一阶电路first-order.pptVIP

-RI0 uL t t I0 iL 0 ? = L/R L： i L + – uL R energy eg1 K opens at t=0\，find uv。 电压表量程：50V iL K(t=0) + – uV L=4H R=10? V RV 10k? 10V iL (0+) = iL(0－) = 1 A uV (0+)=－ 10000V V smoking iL K(t=0) + – uV L=4H R=10? V RV 10k? 10V eg2 t=0,K from 1→2，findu12 iL K(t=0) + – 24V 6H 3? 4? 4? 6? + － uL 2? 1 2 iL K(t=0) + – 24V 6H 3? 4? 4? 6? + － uL 2? 1 2 t 0 i L + – uL R summary 2. ? RC:? = RC , RL:? = L/R R:input resistor iL(0+)= iL(0－) uC (0+) = uC (0－) RC RL 动态元件初始能量为零，由t 0电路中外加输入激励作用所产生的响应。 列方程： i K(t=0) US + – uR C + – uC R uC (0－)=0 7.3 zero-state response 非齐次线性常微分方程 解答形式为： 1. RC电路的零状态响应 零状态响应 齐次方程通解 非齐次方程特解 It is independent of external sources—steady response Complete solution uC (0+)=A+US= 0 A= － US Natural response Forced response（强制分量，稳态分量） -US uC‘ uC“ US t i 0 t uc 0 连续函数 跃变 steady（forced） transient（natural） + （2）?＝RC。 （3）response is rational to sources （4）energy C： Sources supply： R: R C + - US Sources supply=R+C K closes at t=0 , uC（0－）=0，find: （1）u and i of C （2）t if uC＝80V 500? 10?F + - 100V K + － uC i （2）uC＝80V 2. zero-state response of RL iL K(t=0) US + – uR L + – uL R iL(0－)=0： t uL US t iL 0 0 eg1 t=0 ,K opens，find iL、uL (t0) iL K + – uL 2H R 80? 10A 200? 300? iL + – uL 2H 10A Req t0 eg2 t=0 ,K opens，find iL、uL (t0) iL K + – uL 2H 10? 2A 10? 5? + – u iL K + – uL 2H 10? 2A 10? 5? + – u t0 iL + – uL 2H US Req + － 7.4 complete response Resonses which is due to initial conditions and external sources. complete response i K(t=0) US + – uR C + – uC R uC(t) = uC + uC uC (0－)=U0 RC： ?=RC steady uC = US transient uC (0+)=A+US=U0 ? A=U0 - US forced(steady) natural(transient) * chap7 first-order circuits 2. zero-input response zero-state response complete response difficulties 3. State response, transient response 1. Initial conditionsl A circuit is called a transient one if it contains capacitors or inductors. 1. 动态电路transient circuits Initial conditions eg + - us R1 R2 （t=0） i 0 t i 过渡期为零 Trans