Kevin Aylward wrote:
gwhite wrote:
The simple fact is you are wrong in thinking you can all of the sudden
make up your own definition of linearity, or carry forward without
challenge the mistaken definition of others.
Absolute crap. Show me one respectable math reference that says if
y=exp(x), that y is a linear function of x.
You were right about one
Show me one real practical example that does not use a device with a
functional relation between input and output voltage/current that is
linear, as I defined above. As did note as an after thought, it may be
possible in principle, for example, maybe one could construct a true,
linear with voltage, voltage controlled resistor. However, I am not
aware of such magic devices.
The physical reality is that it is not possible. Produce one and I will
retract my claim.
A light dependant resistor. One input drives a LED via a linearizer
to compensate for LDR non-linearity. The LDR resistance is unaffected
by the voltage across it. Therefore, the resulting current
Io=f(V1,V2)= k.V1*V2 (4-quadrant multiplier or compensated gilbert cell)
The circuit output is *superposition linear* relative to each input.
dIo/dV1=k.V2, dIo/dV2=k.V1 (partial derivatives). In mixer operation,
Io=f(Vin,Vosc). Vosc is an independant time-varying signal.
Therefore, Io=f(Vin,Vosc(t)) or Io(t)=g(Vin,t). Because Io vs Vin
is linear (4-quad multiplier), then dIo/dVin= g'(t) ie: a function
of time only. This is the definition of a linear time-varying
circuit.
that is incorrect. You confuse the time-invariance property with the
linearity property. You believe LTI systems are the *only* linear
systems -- they are not according to the widely accepted and published
definition of linearity.
No. Linearity is widely understood to have many definitions. I have
explained some of these already.
An ideal multiplier is considered nonlinear with respect to a certain
signal if a component of that signal is applied to *both* inputs
simultaneously. Then:
Io=k.(V1+a.V2)(a.V1+V2)= k.( aV1^2 + a.V2^2 + (1+a^2).V1.V2 )
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