[SI-LIST] Re: Square wave harmonics
- From: sainath@xxxxxxxxxxxxx (Sainath Nimmagadda)
- To: <cpad@xxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Tue, 27 Nov 2001 11:16:54 -0800
Chris,
Just curious, what imperfections did you find with Maxwell equations?
Sainath
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Chris Padilla
Sent: Tuesday, November 27, 2001 10:57 AM
To: si-list@xxxxxxxxxxxxx
Subject: [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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