Re: Calc. energy harmonics


"Jim Slatter" <jimslatter@xxxxxxxxxxxxx> wrote in message
news:uklfj3l7ee7tht7aft7s365ttk3ht2mjfv@xxxxxxxxxx
:
: >> > For example, an RF fundamental and the frequency obtained by dividing
: >> > it in successively in two 20 or 30 times.
: >>
: >> > Thank you,
: >>
: >> > Jim Slatter
: >>
: >> Wouldn't that depend on the shape of the waveform?
: >
: >Indeed it does. Pure sine waves, for example, have no harmonics. A
: >distorted sine wave has harmonics proportional to the percentage of
: >distortion.
: >
: >Harry C.
: >
:
: I am referring to a "resonant" frequency irrespective of waveform.
: Here is a specific example. I have two separate signals of equal
: amplitude. One is a 1GHz sinewave, the other is 1GHz divided by 2
: twenty times to produce a distant lower octave.
:
: How do I calculate the _proportion_ of energy density of the distant
: octave compared to that of the fundamental, assuming all else is
: equal?
:
: Jim Slatter

Let's begin by getting some terminology at least consistent.
The "fundamental" is the lower frequency of the two, the
1 GHz is a harmonic of that.
Next comes "resonant". One tine of a tuning fork is
resonant with the other at one frequency only, and that is
the fundamental. Normally tuning fork tines are identical
in shape, but they do not have to be in order to be resonant
at the fundamental, for if one is (say) tapered you need
not have resonance at a harmonic.
The sounding board radiates the sound energy and damps
the vibration of the tuning fork (why?) but is not itself resonant.
There is no such animal as a "resonant frequency irrespective
of waveform", you need to state what it resonates with.

Now let's get to your question.
One again we need to be pedantic with terminology, many
people confuse energy with power and that is crucial to what
you ask.
If I lift a brick and place it on a shelf I've given it sufficient
energy to break my toe, should it fall. If I repeatedly lift and
let it fall it can break 10 toes. If I lift it and lower it gently
it doesn't break any toes. Note that I can do this rapidly
or spend a lifetime lifting and lowering very slowly,
the energy transfer is no different.
Now lets move up a step. We put a current through an
incandescent light bulb (lift the brick) and the filament glows,
radiating light (breaks a toe). Next we reverse the current
and the same thing happens, the filament radiates. Without
changing the voltage (height of the shelf) we can change
the frequency and the bulb will glow at a temperature which
is approximately proportional to the frequency as it heats,
radiates and cools. ALSO, the heating depends on
the mark / space ratio. We can have (say) a 60 Hz sine, or
we can have a 60 Hz square or triangular signal, and
the square wave can be forward for 99% of the time
and 1% off and still be 60Hz, or it can be 1% forward
and 99% off. A dimmer switch (thyristor or triac) typically
controls part of a sine wave, switching the current on at
some point in the cycle. What you are interested in and the
answer to your question is the area under the curve.
http://static.howstuffworks.com/gif/dimmer-switch-diagram-6.gif

So... the power radiated is a function of
1) Voltage
2) Current
3) Frequency
4) Waveform shape
5) Duty cycle
6) Time.
The energy radiated is the area under the curve for half a cycle
and includes heat, not just light.
Incandescent bulbs do not resonate.



.

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