[分享] Time Variance
218 查看
0 回复
 楼主 | 发布于 2022-11-24 | 只看楼主
分享到:

        A system is linear if its output can be expressed as a linear combination(superposition)of responses to individual inputs. More specificallyif the output in response to inputs x1(t) and x2(t) can be respectively expressed as y1(t) = f[x1(t)] ; y2(t) = f[x2(t)] then a y1(t) + b y2(t)= f[a x1(t) + b x2(t)] 。

for arbitrary values of a and b. Any system that does not satisfy this condition is nonlinear. Note that,according to this definition,nonzero initial conditions or dc offsets also make a system nonlinear,but we often relax the rule to accommodate these two effects.

Another attribute of systems that may be confused with nonlinearity is time variance. A system is time-invariant if a time shift in its input results in the same time shift in its output. That isif y(t) = f[x(t)]then y(t-τ) = f[x(t-τ)] for arbitrary τ.

As an example of an RF circuit in which time variance plays a critical role and must not be confused with nonlinearitylet us consider the simple switching circuit shown in Fig.2.2(a). The

control terminal of the switch is driven by Vin1(t) = A1cosω1t and the input terminal by Vin2(t) = A2cosω2t. We assume the switch is on if Vin1>0 and off otherwise. Is this system nonlinear or time-variant?If,as depicted in Fig.2.2(b),the input of interest is Vin1(while Vin2 is part of the system and still equal to A2cosω2t),then the system is nonlinear because the control is only sensitive to the polarity of Vin1 and independent of its amplitude. This system is also time-variant because the output depends on Vin2. For example,if Vin1 is constant and positive,

Now consider the case shown in Fig.2.2(c)where the input of interest is Vin2while Vin1 remains part of the system and still equal to A1cosω1t.This system is linear with respect to Vin2. For exampledoubling the amplitude of Vin2 directly doubles that of Vout. The system is also time-variant due to the effect of Vin1.


(0 ) (0 )
回复 举报
  • 发表回复
    0/3000





    举报

    请选择举报类别

    • 广告垃圾
    • 违规内容
    • 恶意灌水
    • 重复发帖

    全部板块

    返回顶部