K7ITM wrote:
On Apr 20, 10:10 pm, Roy Lewallen wrote:
Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). . .
That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

I guess that's the definition of linearity. I'm not sure I've heard
it called superposition before, but rather that the superposition
theorem is a direct result of the linearity of a system. I trust
that's a small definitional issue that doesn't really change what
you're saying.

Cheers,
Tom



Tom,

For most purposes the terms superposition and linearity are
interchangeable. However, for the purists there is a difference.

A system that is deemed linear requires that it has the properties of
both superposition and scalability. These properties are essentially the
same for simple systems, but they are not necessarily the same when
considering complex values. I found some clear examples in a book, "The
Science of Radio", by Paul Nahin.

One example, y(t)=Re{x(t)} describes a system which obeys superposition,
but not scaling. Hint: try a scaling factor of "j". That system is not
linear.

Another example is y(t)=[1/x(t)]*[dx/dt]^2. That system obeys scaling,
but not superposition. Again, it is not linear.

The bottom line is that superposition is necessary, but not sufficient
to ensure linearity.

You are correct that the definitional issue is not relevant to the
current RRAA discussion.

73,
Gene
W4SZ