冲激响应和卷积积分习题

单击以编辑母版标题样式,单击以编辑母版文本样式,第二级,第三级,第四级,第五级,*,一阶、二阶电路习题课2,要 求:,1.,电路的冲激响应,2.,卷积积分求解电路的零状态响应,(,3.,二阶电路方程的列写, 特征根与解的形式的关系, 会求全响应。,1,i,L,+,-,u,L,2,(t)A,1,1,2,1H,求,i,L,和,u,L,的冲激响应。,解：法1,-,+,(t),1,1H,+,-,u,L,i,L,1.,t,在 0,-,_,0,+,间,i,L,不可能是冲激函数,*,2,2,. t 0,+,零输入响应,-,+,(t),1,1H,+,-,u,L,i,L,法2：由阶跃响应求冲激响应,i,L,+,-,u,L,2,(t)A,1,1,2,1H,-,+,(t),1,1H,+,-,u,L,i,L,等效,3,-,+,(t),1,1H,+,-,u,L,i,L,i,L,的阶跃响应,i,L,冲激响应:,u,L,冲激响应:,4,一.用卷积积分求,u,2,+,_,u,s,1,F,2M,u,2,t,(,s,),1,2,u,s,(v),E,u,c,(0,-,)=0,(2)求,u,2,=,u,s,*h(t),第一项积分为：,解,：(1)求,u,s,=,(,t,)时的,u,2,。,5,t,h,(,t,),t,(,s,),1,2,u,s,(v),E,*,法1：,第二项积分为：,1,2,h,(,t-,),t ,1,r,(,t,) = 0,6,1,2,t,1,2,t,1 t 2,合成：,0,(,t,1),7,t-,1,t,-2,1 t 2,t,-1,法2,：,-2,-1,t,1, = 0 t =,1,t,= 0, = -,1, = t -,1,t, 1,r,(,t,)=0,8,1,2,t,*,t,1,1,1,t,t2,r,(t)=0,3,1,1,3,1,t-,1,1,3,t,1,1,t,=t-1,2t3,(1,t,5,3,r,(t)=0,t,1,1,t,3t4,(2t,3),4t,5,(3t,4),10,u,s,y,(,t,),方框为无独立源的线性网络，,当,u,s,=0时响应,解：零状态单位阶跃响应为：,二.,(,设初始条件不变),11,三. 判断下图电路过渡过程的性质。(过阻尼，欠阻尼，临界阻尼),解：(a),1W,5H/6,1F/5,+,u,c,-,特征根为：P,1,= -2 ，P,2,= -3,不振荡(过阻尼),1V,2V,5/6H,2W,4W,1/5F,4W,(a),0.5W,1W,2W,1F,1F,2u,1,u,1,12,(b),e,(t),12,u,n,1,u,n2,特征根为：,(b)解：,振荡(欠阻尼),0.5W,1W,2W,1F,2u,1,u,1,12,(b),e,(t),1F,13,四已知下图电路中,u,c,(0,-,)=1V,i,(0,-,)=2A, t=0时闭合开关，求,u,c,。,解：,整理得：,初值定常数：,1H,0.5F,2W,4W,1V,i,u,c,+,-,14,