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A system is linear if its output can be expressed as a linear combination(superposition)of responses to individual inputs. More specifically,if 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 is,if 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 nonlinearity,let us
consider the simple switching circuit shown in Fig.2.2(a). The
Now consider the
case shown in Fig.2.2(c),where the input of interest is Vin2(while Vin1 remains part of the system and still equal to A1cosω1t).This system is linear
with respect to Vin2. For example,doubling the amplitude
of Vin2 directly doubles that of Vout. The system is also
time-variant due to the effect of Vin1.
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