linear time varying system

[preethi19]

Hi i can understand what a linear, non-linear, time varying and invariant system is. I am trying to understand a linear time varying system. So a non time varying system is nothing but say we have an input x1 and no matter at what time we get the output y1. So again input x2 and at any time we get y2.

Now taking a multiplier. Suppose i1=10nA and i2=20nA. So a multiplier gives a simple multiplication say output is 200nA. So the circuit is build in a way that for this input we get always this required multiplication output. So in this case no matter at what time we see for the same above inputs we'll always get the same output in time domain. so isnt't this time invarying system??? little confused. can somebody pls help!!! Thank you!!!

 

[c_mitra]

When you mention 'varying' you mean a derivative either with respect to space or time. If the derivative is constant, we have a linear system (with respect to time or space). If the derivative is zero, we have a 'invariant' (space or time) system.

Differential equations have boundary conditions or often initial conditions. Taking your example, the output is invariant only during the period the circuit exists. Outside the interval, the output is undefined.

 

[wherati]

An ideal mixer is a classic example of a time varying linear system - from the input port to the output port, not the LO port. If you mix a signal A with the LO and get out signal X and you mix a signal B and get out Y, then mixing A+B will give you X+Y (in an ideal mixer). This establishes linearity. But, if you mix in Acos(wt) and get Xcos(w't + phi) and mix in A cos(w(t+dT)+phi), you will not in general get Xcos(w'(t+dT) + phi). This makes the mixer time variant. A simple multiplier is an LTI system, a mixer is a Linear Time Varying system.