Russell Shaw wrote:
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)


I have already pointed out the light dependant resistor in another post
in this thread, so I did already do a retraction and a qualification on
this point. This was a minor oversight. The distinction is whether or
not the controlling elements output terminals are connected to its
controlling terminals. If the controlling terminals, are connected to
the controlled terminals then we have a non-linear resister de-facto. A
resister can only be linear if its resistance does not depend on the
current through it, or the voltage across it.

In the case of the transistor, the gain is set by its small signal
resistance re=1/gm. However, the control of the value of gm is by its
own current, therefore it has to be non-linear.

An easy way to see this is the transistor is equivalent to a voltage
being applied across a resister re. Make the voltage a sine wave. Now
apply an additional current through the resister. If the resister was
linear, only an additional fixed dc current would flow, the peak to peak
value of the sine wave would not change.

Kevin Aylward

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