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Re: Rewrite of Mutual Inductance Laws for Tesla List

Original poster: "harvey norris by way of Terry Fritz <twftesla-at-qwest-dot-net>" <harvich-at-yahoo-dot-com>

--- Tesla list <tesla-at-pupman-dot-com> wrote:
> Original poster: "Malcolm Watts by way of Terry
> Fritz <twftesla-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>
> Hi Harvey,
> On 16 May 2002, at 8:06, Tesla list wrote:
> > Original poster: "harvey norris by way of Terry
> Fritz
> <twftesla-at-qwest-dot-net>" <harvich-at-yahoo-dot-com>
> > 
> > The laws of Mutual Inductance for air core coils
> only
> > implies a several percentage points effeiciency;
> Which laws are those? In fact you can get k pretty
> close to 1 if the 
> coils have very similar geometries. If there are few
> losses, even if 
> k is quite low, transfer efficiency is demonstrably
> high. I have 
> measured an energy transfer efficiency approaching
> 90% between two 
> coupled air-cored coils with k set to about 0.15.
Yes, but is that situation using a tesla set up where
the frequency of oscillation is increased by means of
an arc gap? Obviously then the efficiency of secondary
action to primary will increase. In this situation
there is no arc gap, or change in frequency among the
components. 480 hz goes in & 480 hz comes out soley
due to mutual induction. The secondary and primaries
have no where near similar geometry where the primary
is a 14 gauge coil (no of turns unknown), of low ohmic
resistance,(1.1 ohm) and the secondary is of high
resistance (1000 ohms containing 20,000 winds of 23
gauge wire)
> > However those laws only specify L1L2 in air core,
> and
> > with increased frequency of input for L1L2 coils
> if we
> > give each of these L quantities an associated C1
> and
> > C2 values, we should expect the mutual induction
> to
> > increase, or more properly the ability of the L1C1
> > primary to excite the L2C2 secondary for
> comparisons
> > here.
> I confess I don't understand any of this. M is a
> function of k and 
> the inductances of the two coils. I don't see where
> capacitance comes 
> into it.
The only input to the primary coil is that made by
connecting the L1 primary coil to 2 of 3 available
outputs from an alternator stator producing 480 hz.
Although the coil is only ~1 ohm, at 480 hz the 10.8
mh primary still has an appreciable impedance of near
30 ohms. To get more current to develope on that
primary we give L1 a C1 value in series, (for
conditions of resonance) Those conditions of course
change if L1 has a secondary in proximity for mutual
inductance. On the first L1 tuning in isolation we
find that a 10 uf value will deliver the best possible
resonance. There are also idiosyncrasies involved in
all of this, where the book derived C values may
differ from what is actually used. For L1 there may
not be such differences, but there are further
complications in that the 1 ohm L1 value will never
come to full conduction by ohms law, especially when
the inductive secondary influence is added. As Paul
Nicholson has noted, the complications involved here
are that R(load) is now getting closer to R(int stator
resistance), thus this dramatically cuts down on the
delivery of the external resonance, when the internal
resistance of the source is taken into account. That
alternator AC source itself is CURRENT LIMITED to a
greater degree than might be suspected. To illustrate:
the 1 ohm resonance might be expected to deliver 1.7
amps at 1.7 volts input. However only .7 amps actually
develope, and the expected voltage rise (by the 30
fold Q factor at 480 hz)to accomplish that conduction
is reduced to over half that needed to cause the
conduction. So we see .7 amps conduction and can not
initially understand why 1.7 amps is not developing.
The reason for this is readily seen by simply placing
a short across the outputs instead at the same
stator/field conditions and measuring the amperage to
see what the source alone will deliver with no load.
In this situation shorting the .7 Amps delivery will
only deliver 1.25 Amps on short, so it is easy to see
that if only 1.25 A is available from the source in
those conditions, this is why we shouldnt expect 1.7
amps to be delivered in identical circumstances whaen
a 1 ohm resonant load is added. The (current limited)
source simply cannot meet the demand being asked for
by the load, when using this low ohmic resonance.

Where all of this became most remarkable is when the
second side of the process was added. I did not at all
set forward with the intention of making a source
frequency air core transformer, this was made by sort
of accident by making further observations of the
current limiting idea. I have described how this DSR1
uses L1C1 in series for resonance, and how it then
takes two of three stator connections (using a single
of three phases) to be enabled. 

We also know that this process is only using one of
three available output phasings of the alternator. I
then began to wonder about ways to use all 3 phases to
be incorporated for a single phase of delivery. This
was accomplished by using what I call a resonant
interphasing. We can place larger Delta Series
Resonances, (DSR's) of 12 ohm .15 henry resonances on
the other two unused phases, but this does do no good
because logically those current flows will both be 120
out of phase with the DSR1 resonance. Now the 1000 ohm
coils themselves will barely make any conduction
themselves without increasing the voltage applied to
them, but by placing that large coil between the two
outer DSR2 resonances, this has the action of
supplying that needed higher voltage, because on
either side of the  larger coil there will be resonant
voltage rise present on each DSR2 midpoint. Then we
can note the reactance of that inner coil conduction
and also give the interphasing coil an equal
capacitive reactance in series. In this way we have
made a resonant transformer, by stacking an interior
resonance within two outer ones as shown with a single
interphasing as

The further advance beyond this point was to consider
that the bottom DSR, (here in this application is
DSR1), actually does nothing for the interphasing and
it can be removed if desired, but a much better option
exists for increasing the overall delivery. Looking at
all the branches involved, we find that the
interphasing has a line parallel to the bottom DSR1
line, and this then implies that the curents on each
of those lines are actually in the proper phasing
arrangements to interact them inductively with each
other. It is in this way we have taken three phases of
input and combined them into one phase for actual
application! This is done by merely placing the DSR1
coil on top of the  interphased high induction coil.
However now each coil sees new conditions of impedance
because a magnetic interaction has been added, thus it
seems sensible that both coils should again be
retuned. There are also two options present, where the
sensible one is to make those fields be in magnetic
unison, not in magnetic opposition. We already know
that magnetic unison will increase the q factor for
both systems so this seems like the better
alternative. But let us then see all 3 circumstances
starting from the isolated case of resonant
interphasing, so that we can see what the initial
conditions before improvement actually are.
Solitary Resonant Interphasing from dual DSR input. 

The parametric stator input of ~1.8 volts (not shown
in that Jpeg) has been increased to 48.4 volts by
resonant interphasing voltage rise, enabling .8 ma
conduction on the interphasal branch. DSR1 coil is
disconnected from stator source, but the voltage meter
acros that coil,(V int) is left intact showing that
coil to be recieving .686 volts by induction from the
larger coil. Thus we know that when the DSR1 coil is
actually energized, there are actually TWO sources of
emf imposed on it, that made by the line connections,
AND that made by induction.
DSR1/ mutual induction for increased voltage rise. 
Now this sounds promising as a technique since the
midpoint pathway of the interphasing has seen its
voltage and amperage conditions doubled where now 82.1
volts is enabling 1.66 ma conduction. The DSR1 coil is
given a new value of 14 uf to account for its new
impedance requirements, but here for magnetic unison
it should actually use 9.5 uf. Only a small
improvement was made using the 9.5 uf value, where
here the 14 uf is left in place to make the next
comparison. DSR1 now is only pulling 167 ma.
Vint/stator voltage shows DSR1 acting q factor.
DSR1/ mutual induction for decreased voltage, but
increased voltage internally 
Now as expected the magnetic opposition has decreased
the interphasal voltage down to 19.39 volts, BUT
instead of decreased amperage conduction on the branch
as a result, this has instead been increased to 3.64
ma. A one ended neon remains in place to detect
increased voltage rise across the plates, where
calculations of the reactance of the 1.05 nf cap show
that at 480 hz, 1000 volts would enable 3.16 ma
consumption, so here it can be estimated that the last
internal voltage rise is 3.64/3.16 * 1000 = 1150 volts
The DSR1 amaperage and Vint values have also ~

NOW, all of this may sound long winded, but it is
necessary to show these things to indicate what was
done next. We Know the (reactive)wattage expended by
DSR1, but we do not know the wattge expended by the
addtional DSR2 connections because that had not yet
been measured. For the first case of solitary
operation, each of the branches pull about 120 ma, and
the parametric stator voltage goes up to about 2
volts, thus for solitary operations of DSR2 the
reactive input is 2* .12, or .24 watts on each leg, or
about .5 watts total. Now let us compare the inside
branch that made .8 ma with 48.4 volts across it. This
only amounts to .038 watts! Thus that efficiency of
resonant voltage transformation compared to
transformer voltage rise seems very inefficient! So
let us then compare the actions for the improved
operation case. In that instance only 60 ma is
recorded on the outside branches with 1.8 volts being
imposed. Because we know that DSR1 is consuming 300
ma, and the other two branches 60 ma apiece, we would
suppose that the total DSR2 expenditure is 2/5ths of
the DSR1 branch. However this is not the entire story
at all, because when we measure the actual stator
input line amperage to the junction serving both DSR2
branches, this logically should be 1.7*(60 ma)= 102
ma, however only 60 ma appears at that junction also!

These questions are quickly resolved by measuring what
the  interphasing branch alone can supply if it were
shorted(without changing the input field conditions)
IT ONLY SUPPLIES 3 MA ON SHORT! So here we have the
incredible situation that 1000 ohms in resonance is
producing 3.6 ma on the junction, but it is supposedly
current limited to 3 ma of delivery on short! This led
to the wondering as to whether any input at all was
needed for DSR2 operation. Started pulling those
connections from the stator, and 1,2,3, the rest is
history, the invention of a air core transformer model
made by accidental reasonings made by meter

DSR2 developes its interior voltage rise, but the
voltage on the outside of the interphasings is
abscent. This is the only difference of operation I
have noted with this recent developement. To show this
Disconnection of DSR2 lines 
Formerly with DSR2 connected we had 19.4 volts across
the interphasing producing 3.64 ma delivery.
Disconnecting those stator lines we now only have 99
mv,(1/10th volt)across the interphasing but there is
3.99 ma amperage delivery. DSR1 slightly increases its
input to account for the secondary loading. One might
also be able to obtain something from the three DSR2
endings of the circuit that were disconnected, I
havent tried that one yet. Let us also compare
resonant voltage delivery efficiency with DSR 2
connections enabled where 60 ma was recorded with 1.8
volts input. This would be 2* 1.8 * .06 = .216 VAR and
for the actual interphasing 19.4 volts enabling 3.6
ma, or  .069 var, but if we use the actual voltages
INSIDE the interphasing approxiamted at 1265 volts *
.0036 A= 4.55 VAR. Additionally that 60 ma across the
DSR2 branches can be downsized to 60ma/1.7 as the
actual stator input becoming .216/1.7= .127 VAR. In
any case here the reduction of the interphasing
(outside)voltage has made the resonant voltage rise
appear to be more efficient, as comparison for what is

> > Since the volt-ampereres measurements only
> indicate
> > possible deviations from actual real power input,
> when
> > it it is shown that the components are actually
> > matched to be as completely resonant as possible,
> the
> > reactive power arguments completely fail to show
> how
> > the the output coils appear to be greater than the
> > input.
> The reactive power in the output circuit is the
> result of an 
> accumulation of energy in that circuit isn't it?

> > 15 Volt Operation 
> >
> > 
> > In that operation there having over 6000 volts
> across
> > the caps,experimentation suggests that all three 
> > voltage lines of conduction making that high
> voltage
> > can be cut from its supply source, and instead THE
> But there is a fundamental difference between two
> mutually coupled 
> inductances and two mutually coupled tuned circuits.
> A tuned circuit 
> is not called a "tank" for nothing. The old sum of
> energy out = 
> energy in minus losses must apply. Energy
> accumulation in a tank 
> takes place *over time*, something which voltmeters
> and ammeters do 
> not take into account with their sluggish responses.
Truly so, but since everything is occuring at source
frequency, I think I can believe the meters, and no HF
effects are coming in to distort those measurements. I
have also used the output to power arc gaps, but not
yet made a sensible combination to power a tesla coil.
> You can of 
> course see such acccumulation occurring on an
> oscilloscope since that 
> instrument does use a *timebase*. 
> > Indeed here is an alternator with no energized
> field
> > exercizing resonance of L1C1 through space to L2C2
> and
> > producing one ended neon discharge! So to complain
> at
> > least to science law makers of presumptions it can
> be
> > said that air core mutual inductance laws do not
> > preclude a non performance factor.
> Fundamentally, the only difference between air-cored
> and material-
> cored coils if the material is not driven close to
> saturation is the 
> higher permeability (hence L of the coils, hence M
> between them). Is 
> there something here that I'm missing?
> Regards,
> malcolm
Tried to explain the extenuating circumstances here,
hope it makes a light at the end of the tunnel, as I
admit this 3 phase stuff gets confusing. In any case
we have a higher amperage component primary with low
resistance winds enabling higher current to be
inputed, and on the other side of things we get a
higher voltage with reduced amperage, and this is
accomplished exactly as a air core transformer at
source frequency. I would normally think this to be
quite remarkable, since no arc gap to enable that
increased secondary performance is used.

Tesla Research Group; Pioneering the Applications of Interphasal Resonances