The paper published only describes superharmonics. None of the
equations illustrate "Subharmonics". Also, It is possible in situations
involving differential equations with a "time/amplitude dependent
non-linearity" to produce fractional frequencies. The simplest example is a
diode (old slow 1n4004 ), about 1 to 10 millihenry inductor and a current
sense resistor all in series. Using a signal generator that can produce up
to 100 volts RMS and starting around several KHz observe the voltage across
the resistor. A HP200CD signal generator will sometimes work if you have
just the right diodes.
You increase amplitude and frequency until you start seeing sharp
pulses. Increase some more and every other pulse disappears. Then decrease
either frequency or amplitude and the pulses will reappear. However, not at
the same level at which they appeared. This is a chaotic behavior. This is
called bifurcation or splitting of modes. Increase level and frequency even
more and more pulses will disappear. You will find that this is not a
stable frequency divider and both amplitude and frequency affect the
results. It is a fun experiment but beyond that of little use. This is
accomplished by the inductance ( an energy storage device) and the diode
which has a relatively long reverse recovery time.
It is sometimes difficult to get it to work and if any of you try it please
report back. I did this around 15 years ago. And it is a some what known
demonstration of chaos among some groups of physicist.
I was not going to muddy the waters with this until some folks
with some knowledge started into the discussion. As far as this by chance
happening in a circuit in a stable way, very not likely. The key word here
is chaotic behavior.
The concept of harmonics comes from harmonic waves with a
fundemental frequency of the 1/T. These are periodic waves. A simple
harmonic wave is a sine or cosine wave. When you introduce a "subharmonic"
you change the period. So the so called "subharmonic" then becomes the
fundamental and the period changes to that of the new fundamental frequency.
Mathematically "subharmonic" is not appropriate.
Nor is the use of mHz for MHz.
Better yet when did DE-9 connectors become DB9? People seem to be
redefining standards all the time.
73
Bill wa4lav
At 12:21 AM 5/22/02 -0400, jeff millar wrote:
>You're quite correct that non-linearities do not directly generate anything
>other than integer harmonics 2f, 3f, etc. But it still possible to generate
>sub-harmonics with a non-linear reactance, a passive circuit, and a pump
>frequency. Because there's two kinds of nonlinearity:
>
> Non-linear resistance...which results in clipping, etc.
> Non-linear reactance...which results in parametric effects
>
>Parametric circuits can have _gain_ at frequencies other than the pump
>frequency. A sub-harmonic arises because the the parametric divice looks
>like negative resistance and produces gain which results in oscillation at
>f/2 or f/3.
>
>Yes, this is unlikely in typical circuits. But the effect is real and
>documented and interesting.
>
>jeff, wa1hco.
>
>
>
>----- Original Message -----
>From: "Tom Rauch" <w8ji@contesting.com>
>To: "Ron" <w8ron@stratos.net>; "jeff millar" <wa1hco@adelphia.net>
>Cc: "'Amps'" <amps@contesting.com>
>Sent: Wednesday, May 22, 2002 12:09 AM
>Subject: Re: [Amps] Non-linear subharmonics was: Nonsense, AL-1500 parasitic
>
>
> > > I still think something in the amp or something in the
> > > feedline/antenna/tower/guy system can cause the problem. In response
> > > to the initial question, I asked about ferrites in the tank. But
> > > maybe a solid state driver could produce the sub-harmonic. If the
> > > measurements are correct, then the spurious is truely a sub-harmonic
> > > and it becomes interesting to find the source.
> >
> > It is especially interesting now that Dave says he duplicated the
> > problem with diodes.
> >
> > I have never been able to generate a submultiple of a signal with an
> > form of non-linear system, including saturated ferrites.
> >
> > I wish it were that simple.
> > > from one > cycle to the next to be lower in frequency. To be an odd
> > > fraction of the > fundamental would mean that the non-linearity
> > > effects one cycle of the rf > fundamental but not the next!
> >
> > That is correct. Dividing frequency requires more than a simple non-
> > linear junction, or a non-linear device like saturated ferrites.
> >
> > Whatever it is it requires that one point in one cycle is *not*
> > treated like the next repeating point. That's why you never find
> > subharmonics generated in solid state or tube-type PA's, ferrites, or
> > conventional diodes. 73, Tom W8JI
> > W8JI@contesting.com
> >
>
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