### The Overunity parametric transformer

Created on 7 July 97

```Date :	07/07/1997 07:01:44
From:	fepps@halcyon.com (Fred Epps)```
```
Here is my design for a parametric transformer that has overunity
characteristics.  Although it is a simple circuit, it is the result of a
great deal of research.  It is based on an earlier design built by
Jean-Louis Naudin which is on his website at: varind40

My new design eliminates the drawbacks of the earlier one and is based
on a clearer understanding of the principles involved. For those of you who
are new to the world of "parametrics" I will briefly explain the principles
behind these devices before launching into a detailed description of how
they can be overunity. To illlustrate these principles I will quote from a
paper which greatly influenced my development of this machine, "On the
Parametric Excitation Of Electric Oscillations" (1)

"As we have shown earlier, starting from energy considerations it is
easy to account for the physical aspects of the excitation of oscillations
by periodic (stepwise) variation of the capacitance of an oscillatory
system not containing any explicit sources of magnetic or electric fields.
We shall briefly repeat this argument for the case of variation of
self-inductance.  Suppose that a current i is flowing in an oscillatory
system consisting of a capacitance C, ohmic resistance R, and self
inductance L, at some instant of time which we shall take as the starting
instant.  At this moment we change L by dL, which is equivalent to
increasing the energy by 1/2 dLi^2.  The system is now left to itself.
After a time equal to 1/4 of the period of the tuned frequency of the
system, all of the energy transforms from magnetic to electrostatic.  At
this moment, when the current falls to zero, we return the self-induction
to its original value, which can evidently be done without expending work,
and again we leave the system alone.  After the next 1/4 period of
resonance oscillations the electrostatic energy transforms fully into
magnetic energy and we can begin a new cycle of variation of L.  If the
energy put in at the beginning of the cycle exceeds that lost during the
cycle, i.e., if

1/2 dLi^2 > 1/2Ri^2 (T/2)

or

dL/L > e

where e is the logarithmic decrement of the natural oscillations of the
system, then the current will be larger at the end of each cycle than at
the beginning.  Thus, repeating these cycles, i.e. changing L with a
frequency twice the mean resonance frequency of the system in such a way
that

dL/L > e

we can excite oscillations in the system without any EMF acting on it, no
matter how small the initial charge.  Even in the absence of the
practically always present random inductions (due to power transmission
lines, terrestrial magnetic fields, atmospheric charges) we can in
principle always find "random charges" in the circuit on account of
statistical fluctuations."

The question is, is it possible to use less energy to change the
inductance or capacitance than is generated in the resonant circuit? I
believe it is, in both inductive and capacitive cases. Because of the
limitations in the art of capacitors, the inductive case has more potential
for higher power outputs.
A parametric transformer was patented by Leslie Wanless in 1971.  This
transformer uses the varying magnetic field of the primary to  periodically
change the L of the secondary, which is part of a resonant circuit as in
the paper quoted above.  Standard EM induction is eliminated by use of
windings at right angles. Since the primary is excited by an AC current at
F the inductance varies at 2F, because there are two magnetic field peaks
in each cycle, one at the positive and one at the negative voltage peaks.
Since the output current is at half the frequency of the parametric
variation as described in the above paper, the output current is half of
2F, or the orginal input frequency F.  This is important for reasons to be
explained shortly.
This form of parametric transformer is not an overunity device because it
is entirely reciprocal:  the magnetic field of the SECONDARY current at F
induces an inductive variation in the PRIMARY at 2F, causing a parametric
current at F which opposes the input current. The inputs and outputs of
such a transformer can be reversed with no change in operation IF the
primary is part of a resonant circuit at frequency F.
I understand that this is complicated and appears to be going nowhere,
but I hope that at least some of you will bear with me.
Examine the circuit shown on Jean-Louis' web page.  The special variable
inductor is driven by a CMOS square wave generator with, of course, a DC
output. Jean-Louis has reported to me that loading the secondary of this
circuit did not load the primary. This was puzzling to me because there
should have been SOME loading of the primary, even with the special core
The explanation is simple and is in two parts:
1)  The input circuit is nonresonant.  Although the output current's
magnetic field still varies the inductance of the primary, it cannot cause
a parametric current opposing the primary current because there is no
capacitor in parallel across the input so that this opposing currnet can
build up.  It dies in every cycle.  This does not eliminate but only
minimizes the "parametric back EMF", however.
2)  More importantly, Jean-Louis used a DC signal for the input.  Recall
that a parametric current flows at half the frequency of variation of the
parameter.  In the Wanless transformer, there are two inductance peaks in
every primary cycle at input frequency F, leading to an output current at
this same frequency F, leading to a parametric back reaction at F which
loads the primary. But in Jean-Louis's circuit, the input is DC so there is
only one inductance peak per cycle at F.  As a result the output frequency
is 1/2F, and the back reaction is at 1/2F. In Jean-Louis's circuit this
The combination of these two factors makes the loading of the primary
"invisible" within the possible range of secondary loads for such a device.
I have designed a transformer which uses these principles to go
overunity.  Please refer to the GIF included with this post.  The inductors
shown consist of two specially-wound standard laminated transformer cores.
The two primaries and the two secondaries are each in series but the
secondaries are wound in opposite directions.  It has been shown that this
is the most efficient method of eliminating  EM induction from the
operation of parametric transformers (2) as the EMFs in the secondaries
cancel out and do not produce a back EMF in the primary.  The driver is a
low-current square wave generator such as the CMOS circuit used by
Jean-Louis, operated at frequency F.  The output circuit consists of a load
and a capacitor such that the resonance is at 1/2 F.
This output is an AC sine wave, despite the DC square wave input. This
can be seen from examining the output waveforms in the Varind 4 tests.
According to the principles we have discussed, a parametric back reaction
waveform develops in the primary at 1/2F because there are two inductance
peaks in every cycle of the output.
Because the primary frequency and the back reaction frequency are
different, it is possible to completely eliminate the back reaction's
effect on the primary and recover the energy of the back reaction using a
simple series-resonant tap as shown in the GIF.
The energy flowing through the primary that would normally partially cancel
the input voltage is now used to drive a second load.
In summation, although it may or may not be possible to eliminate back
EMF in a normal induction motor or transformer it is certainly possible to
eliminate it in certain parametric arrangements because the input and
output frequencies can be made to be different, something which can never
occur in a normal transformer, where the input frequency and the output
frequency are always the same.
Since there is very little loading of the input in the circuit I
describe, many of these devices can be operated in parallel from the same
driver, taking care to reduce series resistance as much as possible.
I will be interested in comments and even more interested in tests made
on devices such as the one I've described.

Fred Epps

1)  "On The Parametric Excitation Of Electric Oscillations' by L.I.
Mandelshtam and N.D. Papaleksi
Zhurnal Teknicheskvoy Fiziki, 4, n.1, p. 5-29, translated for Lawrence
Livermore Laboratories, Feb 1968
2)  "Comparison Of Orthogonal- And Parallel- Flux Variable Inductors" by Z.
H. Meiksin
IEEE Transactions On Industry Applications, V. IA-10, n.3, May/June 1974 ```