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Through the sampling resistance Ri,we can measure the peak voltage Vp of Ri and thus the peak power of the sampling resistance Ri is PR =Vp2 /R (3) The rising slope di/dt can be evaluated with reference to the change from the 10%to 90%of the peak value. 2.The transient process of RC.RL RLC circuits (1)series RC circuits. As shown in Fig.6,electric capacity charge and discharges during the transient process.The signal source supply square-wave signal.During the first half cycle,the voltage of source is +E.it charges the capacitor;the square-wave voltage turns to 0 in the second half cycle,the capacity discharges.The equation of charging process is Fig6 Series RC circuit RCUc+Ue=E dt (4) Initial condition:t=0 =>Uc=0, Uc=E(1-e RC) Ug =iR=Ee RC (5) From the equation of Uc,UR,Uc increases with time t by exponential law,while resistance voltage Ug decrease in the same way,as shown in Fig.7,therein displaying U-t Uc-t、UR-1 curves.. The equation of discharging process: Rcde+U。=0 UR dr (6) Initial condition:t=0,=>U=E thus we have Uc Ee R UR=R=-Ee旋 (8) From the equation of Uc.Ug,they both decay with time Fig 7 Charging and discharging by exponential law.RC=,which has the dimension of process of series RC circuit3 Through the sampling resistance R1, we can measure the peak voltage VP of R1 and thus the peak power of the sampling resistance R1 is 1 2 1 PR = Vp / R (3) The rising slope di/dt can be evaluated with reference to the change from the 10% to 90% of the peak value. 2.The transient process of RC、RL、RLC circuits (1)series RC circuits. As shown in Fig. 6, electric capacity charge and discharges during the transient process. The signal source supply square-wave signal. During the first half cycle, the voltage of source is +E. it charges the capacitor; the square-wave voltage turns to 0 in the second half cycle, the capacity discharges. The equation of charging process is U E t U RC C C + = d d (4) Initial condition: t = 0 => UC = 0, RC t R RC t C U iR Ee U E e − − = = = (1− ) (5) From the equation of UC、UR , UC increases with time t by exponential law, while resistance voltage UR decrease in the same way, as shown in Fig.7, therein displaying U – t、 UC – t、UR – t curves. The equation of discharging process: 0 d d + C = C U t U RC (6) Initial condition: t = 0,=>UC = E thus we have RC t R RC t C U iR Ee U Ee − − = = − = (8) From the equation of UC、UR , they both decay with time by exponential law. RC =τ, which has the dimension of Fig 7 Charging and discharging process of series RC circuit Fig6 Series RC circuit
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