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S平面

数学工程上,s平面是进行拉氏转换复平面的名称。s平面是数学模型,可以不用处理时域下以时间为基础的函数,改为处理频域下的方程式,在工程及物理学上是图象式的分析工具。

时间t的实函数f(t)可以进行s转换转换到s平面,作法是和(s为复数)相乘后再积分,时间范围为,积分后的结果就是转换到s平面下的函数。

一种了解此方程的方法是考虑傅里叶分析。在傅里叶分析中,将正弦及余弦和原信号相乘,所得到的积分可以看出某一频率下的信号(频域下某一频率的能量)。s转换也有类似的效果,而且e-st不止考虑频率,也考虑了e-t的效果。因此s转换不止有频率的资讯,也有衰减量的资讯,例如有阻尼的弦波就可以用s转换准确的表示。

s转换常称为拉氏转换。在s平面上,乘s有类似在时域中微分的效果,除以s则相当于积分。

可以分析s平面上方程式的复数根,并绘制在复平面上,可以看到此系统频率响应及稳定性的相关资讯。

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S平面
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