Ch3 Transient Analysis of CircuitsCh3 Transient Analysis of Circuits -电路的暂态分析电路的暂态分析transient state 暂态 steady state 稳态 transient process 暂态过程 law of switch 换路定理 first-order circuit 一阶电路 three-factor method 三要素法 time constant 时间常数 integral circuit 积分电路 differential circuit 微分电路 Terms:2 2 GraspGrasp law of switch and compute initial value;law of switch and compute initial value;3 3 Concepts ofConcepts of Zero-input Response, Zero-state Zero-input Response, Zero-state Response, Complete ResponseResponse, Complete Response; ;1 1 Understand the concepts of transient stateUnderstand the concepts of transient state、 steady state and physical significance of time steady state and physical significance of time constant;constant;Outline:4 4 Application of three-factor method.Application of three-factor method.For the direct current case, L is short-circuitedFor the direct current case, C is open-circuited+-LinductoruCiC+_capacitorRu+_resistorRu+_resistorRu+_resistorresistorresistorRu+_resistorBefore the movement of Ki = 0 , uC = 0i = 0 , uC= UsTransition process of circuitK+uCUsR Cit = 0Long after K is closedTransition process：the process be undergone by the circuit transienting from one steady state to another steady state . Switching：the circuit (structure or parameter) changes.i+uCUsR CK is closed2. the structure or parameters of the circuit are changedDifferences between steady-state analysis and transient analysisSteady state Transient 1. Long after switching；1. Just after switching;2. iL 、 uC time-varying; 3.Circuit described with algebraic equations ;3. Circuit described with differential equations;2. IL、 UC keep unchanged ;Reasons for transition process1.The circuit contains energy-storage elements L、 C3.13.1 law of Switch and Initial Valueslaw of Switch and Initial ValuesRCRC circuitcircuit: :Note：law of switch is just used to determine the initial value uC、 iL at the moment of switching。 Assumptions：t=0 switching instantt=0 before switching instantt=0+ after switching instantRLRL circuitcircuit：Law of Switch：capacitor voltage and inductor current cannot change abrubtly at the instant of switching.Determination of initial value:Determination of initial value:Outline of solutionOutline of solution：Initial valueInitial value：the value ofthe value of eacheach u u、i i at at t t =0=0+ +in the circuitin the circuit。1.Find uC(0-) or iL(0-) with the aid of the circuit(steady state) before switching.2. Determine uC(0+) or iL(0+) with law of switch.3. Draw equivalent circuit diagram at t=0+.(1) if uC(0-)=0, , Replace capacitor by short circuit;iL(0-)=0, Replace inductor by open circuit.3. Draw equivalent circuit diagram at t=0+.(2) if uC(0-)0, , Replace capacitor by voltage source;iL(0-)0, Replace inductor by current source.Get the value at t=0+，the direction is identical to assumed direction of capacitor voltage and inductor current.4. Find the value of desired variables at t=0+ within 0+ circuit diagram by known methods(Ohms law et al.).Example 1Example 1SolutionSolution： (1) Solve for(1) Solve for According to According to the conditions:the conditions: By law of switch:By law of switch:For the circuit inFor the circuit in FigFig(a). (a). let us let us determine the initial values of each determine the initial values of each voltages and currents. Suppose that voltages and currents. Suppose that the circuit is in steady state before the circuit is in steady state before circuit switching, and Ucircuit switching, and UC C=0=0、I IL L=0.=0.S S(a)(a)C CU R R2 2R R1 1t t=0=0+-L LiC 、uL changedabruptly(2) According to t=0+circuit，solve for initial values of other voltages and currents.S SC CU R R2 2R R1 1t=0t=0+-L L(a) (a) iL(0+ )U iC (0+ )uC (0+)uL(0+)_u2(0+)u1(0+)i1(0+ )R R2 2R1+_+-(b) (b) t = 0+Example Example 2 2Determine the initial values of currents and voltages in Determine the initial values of currents and voltages in circuit shown in Figcircuit shown in Fig. . Suppose that the circuit is in Suppose that the circuit is in steady state before circuit switchingsteady state before circuit switching. .4 42 2+_R RR R2 2R R1 1U U8V8V+ 4 4i i1 14 4i iC C_u uC C_u uL Li iL LR R3 3L LC Ct = 0 equivalent circuit2 2+_R RR R2 2R R1 1U U8V8Vt t =0=0+ 4 4i i1 14 4i iC C_u uC C_u uL Li iL LR R3 34 4Solution：(1) According to t = 0-circuit, and find uC(0)、iL (0 ) ContinuedContinuedAccording to law of switch：4 42 2+_R RR R2 2R R1 1U U8V8V+ 4 4i i1 14 4i iC C_u uC C_u uL Li iL LR R3 3L LC Ct = 0