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Fr. Tom Strikes Again
Subject: Fr. Tom Strikes Again
Date: Thu, 8 May 1997 14:07:45 -0400
From: "Thomas McGahee" <tom_mcgahee-at-sigmais-dot-com>
To: "Tesla List" <tesla-at-pupman-dot-com>
I changed the name of the thread
because it has nothing to do with
Lightning Generators anymore, although
it is true that a chance remark about
the possible RF nature of a lightning
strike did trigger the original response.
When will I learn to keep my mouth shut?
First the post that triggered this reponse:
----------
> From: Tesla List <tesla-at-pupman-dot-com>
> To: tesla-at-poodle.pupman-dot-com
> Subject: Re: Lightning Generator
> Date: Thursday, May 08, 1997 1:33 AM
>
> Subject: Re: Lightning Generator
> Date: Tue, 6 May 1997 17:55:47 -0700 (PDT)
> From: "Edward V. Phillips" <ed-at-alumni.caltech.edu>
> To: tesla-at-pupman-dot-com
>
>
> "Ed,
> It is a single polarity, true... but what makes something RF is the
> "apparent" frequency of a 1/2 cycle, which of course is a unipolar
> definition, is it not? Some Tesla coil builders use a DC supply to
> supply raw power to the tank circuit. The gap fires and we call it
> RF. And to take it to its extreme, a Tesla coil operated in ONE
SHOT
> mode only gets a single half cycle of excitation. But it STILL
> operates as a resonant RF circuit anyhow."
> That is a completely new definition to me! I don't agree
> but don't think the matter is worth pursuing, except to ask how
> you define the frequency of a pulse? Reciprocal of the period?
> Frequency to me is associated, in this context, with harmonic
> motion which doesn't apply. Impulse excitation of a resonant
> circuit is an entirely different matter.
> Ed
Ed,
Since I was the one who wrote the excerpt quoted above, I will
attempt a short explanation. Normally when we are dealing with
frequency we are dealing with a waveform that has a repetitive
nature. In this context it is rather easy to speak of such things as
frequency and period. What begins to mess up people's minds is when
we start talking about the frequency of a single pulse. Or the
MULTIPLE sinewave frequencies that are present in something as
mundane as a stupid square wave!!! Or a triangle wave. Or ANY
waveform that is not PURELY sinusoidal!!!
I *REALLY* don't want to get into Fourier transforms and other such
wonderful things. So let's try to keep it *SIMPLE* here. Yeah, I
know, any time I try to simplify something so the average joe can
comprehend it, someone else is going to come along and flame me for
not giving the full 22 page college textbook answer, complete with
citations. Sigh! But, despite it all, let's press forward, because
what we are really all about on this list is not impressing one
another, but helping one another.
Imagine a 1 MHZ (or 1 Mhz) (or even a 1 Mc) waveform. Let's make it a
wonderfully pure 1 MHZ waveform. The frequency is easy to measure.
You just measure from ANY point on the waveform to the NEXT (or
previous) equivalent point. For the sake of sanity, let's choose as
our starting point the point where the waveform *rises* above zero.
>From THAT point to the NEXT place where it *rises* above zero would
be one PERIOD. The frequency is 1/P where P is the period. Simple
stuff.
Now assume that you have a circuit that can generate exactly 1 cycle
of that 1 MHZ waveform. Why, it would still be a 1MHZ waveform,
wouldn't it? (of course!)
Ah, the sine wave is so neat, so cool, so elegant. It has beauty and
symmetry. OK, so let's apply some of this symmetry stuff and see what
we get if we were to generate exactly ONE HALF of a cycle.
OOPS! No change in polarity! No repetition! No PERIOD!! NO
FREQUENCY!!! My God, there is no way on earth we can figure out its
frequency! So, I guess it must be DC. Well, only if you are looking
at the waveform from the VERY LIMITED definition which was rather
shortsightedly tied down to the concept of *repetition*. I do believe
that MOST intelligent persons looking at the half cycle would be
willing to say "Hey, it looks like if you continued it out the way it
was going, you'd get 1 Mhz as the answer." Give that kid a cigar. Now
put it away, because we don't allow smoking in this school, no matter
how old you are!
The above answer is a good answer (not complete, rigorous, or highly
mathematical, but GOOD). The answer is GOOD because the wave SHAPE in
this case is, in fact, sinusoidal.
Now I give you a 1 MHZ square wave. 50% duty cycle. The real thing.
What is its frequency? By applying the dumb old period and f=1/p
formula you will proudly come up with the answer "1 MHZ of course". I
smile at the class and nod approval.
At which time I normally look at my class and smile again and then
say, "Yes, and what are the sine wave frequencies you SEE here?" They
all honestly and correctly (if somewhat hesitantly) say "Why, NONE,
Father Tom!" I smile and give them a nice round of applause. Then I
slowly turn around again and give them the ZINGER: "Yes.... but what
are the sine wave frequencies that are THERE and which you DON'T
see?"
If I got the right answer *here* I would sing a full five minutes of
the Halelujiah Chorus while carrying the triumphant student around on
my shoulders. But it has never happened, and I doubt if it ever WILL,
because sometimes there is much more to something than we can SEE
with our eyeballs. Sometimes we have to look real close and analyze
and THINK and use our brains, and only THEN do we truly SEE what
stands before us. THAT is what we teachers are for. To help students
THINK!
A 1 MHZ sine wave and a 1 Mhz square wave are BOTH 1 MHZ frequency.
Believe it or not, they BOTH contain 1 MHZ *SINE* waves. Strangely
Believe It Or NOT, the square wave contains a whole SLEW of other
sine waves as well!!! I'll let YOU guess how *MANY*. Yep, it's a big
humongous number!
If you don't believe me, well, that doesn't change the facts. I don't
make up the facts. I just report them.
Some people can go to college, get a degree, do all the Fourier
transforms and get the right answers and STILL don't understand what
they are *DOING*. I treasure the moments when my students REALLY open
their eyes and see with their MINDS and not just their eyeballs. It
gives me hope. It gives me JOY!!! (I DON'T teach my kids Fourier
transforms. I teach them to LOOK beyond the obvious. I figure they'll
get enough of the math stuff when they go to college. I want to get
them all fired up about learning, not fry their brains on formulae.)
What if you had a 1 MHZ wave that was 25% duty cycle (as opposed to
50% duty cycle)? Wouldn't THAT also have a part of itself that was 1
MHZ sine wave? YES, but not *as much* as that 50% squarewave. And if
you've guessed that there is a fair amount of 2 MHZ sine wave in the
25% duty cycle waveform, then give yourself a pat on the back,
because you are beginning to see (if not all of it), at least a PART
of what I am trying to get at. If there is something gnawing away at
the back of your brain saying that just possibly there might have
been some 2 MHZ sine wave in the 50% duty cycle square wave, TOO, but
probably LESS than there is in the 25% duty cycle waveform, then you
are on the road to understanding. (It's a great feeling, ain't it!)
OK, so now that Fr. Tom has wasted a good five minutes of your life
(and MUCH more of *his* life) giving you a little mini-taste of sine
and square waves, you may be asking yourself the question: "Yes, but
what has this got to do with the original question???"
Why, *everything*, of course! A single pulse, if shaped like a sine
wave (so far at least), will have characteristics amazingly like a
sine wave of the frequency it would have had if it had continued
being a sine wave. Elementary, my dear Watson, elementary!
A *fast* rise and fall time predominantly square wave pulse will have
many many many many many equivalent sine waves "composing" itself.
That is the connection with the previous discussion. BUT, of ALL the
sine waves that it contains, it is the sine wave whose EDGES you can
already SEE that will predominate. Now if I told you the silly pulse
looked an awful lot like a half cycle of, say, a 1 MHZ waveform, what
would YOU say the PREDOMINANT frequency was? (Don't be bashful. My
students would yell out "1 MHZ, *OF COURSE!*")
And so, that is why I said that:
> It is a single polarity, true... but what makes something RF is the
> "apparent" frequency of a 1/2 cycle, which of course is a unipolar
> definition, is it not?
If I have befuddled anyone I apologize. Engineers and math freaks,
lovers of Fourier transforms and other such things: forgive me if my
puny examples do not do justice to the subject. My only excuse for
such ravings is that I believe that most normal people can understand
a lot more than most people think they can. I further believe that
all too often people make things unnecessarily boring because of
being over-mathematized. We need the math. But we need the
UNDERSTANDING even more.
If I have helped one coiler to either learn something here or at
least have some fun trying, then I will count this day a success.
Fr. Tom McGahee