It's not clear to me whether you're proposing an alternative definition
for linearity or for superposition. I've never seen superposition
defined as other than that the sum of responses to individual
excitations be equal to the response to the sum of the excitations --
that's the definition in Pearson & Maler's _Introductory Circuit
Analysis_, Van Valkenburg's _Network Analysis_, and the rather old
edition of the _IEEE Standard Dictonary of Electrical and Electronic
Terms_ I have. Do you have a reference that gives the definition you
propose for superposition?

If on the other hand the alternative definition is only for linearity,
we'd then be faced with the possibility of having a linear (and
time-invariant) circuit which doesn't satisfy superposition. That's not
a pleasant circumstance to ponder.

Roy Lewallen, W7EL

K7ITM wrote:
I recall a prof or two arm-waving over that one. However, I think if
you formulate your definition of linearity properly, the transfer
function y=mx+b will still satisfy linearity. Specifically, if the
_response_ is the _change_ that occurs in the output going from x=0 to
x=x1, then the response for x1 is (m*x1+b)-(m*0+b) = m*x1, and of
course for x2, it's m*x2. The response for x=x1+x2 is m*(x1+x2), which
is exactly the sum of the responses for x1 and x2.

Similarly, for a mixer/LO system with RF input and IF output, if the
mixer is unbalanced and lets LO get through, it is still a linear
system if the change in output when go from zero input to input x1(t)
plus the change in output when you go from zero input to input x2(t) is
equal to the change in output when you go from zero input to input
(x1(t)+x2(t)).

But note that a mixer/LO system is NOT time invariant, because the
output for x1(t+delta) is in general NOT the same as the output shifted
in time by delta for input x1(t).

You can most certainly find text books that define linearity
differently than I did above. I find the definition above to be a more
useful one, however, and it seems to be the one generally accepted in
practice, even if it's not stated accurately in words.

Cheers,
Tom