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Thank you Groundloop & Mark for the answer,

It makes sense now, you learn something new everyday.

@All,

The first run of the unit has been done. I do not have all the Ni-Mh batteries
charged up yet, so I did run a test with 4 capacitors on the switch part and
one Ni-Mh battery to power the oscillator. When I flipped the CH switch (switch
for back feeding energy from the switch into the oscillator run battery) then
the output did go to zero (or very close) volt.

Groundloop.

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@geotron,

My replica did work as designed and the switch did do what it was supose to do,
but did not do anything that even closely can be considered over unity. The
switch itself did use 30mA just to run without a load. With load, the five 200mA
batteries did drain in 90 minutes. The switching did not produce enough "extra"
power to keep the run battery charged with the charge switch closed.

That said, the method of using audio transformers to control the transistors on
and off did work. So if you build a 4011 based oscillator then it is possible to
use transformers to control the transistors. Use a 4000 series IC. Those IC's
can take up to max. 18 volt. The 74 series IC's is designed to run on 5 volt.

Groundloop.

@geotron,

You need to use a CD4011BE or compatible.
This IC runs from 3 to 15 volt.

The CD40117BEE4 will NOT work in your oscillator.

Groundloop.

Ok, I've been searching around for them (CD4011BE), and
the only place seems to be Farnell at the moment. It is
confusing to me dealing with the wide variety of suffixes.

Is there any kind of reference that shows explicitly
what these letters and numbers stand for?

I've been studying the original schematic for this timer,
having drawn it down on paper, and had to take a look at
your digital representation of it Groundloop because I
couldn't make out the label on the item which I've circled
in the pic attached.

As a matter of fact I still don't understand what it is.
The 'R3' indicates to me that its a resistor, but the '8K2'
seems foreign to me. Then there's the R4 which I thought
looked like '1.2K', but you've labeled it in much the same
way as the previous one.

Everything else seems fairly self-apparent, excepting
what type of relay it calls for. At Farnell alone there
are close to 8000 choices, including those that even
have their own built-in time delay function... at first
glance I would choose to look in either the 'High Frequency'
or more general 'Relays/Contactors' categories.

Relays at Farnell

If I was going to pick one, it would be the Omron G2R-14-DC12

Well that makes a lot of sense - thanks for clarifying me.

On the matter of relays, the Omron model I've listed above
is rated at 275ohms. I'm not quite certain how this value
would effect the circuit's functionality, or whether it
makes any difference at all for the purpose of the Tesla
Switch...  Honestly I don't see how it could.

Would I be correct in viewing any 12V relay as a suitable fit?

I've been messing around with building my own oscillator
device lately with the use of another project entitled
PC Fan Generator in Half-Baked Ideas. It involves positioning
a small disc magnet near the perimeter of the other ones being
spun by the Fan's motor. Video

It seems to work extremely well, although without a scope
I can't corroborate this, but I'm fairly certain that with a bit
of adjustment I can get it to perform at least 100-200 contacts
per second without too much trouble.

In the video I've glued a matchstick to the outter fan casing and
a small disc magnet - magnet facing towards the spinning ones on
the fan, and an alligator clip is being held to the other side
of the matchstick by attraction to the small disc magnet, vibrating
against the positive contact of the LED bank.

So, it looks as if I may be able to go ahead and order all of my
parts for the main body of the Tesla Switch and hook the finished
device right onto this Magnet Commutator. (?)

The voltage going through it in the video is around 3.3V, although
I've got leads on my supply for 12V as well... its an old ATX supply
scavenged from a non-working computer.

Again, here is my working model illustration for hooking the timer
to the T-Switch. The reason I've brought it back is, I'm not certain
if I would still need the 1K resistor inline with the +12V like is
shown at top...