电路分享基础英文PPT (35).pdf

Classical Solution of First-Order Linear Circuits R-+Ci-+CuSUS 0t CCSdduRCuUtCC1C2uuuParticular solution General solution of homogeneous differential equation SAUFind the for 0.C00uUExample:In the circuit shown in figure Establish the input-output equation of .Solution：Find particular solution Assuming C1=,Substitute it into C00uUThe first order linear differential equation with constant coefficients CCd0duRCuthomogeneous differential equation Set C2ptuKe10RCp 1pRC Characteristic equation tRCKetKeIntegration constant Characteristic root 0SUUKK is determined by initial value 0SKUUC00uUCStuUKeIn summary Find general solution CS0StuUUUe0t CS0ddtuUUiCetR0t t 0 SU0UCut 0 S00UUIRiS0UUif CS0StuUUUe0t S00=ttUUieI eR0t R-+Ci-+CuSUS 0t 0.007 I0 t 0 2 3 5 0etiI I0 I0 e-1 I0 e-2 I0 e-3 I0 e-5 I0 0.368 I0 0.135 I0 0.05 I0 t 0 0IiThe smaller the,the faster the response.It takes 3-5 for the circuit to reach its final state or steady state in engineering.Discussion about .0=ti I e0t 1)Establish the input-output equation of response and determine the initial value of the response.2)Find particular solution of the differential equation.3)Find general solution of the differential equation.5)The integration constant is determined according to the initial value and the response is obtained.4)Add the particular solution and the general solution to obtain the solution to electric quantity.Classical Solution of Dynamic Circuits