[SI-LIST] Re: Square wave harmonics

Okay, I must pipe in with my 2=A2 worth.

Back in college, I recall solving some problem for frequency.  I ended up=20
with a quadratic and as we know, there are two answers in the solution of a=
=20
quadratic.  It turns out one answer was positive frequency and the other=20
was negative frequency.

Negative frequency???

We've always been taught to simply "throw away" the "nonsensical" or=20
"nonphysical" answer in these cases but does this mean they arent "true" in=
=20
some sense?  (One prof talked about anti-matter and negative frequency=20
being related in some guise...yikes!)

Another example from college involved solving for a particular resistor=20
with in a network of resistors (typical torture problem from an eccentric=20
professor).  The final function was a quadratic and you ended up with a=20
positive resistance and a negative resistance as solutions.

Negative resistance???

This one isn't so far fetched.  Gunn diodes take advantage of the region is=
=20
which their I/V plot is negatively sloped.  Oscillators are made taking=20
advantage of this.

In the end, I have concluded that Mathematics is simply (and usually) an=20
elegant way to get a grasp (i.e. model, represent) on our physical=20
environment and it isn't perfect.  After all, don't most of us take=20
Maxwell's Equations as gospel?  ;^)

Chris Padilla
EMC Engineer
Cisco Systems

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