§5-1 The unit-step(阶跃) forcing function We define the unit-step forcing function as a function which is zero for all values of argument which are less than zero and which is unity (1) for all positive values of ts argument u(r) 0x0 0 We must express the forcing function as a function of time u(t) 0t0
§5-1 The unit-step (阶跃) forcing function We define the unit-step forcing function as a function which is zero for all values of argument which are less than zero and which is unity (1) for all positive values of its argument. = 1 0 0 0 ( ) x x u x We must express the forcing function as a function of time. = 1 0 0 0 ( ) t t u t u(t) 1 0 t 0 u( x) x 1
The late(延迟)unit- step forcing function: u(t-t) 0 t to The unit-step forcing function is in itself dimensionless (GA A). If we wish it to represent a voltage, it is necessary to multiply u(t-to) by some constant voltage, such as v. Thus v(o=Vu(t-to) an ideal voltage source which is zero before tto and a constant v aftertto If we wish it to represent a current, it is necessary to multiply u(t-to) by some constant current, such as 1. Thus i(t=u(t-to) is an ideal current source which is zero before tto and a constant l after tto
The late (延迟) unit-step forcing function: − = 0 0 0 1 0 ( ) t t t t u t t ( )0 u t − t 1 0 t t 0 If we wish it to represent a current, it is necessary to multiply u(t-t0 ) by some constant current, such as I. Thus i(t)=Iu(t-t0 ) is an ideal current source which is zero before t=t0 and a constant I after t=t0 . The unit-step forcing function is in itself dimensionless (无量 纲). If we wish it to represent a voltage, it is necessary to multiply u(t-t0 ) by some constant voltage, such as V. Thus v(t)=Vu(t-t0 ) an ideal voltage source which is zero before t=t0 and a constant V after t=t0
The rectangular voltage pulse u(t) 0 tt, r1 D(t)=yu(t-t)-yu(t-t) to(0) u(t-to) 0 (t-t1)
The rectangular voltage pulse: (t) V 0 0 t 1 t t (t) V 0 0 t 1 t t −V ( )0 Vu t − t ( )1 −Vu t − t = 1 0 1 0 0 0 ( ) t t V t t t t t t ( ) ( ) ( ) 0 1 t =Vu t − t −Vu t − t ( )1 −Vu t − t ( )0 Vu t − t − + − +