Two Port Device A two port system contains nothing but a gate that is initially

Question

Two Port Device A two port system contains nothing but a gate that is initially open but closes the first time a step in the input voltage occurs (you could think about this step as a finite discontinuity in the input waveform). Prior to this event, there is no output (zero output), whatever the continuous input; but subsequently the output faithfully follows the input. For instance, for a input V_1 (t) the corresponding output is V_2(t). Smith says, "it is clear to me that the response to V_1 (t - T) is V_2 it - T) no matter what the input waveform V_1 (t) is. Therefore, the system is time-invariant." But Jones says, "I don't agree. I fed some music into that box this morning and nothing came out, but this afternoon I fed the same waveform and it was transmitted perfectly." Is the system time-invariant? Is Smith or Jones wrong? and how could you explain their observations. Is the system linear?

Explanation / Answer

(a) System is time invariant. But both smith and jones are wrong in their reasoning.

Let the output be F(t)=G(s(t),i(t),t)

here s(t) in the step input that causes the switch to ON.

i(t) is the input waveform

t is time

We can notice that F(t)=G(s(t),i(t)) holds for all input i(t) which means that the output is dependant only on present input only. so the system is time in variant.

2) yes the system is linear because adding two or more input signal can add two corresponding output waves. This question can be compared to a tyristor that switches on when there is a sharp increase in current. Yet we model it as a LTI device for solving question in electronics.

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