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

"K7ITM" wrote in message
oups.com...
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


linearity of the system is VERY important. it is what prevents the
waves/fields from interacting and making something new. empty space is
linear, air is (normally) linear, conductors (like antennas) are linear.
consider a conductor in space. if 2 different waves are incident upon it
you can analyze each interaction separately and just add the results.
However, if there is a rusty joint in that conductor you must analyze the
two incident waves together and you end up with not only the sum of their
resultant fields, but also various mixing products and other new stuff. so
yes, linearity is a very important consideration when talking about multiple
waves or fields and assuming superposition is correct.

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

On Apr 21, 7:24 am, Gene Fuller wrote:
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

Thanks, Gene--those examples are helpful. I'll retract what I posted
last night.

Based on the "necessary but not sufficient" statement above, we can
say that superposition does hold in a linear system, so if we specify
a linear system, we do have that guarantee.

Cheers,
Tom

K7ITM wrote:

Thanks, Gene--those examples are helpful. I'll retract what I posted
last night.

Based on the "necessary but not sufficient" statement above, we can
say that superposition does hold in a linear system, so if we specify
a linear system, we do have that guarantee.

And my thanks to both of you.

Roy Lewallen, W7EL