Cecil Moore wrote:

In a linear system, there only needs to be a straight line function
between the input and output. The actual signals on the input wouldn't
be very useful if only straight line functions were allowed on that
input. The current distribution along an antenna element length only
ever approximates a straight line. The only requirement for that
current to obey the rules for a linear system is that it be a
linear function of the source current and it is at every point.

I mostly agree with your definition of linearity. Roy's point that an
offset in the straight line violates superposition is an example of a
straight line violating superposition. Also consider the throwing of
two dice. If the dice act independently they can be considered a
linear system with two outputs (the numbers that show on the dice)
which obeys the law of superposition. If, however, the dice collide
when thrown, they now influence each other, the system becomes
nonlinear, and the law of superposition is violated. It's pretty hard
for me to attach a straight line function to dice.

Mixers are especially interesting beasts when viewed in the light of
superposition. They are obviously highly nonlinear, yet we regularly
speak of mixer linearity. Here is the trick: when the local oscillator
is included in the input signal set, the mixer is highly nonlinear as
the LO influences every signal that comes in drastically, in the sense
of generating new frequencies.

But it is convenient to think of the local oscillator as just an
internal parameter of the mixer, and to not include it in the input
signal set. Under this assumption all the RF input signals
substantially obey the law of superposition (that is, they do not
influence each other) and discussing mixer linearity has enough meaning
that we can characterize it through standard tests. Note also that
under this assumption the output frequencies do not match the input
frequencies in general, yet the law of superposition holds over a wide
dynamic range.

Cecil's point that doubling antenna current will double the current at
each point in the antenna (I'm rephrasing) has a dual in mixers:
doubling any signal will double all the mixer's ouputs due to that
signal alone, and not any other outputs.


73,
Glenn Dixon AC7ZN