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



Roy Lewallen wrote:
Richard Harrison wrote:
Richard Clark, KB7QHC wrote:
"Who. in your estimation, does qualify to discuss it?"

If it`s about antennas, I nominate Kraus. If it`s about mathematics,
many marhematicians qualify.

In algebra, y = mx + b, (the point slope formula), is called linear
because it is the graph of a straight line.
. . .

But of course you realize that the function y = mx + b doesn't meet the
requirements of a linear function when applied to network theory.

Roy Lewallen, W7EL