=l(R1+R2) Completely the same If 1(t)is limited(oc), v(t)is milarly, when paralleled: G=G+G? a continuous function (t)=r(0)+-|r(n)d(r) The voltage of the capacitance C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals 2.The equivalent of dynamic elements 3.The equivalent of source Inductance: i(t).1(0)0 v()=L i(t) Ifv(t) is limited(≠∞,f(t)isa ontinuous function. f components paralleled with the ideal voltage source have nothing to do with the outer circuits. ()=1(0)+7v(d( The current of the inductance can It change shapely omponents in series wah the ideal current source have nothing to do wih the outer circuits. C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals k Network 3. The equivalent of source: (equivalent of practical source) 3. The equivalent of source: (equivalent of practical source) i(t) R Practical vltage E Thevenin's [equivalent condition: VR1. Ideal voltage Practical source i(t) i(t) Source R, v(t) R v(t) v(t=RL-R.i(t Practical curre Nortons source circuits
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 + I R - V Similarly, when paralleled: G=G1+G2 V I + - R1 R2 1.The equivalent of resistance elements = R=R1+R2 I-V equations Completely the same V=IR1+IR2=I(R1+R2) V=IR 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 = + t i t d t C v t v 0 ( ) ( ) 1 ( ) (0) 2.The equivalent of dynamic elements + v(t) - i(t) dt dv t i t C ( ) ( ) = Capacitance : The voltage of the capacitance can’t change shapely. If i(t) is limited (≠∝), v(t) is a continuous function. *** 0 v V (0) = + v(t) - i(t) + - V V s = 0 v(0) 0 = 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 + ∫ t v t d t wwhu 北京大学 L i t I 0 ( ) ( ) 1 ( ) (0) dt di t v t L ( ) ( ) = Inductance : The current of the inductance can’t change shapely. If v (t) is limited (≠∝), i(t) is a continuous function. + v(t) - i(t) I(0)≠0 I(0)=0 + v(t) - i(t) Is= I(0) *** 2.The equivalent of dynamic elements 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 is1 is2 s = ∑ si i i ＋ － ++ - ＋ － ++ - ＋ － ++ - s = ∑ si v v 3.The equivalent of source + - = ? + - = ? *** Components paralleled with the ideal voltage source have nothing to do with the outer circuits. Components in series with the ideal current source have nothing to do with the outer circuits. 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) 0 I V I=Is 0 I V V=Vs Ideal voltage source 0 I V Is Vs + - vs Rs Is Rs + - + - v(t) i(t) v(t) i(t) C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) Ideal current source Practical 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 Practical voltage 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) equivalent condition： Vs =Rs I Thévenin's s source circuits Norton’s source circuits *** C1-3：Equivalent of the Linear Network with Two Terminals 3.The equivalent of source: (equivalent of practical source) Practical current source
C1-3: Equivalent of the Linear Network with Two Terminals (One-port Network Tea break/ Example 20 =0.375A 19 果是个12 白 C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals 4.The transfer of source( Equivalent of network with more terminals): 4.The transfer of source(Equivalent of network with more terminals) The transfer of current source. Example: the benefits of the transfer of source V32=,-12R2 The same port characteristic V12=1R1-l2R2 C1-3: Equivalent of the Linear Network with Two Terminals C1-3: Equivalent of the Linear Network with Two Terminals 5. Equivalent of the one-port network with controlled source 1 )Equivalent to source: When the controlling parameters is outside the network which is equivalent, the controlled source has a active ①2A characteristic, which can be deal with like an independent source quivalent to source: When the controlling paran V=V, +41,-2al inside the network which is equivalent, we can only write down the equations using KCL or KVL, and acquire the I-V relationship (1)let,=10a=1/2V=10+3l1 the port. V=10+3(2+1) 2A
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 Example : + - - + 1Ω 1Ω 2Ω 2Ω 1V 2Ω 1V I=？ + - - + 1Ω 2Ω 0.5V 2Ω 1V I=？ + - 1Ω 1Ω 2Ω 0.5A 2Ω 1V I=？ 2Ω 2Ω 1Ω I=？ 0.25A 2Ω 0.5A 1Ω 1Ω I=0.375A 0.75A 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 Tea break！ Tea break！ 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 4.The transfer of source (Equivalent of network with more terminals)： R1 + - I2 R2 I1 I3= I1+ I V 2 s 12 1 1 2 2 31 1 1 32 2 2 V I R I R V V I R V V I R s s = − = − = − 3 2 1 + - I2 R2 I1 + - R1 Vs Vs I3 3 2 1 The same port characteristic (the same I-V equations) 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 The transfer of current source: R1 R2 R1 R2 Example: the benefits of the transfer of source + - - + + - C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network) 4.The transfer of source (Equivalent of network with more terminals)： 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 5. Equivalent of the one-port network with controlled source: 1)Equivalent to source: When the controlling parameters is outside the network which is equivalent, the controlled source has a active characteristic, which can be deal with like an independent source. 2)Not equivalent to source: When the controlling parameters is inside the network which is equivalent, we can only write down the equations using KCL or KVL, and acquire the I-V relationship of the port. 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 Example: 4Ω 1I + - s 2A V 1 2αI + - + - 2Ω 2Ω 2A 1 αI Vs 1I 1 1 V V 4I 2 I = s + − α (1) let Vs =10 α =1/ 2 1 V =10 + 3I + - V I + - V I + - 2A 3Ω 10V I1 + - V I 3Ω + - 16V + - V I V=10+3(2+I) =16+3I C1-3：Equivalent of the Linear Network with Two Terminals (One-port Network)
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)
Thevenin's theorem and Norton's theorem Thevenin's theorem and Nortons theorem open-circuit voltage Voc? short circuit current Isd? Reference direction Isc equivalent resistance R -? Reu is equivalent input resistance while setting the sourees in the network to zero 、{ N 2. Summe the port's I Thevenin's souree Norton's souree V/I Thevenin's theorem and Nortons theorem Thevenin's theorem and Nortons theorem Example Example Ifv=10a=112 6V Open-circuit voltage Voc? hort- circuit current lsc- l=2 =V+41-2al1=10+8-2=16 al,+V+4J.=0 中kc=16/3 Thevenin's theorem and Norton's theorem Cl-3: Equivalent of the Linear Network with Two Terminals If.=10a=1/2 Equivalent resistance Req Solution l =-2al+4l Norton’ s theoren R=V/I Verification: Vo lR →16=16/3×3 nins and Norton's source cireuits' transform we simplify the circuit directly
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 open-circuit voltage VOC=？ short circuit current ISC=？ Req is equivalent input resistance while setting the sources in the network to zero. 1.Set to zero 2.Asumme the port’s I-V equivalent resistance Req=？ *** Ns Ns V=0 ISC + - Ns Ns I=0 VOC + - N0 N0 I V + - Req = V/I 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 Ns Ns V=0 ISC + - Ns Ns I=0 VOC + - Thévenin's theorem and Norton's theorem Reference direction: *** Req VOC + - Norton’s source I Req SC Thévenin‘s source 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 Example: If: Vs =10 α =1/ 2 3Ω + - 16V 4Ω 1I + - 2A Vs 1 2αI + - V I + - Open-circuit voltage VOC=？ 4Ω I1 = 2A + - 2A Vs 1 2αI + - + - Voc 4 2 10 8 2 16 Voc =Vs + I1 − αI1 = + − = Thévenin's theorem and Norton's theorem Ns Ns I=0 VOC + - 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 Example: If: Vs =10 α =1/ 2 3Ω + - 16V 4Ω 1I + - 2A Vs 1 2αI + - V I + - 2 4 0 − αI1 +Vs + I1 = Short-circuit current ISC=？ Isc=16/3 4Ω sc I = 2 − I 1 + - 2A Vs 1 2αI Isc + - Thévenin's theorem and Norton's theorem Ns Ns V=0 ISC + - 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 Example: If: Vs =10 α =1/ 2 3Ω + - 16V 4Ω 1I + - 2A Vs 1 2αI + - Req = V/I Equivalent resistance Req=？ + - V 4Ω 1 I I 1 2αI + - I = I 1 V = −2αI + 4I = = −2α + 4 = 3 I V Req Verification: VOC=ISCReq Æ 16 = 16/3 × 3 Thévenin's theorem and Norton's theorem N0 N0 I V + - 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 160 8 160 20V 40 120 1A Ω Ω Ω Ω Ω + - 5uF question： Thévenin's source circuit Solution 1: Solution 2: According to Thévenin‘s and Norton’s source circuits’ transform, we can simplify the circuit directly. Example: According to Thévenin's theorem and Norton's theorem C1-3：Equivalent of the Linear Network with Two Terminals Zeq VOC + - Ns Ns V=0 ISC + - Ns Ns I=0 VOC + -
C1-3: Equivalent of the Linear Network with Two Te Thevenin's theorem and Nortons theorem 44V N 1.1A40 Bo 1600 品i2 2 A (t) N Chapter 1 Introductory Linear Circuit Analys Cl-1: Introduction to Linear Circuit Analvsis d Parameter Hypothesis, Basic Approaches Method of equations Basic Terminology. Reference C1-2, Common circuit elements and Their Ca lassification of components, resistance Basic elements led source、dyna C1-3: Equivalent of the Linear Network with Ty t, the transfer of Method of equivalent ivalent of 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 40Ω 160Ω 1A + 4V - 32Ω 8Ω 160Ω 1/8A 1A 例： 160 8 160 20V 40 120 1A Ω Ω Ω Ω Ω + - 5uF 160X40/200=32 C1-3：Equivalent of the Linear Network with Two Terminals 160Ω 40Ω 1.1A 200Ω + 44V - 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 Req VOC + - Ns Ns equivalent NL NN NL NN N x(t) y(t) Thévenin's theorem and Norton's theorem 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 The concept of equivalent, the transfer of source, Thévenin's theorem , Norton's theorem (the equivalent of source) C1-1：Introduction to Linear Circuit Analysis Lumped Parameter Hypothesis, Basic Approaches, Basic Parameters, Basic Terminology, Reference direction, Fundamental Law（KVL、KCL、VCR） C1-2：Common circuit elements and Their Constraint Equations Classification of components、 resistance element 、 independent source 、controlled source、 dynamic element Method of equations Method of equivalent Basic elements Chapter 1 Introductory Linear Circuit Analysis ----From time-domain analysis to frequency-domain analysis