Jan 29, 2000
I'm going to build an odd transformer like that shown in Fig. 1
below, using 6 steel washers, 5" outer diameter, as shown. The steel
washers make for poor transformer cores so it should only handle only
a few watts in the secondary, even if the primary windings were
wrapped completely around the steel washers in the conventional
manner. This transformer design is odd or unusual because the
primary winding has zero turns around the steel washers used as core
material. The field induced in the steel is all fringe field. The
primary winding should therefore (unfortunately) have zero magneto
motive force (mmf) and thus no coupling to the secondary, because n*i
= 0. However, the wide exposure of the fringe field of the primary
coil to the washer should provide a strong magnetizing H field in
steel washers, thus producing a strong maximum field intensity B in
each of the 6 cores. This creates the seemingly paradoxical
situation that the odd transformer has zero primary turns, yet
creates a strong flux in the core material.
HIGH CURRENT SECONDARY?
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
S S
------------>------- S -------<------------ S
| ::::::::::::::| S |:::::::::::::: | S
| -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
| ------->------- S -------<------- | S
| ::::::::::::::| S |:::::::::::::: ^ S
| -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
| ------->------- S -------<------- | S
| ::::::::::::::| S |:::::::::::::: | S
v -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
| ------->------- S -------<------- | S
| ::::::::::::::| S |:::::::::::::: | S
| -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
| ------->------- S -------<------- | S
| ::::::::::::::| S |:::::::::::::: | S
| -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
| ------->------- S -------<------- ^ S
| ::::::::::::::| S |:::::::::::::: | S
| -------<------- S ------->------- | S
| |xxxxxxxxxxxxxx S xxxxxxxxxxxxxx| | S
o ------->------- S -------<------- X S
::::::::::::::| S |:::::::::::::: S
X-----------<------- S ------->-----------o S
S S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
::: - Insulating wood washers used as spacers
xxx - Flat wide steel washers, each used as a core
--| - Copper windings
SSS - Secondary "winding" - a straight copper conductor
well insulated from cores and primaries
X - Current into page
o - Current out of page
Fig. 1 - Cross section of odd transformer
One possible resolution of this seeming paradox is that the zero (or
nearly zero) mmf of the primary is quickly countered by any back flux
produced by any current which is induced in the secondary, thus
conserving energy. Therefore strong field intensity would only
exist in the core material when the secondary is not in a closed
circuit. The (likely) net effect is a weakly coupled primary and
secondary. It is thus of interest to add a second secondary coil to
the transformer to be used as a high impedance voltage sensing coil
which can sense, by the voltage induced in it, the rate of flux
change occurring in the cores when the main secondary coil forms
either an open or closed circuit.
I figure that, just to get some experience with this hopefully novel
situation, it will be convenient to do the wrappings in #12 wire, and
drive the primary windings at about 10 amps. Much larger currents
are feasible on a momentary basis, but the transformer should be able
to handle 10 amps on a continuous basis unless the steel core
material cannot be cooled properly. Unfortunately, due to the poor
core material quality, most all the energy input will go to heat in
the core material. I expect, based on experience gained testing the
steel washers as cores with conventional windings, that the required
primary voltage will be about 12 volts. It may be less due to the
fact the odd primary geometry should have a low inductance compared
to a conventional winding, due to having zero turns about the core,
but this remains to be seen. I figure to get about 56 "turns" in
the primary winding, as this fits through the 2.5" steel core holes
in a single layer.
The 56 primary windings in this case will all be in series as a
matter of convenience. However, they could be driven all in
parallel to obtain a low impedance primary. Further, each winding as
shown in Fig. 1 is in series between each of the cores. This could
also be changed to make each (partial) turn about each of the 6 cores
in parallel. In such a configuration the primary could be driven at
very high dI/dt rates, thus at high frequencies, and with a very low
primary/secondary turns ratio. This low impedance configuration,
especially when used in conjunction with ferrite cores, might be
useful for placing large high voltage pulses in the secondary.
Jan 31, 2000
The principle reason for interest in the Fig. 1 configuration is
that, provided the wood "::::..." is exchanged for the steel
"xxxx...", and vice versa, the steel cores are then all within the
primary current loops, and thus the transformer is normal. If the
transformer were very long, and the secondary loop very wide, I don't
think there would be any difference in the degree of magnetization of
the most central steel washers in the stack, be they on the inside or
outside of the coil. In other words, the cores should not see any
difference in their magnetization depending on whether they are
inside or outside the primary, since the field doing the
magnetization is principally a fringe field and not the coil field.
It seems paradoxical that, as the size of such a device increases,
especially the minor radius, i.e. the core diameter, the coupling of
the secondary to the core appears to decrease, while the coupling of
the primary to the core remains constant. It appears the coupling of
the primary to the secondary is not equal to the coupling of he
secondary to the primary - but that may just be due to my confusion.
Feb 4, 2000
The odd transformer was completed with 6 steel cores, 56 primary
turns made of #12 wire, and 28 turns of #10 secondary wire (I could
only get 28 turns through the 2" plastic core tube.) In addition, a
30 turn voltage sensing secondary made of about #24 wire was included.
The primary was made of 56 pieces of 33" long #12 wire joined
together by twisting to make a 154' long primary. The secondary was
made of 2 pieces of #10 wire, each 24.5' long, and having 14 turns of
21" #10 wire. The inductance of the primary was measured by meter at
0.83 mH, as compared to a normal transformer made with a single steel
washer core, which measured 0.22 mH for 53 turns.
A 0.68 ohm 25 W resistor was placed in the secondary circuit in order
to measure secondary current. The results are summarized in the
following table:
Secondary circuit closed Secondary circuit open
----------------------- -----------------------
Amps Vrms Vpk-pk Amps Vrms Vpk-pk
Primary 9.96 2.59 7.80 9.98 2.59 7.8
Secondary 0.153* 0.071* 0.216* 0.00 0.139 0.424
Sense -- 0.153 0.464 -- 0.162 0.488
Resisitor 0.153* 0.104 0.320 0.00 0.00 0.00
* - indicates calculated value
Sense at (0.153 V) for 30 turns is 0.00510 V/turn, which for 28 turns
gives 0.143 V for the secondary.
(0.104 V)/(0.68 ohm) = 0.153 A secondary.
(0.153 A)*(0.143 V) = 0.0219 W secondary.
(9.96A)*(2.59 V) = 25.796 W input to primary when secondary closed.
(9.98A)*(2.59 V) = 25.848 W input to primary when secondary open??
Coupling factor = (0.0219 W out)/(25.8 W in) = 0.000849
CONCLUSION
The lack of coupling is remarkable. This low level of coupling might
even be attributed primarily to the air core coupling of the primary
to the secondary. This seems to bear out the notion that nearly all
the flux is indeed included inside the toroidal primary coil, and
excluded from the core material, or at least self-nullifying in the
vicinity of the steel core material, which is topologically outside
the primary coil surface. I would have expected the fringe field to
be strong in the vicinity of the steel core material due to the
strong surface distortion there, but apparently not.
An alternative interpretation might be that there is zero mmf, due to
the total turns about each steel core being zero. However, this
interpretation doesn't wash because the sense coil voltage does not
very much when the secondary coil is opened. This means that d phi/
dt does not change much, thus the core flux does not increase much
even when there is no load on the secondary to reverse or negate the
flux.
The only unusual thing noted in the experiment was that the current
actually increased very very slightly when the secondary was opened.
It was not a significant amount, and the current was gradually
changing as the core warmed up, but the current increase upon opening
the secondary was very repeatable.
It is notable that the small voltage rms values, computed by TEK
TDS220 scope, are not very accurate. Comparing the secondary volts/
turn to the sense coil volts/turn when the secondary is open shows a
roughly 10 percent discrepancy, which should be a rough estimate of
error for the low voltage values. This degree of accuracy is plenty
sufficient to support the conclusion, namely that there is almost no
electrical power output compared to power input.
