§ 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,
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01
00)(
x
xxu
We must express the forcing function as a function
of time.
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01
00)(
t
ttu
)(tu
1
0
t
0
)(xu
x
1
The late (延迟 ) unit-step forcing function:
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???
0
0
0 1
0)(
tt
ttttu
)( 0ttu ?
1
0t
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:
)(t?
V
0
0t 1t
t
)(t?
V
0 0t
1t t
V?
)( 0ttVu ?
)( 1ttVu ??
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1
10
0
0
0
)(
tt
tttV
tt
t?
)()()( 10 ttVuttVut ?????
)( 1ttVu ??
)( 0ttVu ?
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