二阶电路second-order.ppt

? is the damping factor or the neper frequency. (衰减系数/奈培频率)。 ?0 is known as the resonant frequency. S1,2 are called natural frequencies, they are associated with the natural response of the circuit. Overdamped case (过阻尼) The critically damped case (临界阻尼) S1=S2= ??= ?R/2L Underdamped case (欠阻尼) S1,2 are complex. Having both L and C allows the flow of energy back and forth between the two. Undamped case (无阻尼) α=0，S1,2=?j?0 * chap8 second-order circuits keystone：concepts Second-Order Circuits： A second-order circuit is characterized by a second-order differential equation. It consists of resistors and the equivalent of two energy storage elements. 1 zero-input responses of second-order circuits uc(0+)=U0 i(0+)=0 1. zero-input responses R L C + - i uc uc(0+)=U0 i(0+)=0 i(0+)=0 uc(0+)=U0 or 2. 3 cases 过阻尼 临界阻尼 欠阻尼 Eigen roots： The complete solution： S1 and S2 are real and unequal S1,2 are equal and real. the damping frequency S1,2= ???j?d S1,2 are pure imaginary. The response is overdamped when S1,2 are unequal and real, critically damped when S1,2 are equal and real, underdamped when S1,2 are complex, and undamped when S1,2 are pure imaginary. The damping effect is due to the presence of natural frequencies S1 and S2. *