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#61
07-25-2012, 07:27 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Seven (1 of 3)

(1) Magnetism is a product of two factors;

One, the Magneto-Motive Force, is, in Ampere-Turn,

Two, The Magnetic Inductance, L, in Henry.

Variation of one or both of these factors results in the variation of the quantity of magnetism. In turn this variation in magnetism develops and E.M.F. in direct proportion to the time rate of this variation. This E.M.F. is developed thru Parameter Variation.

Variation of the parameter magneto-motive force is brought about by the variation of the current, i, in ampere which produces this M.M.F. The M.M.F. and its current are related by,

Or,

Where

n = Number of Turns.

This number, n, is the ratio of M.M.F. to its current, and it serves as a magnification factor for current flow.

Variation of the parameter Inductance is brought about by the variation of the factor

Where

is the magnetic permeability, in centimeter

is the magnetic path length, in centimeter.

This factor, , is the effective permeability of the magnetic circuit. The magnetic permeability is a characteristic of the medium which supports the magnetic induction. This is not to be confused with the relative permeability. The magnetic permeability

, centimeter

is an Aether constant derived from One Over c Square. The relation is given by,

Where

c is the Velocity of Light.

Hence the relation is given as

This is the magnetic permeability. In order to simplify mathematical expression the relative permeability is often used. It is given by the relation

Where

is the magnetic permeability of free space or the Aether. Here then exists three expressions for permeability;

One, Magnetic Permeability,

, Centimeter,

Two, Effective Permeability,

, Numeric,

Three, Relative Permeability,

, Numeric.
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#62
07-25-2012, 07:27 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Seven (2 of 3)

(2) The general expression for magnetic inductance is given by the relation,

Where

A is the sectional area of the magnetic induction, in centimeter square

is the total flux inter-linkages between the current, i, and the magnetic induction, .

is the effective permeability, a numeric.

For a unit turn the relation becomes,

The relation hereby derived is given as,

This parameter,
, is called the Reluctance of the magnetic circuit. This reluctance is a mathematical fiction given to give an analogy between the magnetic circuit, and the electric circuit. Where it is resistance in an electric circuit, it is a reluctance in a magnetic circuit. Reluctance is hereby a magnetic resistance. This analogy does not recommend itself. It has become commonplace to express parameter variation in terms of Variable Reluctance. Such is the “Variable Reluctance Generator”. The factor, , the effective permeability is more suited for the expression of parameter variation.

The two basic expressions for Magnetic Parameter Variation are thus,

The expression of parameter variation of current,

And the expression of parameter variation of Inductance,

(3) The Magnetic Inductance is formed from several factors, or sub-parameters,

n, Number of Turns,

A, Sectional Area,

, Path Length,

, Magnetic Permeability.

The number of turns, and the sectional area are in general invariant. The number of turns is fixed by the impedance, and the sectional area is fixed by the volt-ampere capacity. The path length can be variable by mechanical means. The magnetic permeability can be made variable by magnetic means.

The path length and the magnetic permeability are directly related as they have the same dimension, centimeter. They are both lengths, and their ratio is the effective permeability. This is the parameter to undergo variation.

(4) Permeability works thru the dimension of length, here in centimeter. The length of a magnetic flux line determines the amount of M.M.F. required to maintain that length. A force is required to hold this line in place. The more the flux line is stretched out, the greater the M.M.F. required. This determines the magnetic gradient along the flux line as,

The flux lines are elastic, if stretched out, they hold the energy required in this stretching and it returns when the stretching force is withdrawn. During the interval in which the flux line expands or contracts an E.M.F. is developed to facilitate the movement of energy into, or out of, the elastivity of the magnetic flux line.

If now the magnetic permeability is made to increase, the M.M.F., and thus the current, required to maintain a flux line at a certain length is decreased in proportion to the increase in permeability

Hence the magnetic permeability acts to shorten the lines of magnetic induction. This is to say that the magnetic permeability allows the magnetism to contract into it. In a magnetic path of centimeter length, a path of high permeability has a much longer effective path length than that of a low permeability. The relation is given as

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#63
07-25-2012, 07:28 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Seven (3 of 3)

Where

is the relative permeability, a numeric proportion. For example, iron has a relative permeability of,

= 1000 numeric.

A portion of this iron is in the magnetic path and the length of this portion of iron is,

= 1 , centimeter

The effective path length along this iron is then given as

If this magnetic permeability undergoes parameter variation, it results in an effective variation in path length, this for the Magnetic Induction.

(5) The effective permeability can be made variable thru mechanical and magnetic means. Variation is produced mechanically by the insertion and removal of permeable material into & out of the path of magnetic induction. This results in the variation of the effective path length, and thus a variation of the effective permeability, .

In many magnetic materials their magnetic permeability is a function of the flux densities within these materials. The greater the flux density, the less the permeability. When the flux density is increased beyond a certain point the magnetic permeability of the material becomes that of free space. This is known as Saturation. Hereby the magnetic permeable material can be made to vary its permeability by the application of a magnetic field of induction. This in turn gives variation to the effective permeability,
, and thus a variation in effective path length.

(6) The general expression for magnetic induction is given by the relation,

In this relation two parameters can be varied. One is the current can be made variable, in turn giving a variation of M.M.F. The other is the effective permeability can be made variable, this in turn giving a variation of inductance. The current, i, and the effective permeability,
, undergo variation and give rise to a variation of Magnetism, . This variation of magnetism develops and E.M.F. Three basic relations exist,

One,

Two,

Three,

These fundamental relations bear resemblance to those of Ohm's Law, as basic expressions of proportionality.

Relation one expresses a conservation of magnetism, . This gives the Motor-Generator relation. Here an increase in current relates to a decrease in inductance, or an increase in inductance relates to a decrease in current. This proportionality maintains a constant quantity of magnetism.

Relation two expresses a conservation of Current, i. This gives the variable parameter relation. Here an increase in magnetism relates to an increase in inductance, or a decrease in inductance relates to a decrease in magnetism. This proportionality maintains a constant current.

Relation three expresses a conservation of inductance. This gives the reactance coil relation. Here an increase in magnetism relates to an increase in current, or a decrease in current relates to a decrease in magnetism.

In any one of these three various conditions that give rise to a variation in magnetism the E.M.F. which results from this variation transfers energy into, or out of, the Magnetic Field of Induction, . Here derived is a more general expression for the Law of E.M. Induction for the study of parameter variation in electro-magnetic systems.

BK DE N6KPH
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#64
07-25-2012, 07:52 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by jake But here is the diagram I was talking about. Does anyone know why in this setup the secondary and extra are joined.
I believe the "NO METALLIC CONNECTION" was primarily for the testing, this allows us to determine the "maximum" frequency of the coil. That diagram is also lacking the secondary condenser.

If the extra coil was connected through the condenser rings with NO metallic connection, then you would also need an additional adjustable air condenser across the secondary because I don't think it will be possible to tune the secondary to a low enough frequency with only the extra coil connected through the rings.

So I think, you will need to play around with it

 This could be wrong in terms of a proper explanation, but I think there's what could be called something like an "effective coupling capacity" when the thing is in operation. That is, the frequency is raised when the coils are metallically connected, as if an effective coupling capacitance comes into play as opposed to a straight forward metallic connection. So the metallic connection with the secondary is different than the metallic connection in the extra coil test setup.
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Last edited by dR-Green; 07-25-2012 at 08:04 PM.
#65
07-26-2012, 04:47 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Eight.

Magnetic Parameter Variation can be divided into two categories. One is the variation of the M.M.F., thru variation of the Current, i. The other is the variation of the Inductance thru variation of the Effective Path Permeability, . Current, i, and permeability factor, , are the two parameters which can undergo variation in order to give a variation in the quantity of Magnetism, .

The condition in which only the current undergoes variation exists with the Reactance Coil. Here the inductance is a constant, it is a factor of proportionality. This is expressed in the relation,

Here a sine wave of current develops a sine wave of magnetism. Both waves exist in a direct proportion, L, and are thus “in phase”.

For the Reactance Coil the Law of Energy Conservation is satisfied. All the energy given to the magnetism is given back by the magnetism, no gain or loss. This movement of energy is facilitated by the induced E.M.F.

The condition in which only the Inductance undergoes the Parameter Variation exists with the Magnetic Amplifier, or the General Parametric Apparatus. Here the current is constant, it is a factor of proportionality. This is expressed by the relation,

Here a sine wave of Inductance Variation develops a sine wave of Magnetism. Both wave exist in direct proportion, i, and thus are in phase. Energy is exchanged thru the developed Induced E.M.F.

Here the Law of Energy Conservation is not satisfied. The Energy given to the Magnetism is not the Energy given back by the Magnetism, there is a gain or loos of Energy. In this situation the Law of Energy Continuity must be considered.

The condition in which the Magnetism is a constant is the Motor-Generator. This is expressed by the relation

Here it is both the Current, i, undergoing variation and the Inductance, L, undergoing variation, these in an Inverse Proportion in order to maintain a constant Magnetism. As sine wave of Inductance gives a sine wave of Current, but here the two waves are in Phase Opposition, that is, “out of phase”.

Because the Magnetism is “Static” no Energy is exchanged. Thus no “Energy Law” is involved in this condition of constant Magnetism. Hereby no E.M.F. is developed, the E.M.F. of the Motor-Generator is derived solely from the Rotation of the machine. The Law of Energy Continuity is involved here in that the Mechanical Energy consumed by the shaft re-appears as Electrical Energy produced by the armature windings, this representing a Generator. The reverse is true for a Motor. In each case the form of Energy is not conserved, it is consumed, or it is produced. Thus the Law of Energy Continuity expresses the Energy relationship.

For the condition of Inductance Parameter Variation and a constant Current the Magnetic Energy is not conserved. While for the Motor-Generator the Law of Energy Continuity is obvious, it is not so for the Parameter Variation apparatus. Here the Law of Energy Continuity is not identifiable, it is somewhat Indeterminate. This now brings into question the Law of Energy Perpetuity, this is to say Energy goes on forever just as it has existed forever As written in the Bible; “As it was in the Beginning, so it shall be, for now and Ever-more:. The Law of Energy Perpetuity is similar to a Religious Law, to be defended and upheld by the “Church”. Amen.

BK DE N6KPH
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#66
07-26-2012, 06:12 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
The Law of Electro-Magnetic Induction, Nine.

The basic characteristics of the Three Principle Conditions has been considered.

One, The Reactance Coil

Two, The Variable Parameter Apparatus

Three, The Motor-Generator.

For the Reactance Coil it is a sine wave of Current variation, for the Parameter Apparatus it is a sine wave of Inductance variation, and for the Motor-Generator it is a sine wave of shaft rotation, these sine waves give rise to a sine wave of Electro-Motive Force.

While it is that conditions one and three are generally understood, not so with condition two. The development of an E.M.F. by variation of the Permeability Factor, , is a non-conventional methodology. The most notable apparatus for this purpose is the Alexanderson Alternator. Also the Alexanderson Magnetic Amplifier can serve as a Generator of and Alternating E.M.F. but this has not found practical application. Little exists to facilitate study.

(1) An example of Magnetic Parameter Variation can be found in the phenomena of Hysteresis. It is a natural phenomena characteristic of certain Magnetic materials, such as Iron. Hysteresis gives rise to an Energy loss in the cycle of Magnetic Induction. For example, if the Reactance Coil has a Magnetic path consisting mostly of Steel, the Energy taken by the Magnetism is not all given back by the Magnetism, part is lost. In conformance to the Law of Energy Continuity it is presumed that the Energy is continued in the form of Heat. Hysteresis results in the heating up of the Steel which makes up the Magnetic path. It was the pioneering work of Steinmetz that led to an understanding of Hysteresis, a major advancement in the engineering of A.C. machinery.

In general the phenomena of Hysteresis is lumped together with the phenomena of Magnetic saturation. This is an un-fortunate circumstance. While in general the Hysteresis Cycle gives rise to a gain of loss, the Saturation only distorts the wave. The gain or loss of energy is produced by the Hysteresis component of a Magnetic Cycle, not the Saturation component.

(2) Hysteresis is defined as a Time Displacement, it is derived from the Greek work defining “To Lag”. Here with Hysteresis it is that Cause is displaced in time from Effect. This is to say that Action and Reaction no longer exist in the same Time Frame, one can lag or lead the other.

For the condition of Hysteresis loss in Magnetic material, the current, i, and the M.M.F. produced is displaced in time from the co-responding Magnetic Induction. The M.M.F. causing the effect of Magnetism exists at a different time than that of the M.M.F. Here the sine wave of current has fallen out of step with the sine wave of Magnetism. The Induced E.M.F. is the cosine wave, that is the rate of change of the sine wave of Magnetism. When the M.M.F. is in step with the Magnetism, that is “in phase”, the cosine wave of E.M.F. is “in quadrature phase” with the Current. Here the Energy of the Magnetism is conserved. When the Magnetism has fallen out of step with the Current a quadrature relation no longer exists with the Current and the Induced E.M.F. This introduces an Energy Component into the E.M.F. and the Energy of the Magnetism is not conserved. The degree by which the Current is out of step with the Magnetism, and accordingly the E.M.F. is known as the Angle of Hysteresis, .

In general if this angle, , Lags, Energy is lost and if it Leads, Energy is is gained, by the Magnetic Field of Induction. The Law of Energy Continuity requires the Energy lost or gained to continue as heat or mechanical activity.

(3) Let the quantity of Magnetism at any instant in time, or arbitrary phase angle, be represented by the relation,

If the wave of Current is displaced in phase from its co-responding wave of Magnetism, the Current existing at the time of Magnetism is foreign, it is from another time. The Cause is not present for its Effect. This foreign relation exists thru the Inductance, and the Hysteresis Cycle gives rise to the Variation of this Inductance maintaining the Magnetism at that instant in Time. Thus in the sine wave of Magnetism there exists a co-responding sine wave of Inductance variation, the sine wave of Current will shift in phase to accommodate the sine wave of Inductance variation. This exists in the Reactance Coil with a Hysteresis Loss. Here the sine wave of Current gives rise to a sine wave of Magnetism. This is in phase if the Inductance remains constant. It is however that the Hysteresis gives rise to a sine wave of Inductance variation and this gives rise to a co-responding phase displacement between the Current and the Magnetism. The factor by which Energy is lost via Hysteresis is given by the relation

Where, , is the angle of Hysteresis, and, a, is the Power Factor of the Reactance Coil.

In the general situation, if a Reactance Coil exists in which a sine wave of Induction variation is applied, the Reactance Coil can be made to consume Energy for a lagging Hysteresis angle, and to produce Energy for a leading Hysteresis angle.

BK DE N6KPH
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#67
07-28-2012, 01:35 PM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Tuning setup for secomdary coil

dR-Green:
I have put winding on my newly built secondary coil frame. I have used the 5.5 mm wire spacing first. I have done the tests with just the one condenser ring on top of the frame, connected as Eric specified. Got 3 readings with various can elevation above the secondary. In your post #760 how did you measure the condenser ring to be 11.8 pF? Then when you tuning the extra coil this same condenser ring is now 12.59 pF. I do understand that my condenser ring has different size than yours, but how am I to measure the value(s)? I think I have to play with the distance between the two condenser rings to get the max frequency response. I must be missing something from Eric's extensive instructions.
Once I do similar tuning as you done in post #790, I will rewind the secondary with 4 mm wire spacing then do all the above described testing and finally rewind again with 3.5 mm wire spacing an repeat the procedure. This way I can verify the best wire spacing for max frequency response. Thank you.
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#68
07-29-2012, 09:34 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Nhopa dR-Green: In your post #760 how did you measure the condenser ring to be 11.8 pF? Then when you tuning the extra coil this same condenser ring is now 12.59 pF. I do understand that my condenser ring has different size than yours, but how am I to measure the value(s)? I think I have to play with the distance between the two condenser rings to get the max frequency response. I must be missing something from Eric's extensive instructions. Once I do similar tuning as you done in post #790, I will rewind the secondary with 4 mm wire spacing then do all the above described testing and finally rewind again with 3.5 mm wire spacing an repeat the procedure. This way I can verify the best wire spacing for max frequency response. Thank you.
I used a capacitance meter Search for "LC100-A" on ebay to find it. It's cheap but very sensitive so pretty good even for measuring the capacitance between the top terminal and the ground plane (although the accuracy of that hasn't been verified, as long as it's constant then it will do nicely for reference).

Yes you have to adjust the rings spacing for maximum response. First set your oscillator to "F" or the intended frequency (in my case 3670 kc). Then adjust the rings until you see the peak at that frequency. Now the secondary is tuned for that test.

By connecting the extra coil, the secondary frequency is then found to be too high, so the rings capacitance has to be increased.

Although this was with the original extra coil wire length with no terminal capacitance, bringing a terminal into the equation complicates it a bit so better if you still have the original extra coil at this point. The rise in frequency will easily be seen.

 Otherwise, on capacitance, look at lecture 7 here

MIT 8.02 Electricity and Magnetism : MIT OpenCourseWare : Free Download & Streaming : Internet Archive

I think it's explained in that, but you might (should) need to get some information from earlier lectures relating to electric charge and electrostatic potential etc. I can't check it now because I'm having computer problems in the way of it turning itself off whenever I try to do something productive

Looking forward to seeing the results anyway
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Last edited by dR-Green; 07-30-2012 at 12:58 AM.
#69
07-30-2012, 10:05 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Ten (1 of 2)

(1) Hysteresis is described as the separation in time between cause and effect. Cause and Effect relations can be expressed as points on a curve, normally this curve is a straight line. In the graphical representation of electronic devices this curve is called a Load Line. A straight line gives the condition of a direct relation between Cause and Effect.

As an example is the condition where the E.M.F., E, is the cause, and the Current, i, is the effect,

The Proportionality, R, exists between Cause, E, and Effect, i, and here it is a Resistance. If the Cause, E, is given graphically as a vertical co-ordinate, the resulting Load Line is the graphical plot of the Proportionality between the Cause, E, and the Effect, i.

For the condition of a constant fixed resistance, R, in Ohm the Load Line is a straight line. The slope of this line is the instantaneous ratio of the E.M.F. to the Current, and it is constant anywhere along the line. No differential relation exists in that the ratio of any E.M.F. to its co-responding current is always the same value. It is a constant resistance, R.

This is known as a Linear relationship.

(2) Electrical devices such as Incandescent Lamps or Thyrites do not exhibit a direct relation between cause and effect. For example, the Lamp shows and Increasing Resistance for and Increasing Current, and a Thyrite shows a decreasing Resistance for an increasing applied E.M.F. Here the Load Line is no longer straight, but it is now curved in a parabolic form. The slope is no longer constant but varies with position along the curve. An E.M.F. and its co-responding Current have a different ratio than another E.M.F. and Current taken at another point on the curve. The variation of the slope represents the variation of Resistance,

Cause and Effect are now in Dis-Proportion to each other. Here Effect can become exaggerated by the cause and a sine wave of E.M.F. no longer gives rise to a sine wave of Current, distortion results. This is known as a Non-Linear relationship. Magnetic Saturation in Magnetic material is one such disproportional relationship, here between the M.M.F. and the Magnetic Induction, the Load Lines are known as the Saturation Curves of the Magnetic Material.

In both the Linear and the Non-Linear relation every E.M.F. has one and only one co-responding current. These exist at one unique point on the Proportionality Curve. The Relationship here is Uni-Valent, or single valued.

(3) Another more complex relation can exist between Cause, E, and Effect, i. In this relationship Cause and Effect become Dis-Joint. Here the curve for rising values is not the same curve as for falling values. In this situation the graphical expressions of the relation is no longer Linear, nor is it non-Linear, it is now an Elliptical relationship. In the Non-Linear relationship the limit in curvature is the straight line, here the curvature is Infinitesimal. Likewise for the Elliptical relationship, the limit in ellipticity is the full circle, a limiting case for Elliptical curvature. When the “Load Line” is a circle the Proportionality Factor of Resistance becomes the Dis-Proportionality Factor of Reactance.

Reactance is Resistance in constant variation at an angular rate of . Here the Resistance is the Reaction of the Inductance to the constantly variable current,

(4) For the condition of the Elliptical Load Line, the point by point relationship is no longer uni-valent, for each Cause, or E.M.F., E, there exist two co-responding Effects, or Currents, i. These two Effects exist displaced in Time. Likewise, for each Effect, Current, i, there exists two co-responding Causes, E.M.F.s. These two Causes exist displaced in Time. Where it is the Linear or Non-Linear relationship is a Uni-Valent function, it is for the Circular and Elliptical relationships a Quadra-Valent function.

For the condition of the Linear and the Non-Linear relationships, As the Cause, or E.M.F. becomes smaller and smaller, likewise the Effect or Current becomes smaller and smaller. For both Proportionate and Dis-Proportionate relationships a zero Cause has a co-responding zero Effect. Both become zero together, Uni-Valent.

For the condition of the Circular and Elliptical relationships, these Quadra-Valent functions arrive at zero points in four locations on the curve, two for the Cause, E.M.F. and two for the Effect, Current. The two zero points for E.M.F. are displaced in Time as are the two zero points for Current, and all four zeros are displaced in Time from each other. Moreover here exists a unique situation where a Cause, E.M.F. can have zero Effect, Current, or and Effect, Current, can have no Cause, E.M.F. Cause and Effect are here Dis-Joint from each other. This condition can be called the Hysteretic Cycle of Proportionality.

(5) In its most general form, ruling out Non-Linearity, the Load Line can be considered a Circle rotating on an axis, this axis in the plane of the Circle and normal to its curvature, bisecting it. As this circle is turned on its axis it begins to contract into an ellipse. Continuing the rotation further, upon reaching one quadrant, 90 degrees, of rotation, the circle has completely contracted into a line with a slope of one, a 45 degree line. This quadrantal rotation represents the transformation from Reactance to Resistance. The angle by which the circle is displaced towards the line is called the Angle of Hysteresis, .

In order to carry the angle, , beyond one quadrant one more transformation is required. Here the circle has a pair of rotational axes, these also in a quadrature relation, dividing the circle into four quadrants. As the angle, , passes beyond 90 degree the rotational axis is shifted to the quadrantal axis and it is inverted. As the line opens into an ellipse the position of this curve now travels in the opposite direction, the A.C. wave now rotates around the Load-Line in the opposite direction. Continuing to advance angle, , another 90 degrees, upon reaching two quadrants the line has opened up again into a full circle with a cyclic direction opposite to the circle at the start when the angle, , was zero. This now is a Negative Reactance. Where the first quadrant of rotation transformed Reactance into Resistance, the second of rotation transforms Resistance into Negative Reactance. Continuing to carry the rotational, or Hysteretic Angle, , beyond two quadrants, or 180° degrees, again contracts this counter-circle back into an ellipse. However the slope of this ellipse is now backwards, or negative, this as well as counter-cyclic. Upon reaching the next quadrant of rotation the ellipse has contracted into a line but now the line has a negative slope. Here is the unique situation where an increasing Cause, E.M.F. has a co-responding decreasing Effect, Current. Inversely, it is the greater the Effect, the less the Cause required to produce this Effect. This is a condition of Negative Resistance.
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#70
07-30-2012, 10:06 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Ten (2 of 2)

Upon passing thru this inverse Linear relationship the rotational axis of the Load Line Circle is shifted back to the original. As angle, , is carried past three quadrants, or 270 degrees, the Load Line again opens into a Ellipse of positive slope and normal rotation. Continued rotation returns the Load Line back to the original circle of Reactance at four quadrants or 360 degrees.

(6) In symbolic form, for the four quadrants thru which the Angle of Hysteresis is rotated it is

Here the Versor Operator, , expressed the Angle of Hysteresis, , in quadrantal form.

In any intermediate angle between quadrantal angles of 0, 90, 180, 270, the values of Reactance and Resistance combine in a quadrantal vector relationship, this for intermediate angles in the first quadrant the relation is given as,

This is the Hysteretic Impedance for the first quadrant, and

Here, , is a Positive Impedance but now the Resistance has become an imaginary quantity. Likewise for the opposing quadrant the relation is given as,

Or by resolving powers of , it is

Here it is a negative Hysteretic Impedance. Hence Reactance and Resistance can be synthesized in Positive or Negative forms by positioning the Angle of Hysteresis, .

BK DE N6KPH
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#71
07-30-2012, 10:32 PM
 Web000x Silver Member Join Date: Apr 2009 Posts: 547
Thank you Eric,

As you know, I have studied your works for a couple of years now trying to gain insight and it has not been until recently that my mind has began to really connect the puzzle pieces of your "Symbolic Representation of the Generalized Electric Wave in Time" book. I have to say that I am truly impressed with your ability to organize electrical phenomena symbolically. The series of writings that you have been putting into the public domain has been the most articulate, well-written information that I have ever read regarding electrical phenomena. I believe your transmissions to be priceless.

Just a reminder to all, Eric is doing all of this in hopes that he will receive some type of compensation for all of his efforts. If you feel that you are taking away anything of value from his transmissions, please donate what you can. I can assure you that he is not living a life of luxury.

Dave
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Last edited by Web000x; 07-30-2012 at 11:29 PM.
#72
07-31-2012, 11:20 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
The Law of Electro Magnetic Induction, Eleven.

(1) Magnetic materials such as Iron exhibit internal parameter variations during a Magnetic cycle of Induction. These can be divided into two distinct phenomena, Saturation and Hysteresis. It has become commonplace to consider the two as a single phenomena, but this leads to misleading concepts. Saturation and Hysteresis must be analyzed separately.

Saturation gives rise to a Non-Linear loadline. The path taken by a point on this curve thru the A.C. cycle follows the same path up the curve as down the curve. This curve defines a single path. Also, here in the Iron, the Saturation curve is Symmetrical, both positive and negative values give the same curvature. The Non-Linearity of the Saturation curve gives rise to Dis-Proportion between cause and effect. This in turn distorts the wave into a non-sinusoidal form. A series of odd ordered harmonics is produced by this non-linear distortion. This is an Amplitude Distortion of the A.C. wave.

Hysteresis gives rise to an Elliptical loadline. A point on this curve does not follow the same path up the curve, as that path down the curve. Each path is on one or the other side of the elliptical curve. This path is now a loop. The elliptical load line is ultimately derived from a linear curve as a side view of a rotating circle. Hence the distortion produced is not an amplitude distortion as normally considered. In the elliptical curve the distortion is not the result of a dis-proportionate relation between cause and effect as with the Saturation, rather it is that cause and effect have become separated in a time loop. Thereby Hysteresis gives rise to a Phase Distortion in the A.C. wave.

Parameter variation of Inductance by external means, thru rotation or controlled saturation, can be utilized to develop synthesized Saturation and Hysteresis curves unique from those of the Iron itself. The practical knowledge in this realm is very limited. Experimentation is required here.

The principle apparatus utilizing parameter variation are the developments of Ernst Alexanderson, the Variable Induction Alternator

and the Magnetic Amplifier.

The alternator is a complex machine but the Mag-Amp is a quite simple device. The Mag-Amp is where to begin the study of parameter variation.

The utilization of the Mag-Amp as a parameter variation device is somewhat different than its use as an amplifier. As an amplifier it serves as a variable Impedance, consuming E.M.F. as a Reactance Coil. In the situation of parameter variation this device is called upon to produce an E.M.F. and thereby function as an A.C. generator. One important feature of the Mag-Amp is that the control windings are Electro-Magnetically isolated from the power windings. The Magnetic circuit of the Mag-Amp acts as a balanced bridge, giving a cancellation of power flux in the control winding. Hereby no energy can be exchanged between control circuits and power circuits. This is a consideration in the Law of Energy Continuity.

(3) C.P. Steinmetz, in his editions of “Theory and Calculation of A.C. Phenomena”, does not development Saturation and Hysteresis as separate and distinct phenomena. Saturation and Hysteresis are combined in the Magnetic material giving rise to a Distortion Complex of phase shifted harmonics. This is a composite of the separate amplitude and phase distortions. Little is given in the A.C. book that relates to the utilization of parameter variation for the generation of Electro-Motive Force and the transfer of Electric Energy thereby. Steinmetz only considers situations where Saturation and Hysteresis are considered as parasitic phenomena, these to be minimized. In later chapters, “Reaction Machines” and “Distortion of Waveshape and Its Causes”, Steinmetz develops an analysis of parameter variation and the E.M.F.s developed thereby.

A considerable portion of the Steinmetz A.C. book is devoted to the Synchronous Machine,

such as the common polyphase Alternator and the Synchronous Motor. The Synchronous Machine, a development of Nikola Tesla, is the principle apparatus of Electric Power Engineering. Nearly all Electric Energy is generated by Synchronous Alternators, their first major application at the Niagara Power Plant.

(4) The Synchronous Machine has applications other than converting mechanical to electrical Energy as a generator, or converting electrical energy to mechanical Energy as a motor. The Synchronous Machine can synthesized Electric Power. Here the machine operates with no mechanical connection to the shaft whatsoever, it is spinning freely in synchronism with the applied A.C. wave.

When the Synchronous Machine is operating in perfect synchronism with an A.C. power line, no power flows into, or out of, the A.C. power line. Here the rotor is in exact step with the rotation of the A.C. wave developed by the machine stator. Both rotations are in phase unison, top dead center on the rotor is top dead center on the stator, the two rotations in synchronism. In order to maintain this condition the machine must be excited by a specific quantity of Magnetism, this produced by the Field Current. This specific value is determined by the condition of no power flow between the machine and the power line. Here the E.M.F. of the machine just matches the E.M.F. of the line, not cross current exists. This is a neutral condition.

If the Field Current (and excitation) is increased beyond the value required for a neutral condition, the rotor pushes ahead of the rotating A.C. wave to a position advanced in phase, but still rotating in synchronism with the wave. With increasing excitation the machine begins to draw a leading Current from the power line, the greater the excitation, the greater the current taken by the machine from the line. Since these Currents are reactive no Energy is expended in maintaining them. Here the Synchronous Machine is exhibiting the characteristics of and Electro-Static Condenser and in this manner of operation it is called a Synchronous Condenser.

Inversely, reducing the Field Current below that required to maintain a neutral condition, the rotor falls behind the A.C. wave of the stator, this to a position retarded in phase while rotating with the A.C. wave. The less the excitation, the more the rotor lags behind the stator. With decreasing excitation the Machine draws a lagging Current from the power line, the less the excitation, the more Current is drawn. Here the machine is exhibiting the characteristics of a Reactance Coil. This can be called a Synchronous Reactor.

In this manner the Synchronous Machine is operating as a two terminal Reactance Arm. There is no connection to the rotating shaft. The Machine can synthesize an actual Inductor or Condenser. Operating in this manner the machine can create a substantial reactive power flow, this flow controlled by the D.C. excitation of the machine. This Controlled Reactance is used at the end of long distant power lines in order to regulate the voltage and phase at lines end.

As a reactance arm the two terminals (per phase) serve as input and serve as output. There is only one power line. The Energy flows into the machine during one part of the Cycle, and Energy flows out of the machine during another part of the Cycle. Here input and output are separated in Time rather than space. The Energy is caught in a Hysteresis Loop.

It is important to note here that this machine is operating as a Synthesizer. The power flow of Condensers and Reactors are developed by synthesis, without the intense Dielectric and Magnetic Fields that normally are required to create this flow, or surging, of Electric Energy. Here a “Synthetic Power” is derived from a dynamic of parameter variational form.

BK DE N6KPH
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#73
08-01-2012, 09:27 AM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Secondary and extra coil tuning

Hi dR-Green: Thank you for the help with the set up. With the 5.5 mm wire spacing I done 3 tests with can at 16 cm, 8 cm and 1 cm above secondary. The lower the can was the higher the frequency reading (although not by much). While keeping the can on the axis of the secondary I set the frequency to 1,188 Kc (my target frequency) and kept raising the condenser ring until at 64 mm above the the top ring I got max meter reading. I then took the can and measured the meter response in the radial direction from the top ring which was at approximately 4 cm from the top ring. Next I placed my old extra coil on top of the secondary and connected per your diagram. This extra coil will be redone with about #13 AWG wire, currently the wire is #25 AWG and 124.25 turns with a tap at 49.5 turns.
When the can held radial to the top ring I get two resonant peaks, the 1st @ 724 Kc and the 2nd @ 1,267.3 Kc. If I connect the extra to the top of secondary via the top ring at the 49.5 turn tap point then the first resonant peak is @925.5 Kc and the 2nd @ 1,186 Kc. During these measurements I left the condenser ring at 64 mm above the top ring. I think my results are good but comments are welcome. Next I will rewind the secondary with 4 mm wire spacing to see if I can increase the secondary's response frequency. If I see an increase then I will rewind for 3.5 mm wire spacing if not then I will do a final rewind at 5 mm wire spacing.
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#74
08-02-2012, 12:02 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Nhopa When the can held radial to the top ring I get two resonant peaks, the 1st @ 724 Kc and the 2nd @ 1,267.3 Kc.
Very good What you could also do there now is adjust the condenser rings to make it resonant at 1188 kc and then see what frequency the secondary is tuned to, just for future reference.

4cm pickup distance sounds a bit close. Yours might not be as sensitive as mine at a higher frequency, but be careful you're not bringing the frequency down by having it too close.

I think 4mm spacing will give a lower frequency due to the extra capacitance, also the height to width ratio would be less so that would also contribute to it being lower? Is any of them 62%? It will be good data to have anyway
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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

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#75
08-02-2012, 12:55 AM
 Spokane1 Senior Member Join Date: Aug 2008 Posts: 356
Reproduction 1989 Dollard Demonstration Device (DDD)

Dear T-Rex,

I have built a first version "Wagon Wheel" Tesla pancake coil as close as I can to what appears in the vintage video. Right now I'm still doing shake down tests and collecting working instrumentation. (I didn't realize that I have 3 signal generators that don't work). So, all the following measurements are tentative.

You mentioned that the primary and secondary were tunned to resonate at harmonic frequencies.

Right now my primary rings at 5.4 MHz (using 7350 pF from a vacuum variable capacitor with 1.4 uH in the copper strip primary). The secondary rings at 2.7 MHz. with a measured inductance of 217 uH in the open circuit mode with a 5-pie section 17 mH RF loading inductor in series. Is this the intent of this system to have the secondary oscillate at a lower harmonic than the primary?

This seems to be a 1:2 harmonic ratio. Is it deseriable to shoot for a 1:3 relationship to take advantage of harmonic voltage addition?

If this device is to operate in transmission line mode just where should the minimums and maximums take place?

The NE-34 lamps lights up nicely, but I don't have any observable action on my appliance lamp. Right now I'm working at the lowest Diathermy input current setting.

The 1B22 arc tubes display purple streamers inside.

Right now I'm using the Diathermy output between the "Low voltage" terminal and the "High voltage terminal". I could use the "Indifferent" terminal as my low side, but I can't tell from the video if this is what you were doing or not.

I noticed that you didn't use the Tesla secondary knob. I was wondering, even though it is not providing a current output it is still in the circuit like a parametric tank element. Was the frequency of this Tesla secondary an important frequency component in the tuning of your transformer?

Spokane1
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#76
08-02-2012, 11:49 AM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Coil tuning

Hi dR-Green:
Thank you for the response. I will eventually do the suggested tests but first I want to find out what is the best wire spacing on the secondary for max frequency response. Second, I will build a new extra coil using #13 AWG in lieu of #25 AWG. The problem with holding the can and the meter is that it do influence the readings, but I have to have short leads from meter to ground and between meter and can in order to minimize their contribution to capacity. I noticed even my body's proximity to the test set up influences the readings, so normally I have to step back after frequency adjustment to see that the meter stays at that maximum. One would need a real laboratory setup to do these tests properly. Who would have thought that Eric's simple CRI sketch would require so much effort to be successful.
If I use a shortened version of the extra coil, i.e. connect at the 49.5 m point then I do get resonance at 1,186 Kc (pretty close to my target 1,188 Kc) with the condenser rings 64 mm apart. Are you suggesting to tune the secondary coil with a full length extra coil for 1,188 Kc by adjusting the rings' spacing?

P.S. Comments from Eric or any of the other builders also welcome, except I know currently we lost Eric to the wilderness.
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#77
08-03-2012, 01:50 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Nhopa Are you suggesting to tune the secondary coil with a full length extra coil for 1,188 Kc by adjusting the rings' spacing?
I don't know yet, but that's how I did it with the old extra coil. Without adding terminal capacitance the only way to tune it to 3670 was with the rings. This is because the secondary frequency is brought up, so it's no longer tuned to 3670 as it was without the extra coil. So I tuned it back down with the rings.

The question in my mind is the balance of secondary to extra coil frequencies. If the secondary is brought up by the extra coil, and the extra coil is brought up by the secondary, then at what point are they both properly tuned to the correct frequency through the rings and terminal capacitance respectively.

To add to that problem, I've been doing tests in trying to figure this out and found that the extra coil direct connection vs 10pF frequency ratio is not constant as different terminal capacities are used, so the tuning relations between the secondary and extra is not linear. Patterns are starting to form but there are still more tests to do, I've been taking all the relevant measurements I could think of so all kinds of relations and graphs could be derived from it which I hope will reveal some interesting stuff. But as Jake said in the coils compendium thread the primary condenser will also bring the frequency of the secondary down, but for the purposes of these tests the intention is/was when I set out to determine the secondary vs extra frequencies, but having all the data in a spreadsheet has revealed more than that, so it might also be interesting to see how/if/what changes when parts are added in the future. So I have my doubts as to the straightforwardness I was hoping for Just takes an hour or two per test to tune the thing when particular frequencies are being aimed for that's all

Is there any particular reason for the tap at 49.5 turns on your extra coil?

 As far as the tests I'm currently doing go, I think it will be most important to see if the results are true universally. If the relations are constant and can be estimated on different scales then we're in business Or at least as far as these particular geometries go. If not then I dunno I'll also be rewinding the secondary with thicker wire after I've tested everything with the existing secondary.
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Last edited by dR-Green; 08-03-2012 at 02:12 AM.
#78
08-03-2012, 10:25 AM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Coil tuning

Hi dR-Green:
The reason for the tap at 49.5 turns was to have a section of the extra coil the same length as the secondary coil length as per a former forum member, who slightly disagreed with Eric on some points. Although, I am following Eric's instructions to the letter, I figured it cost me nothing to place a tap at that point.
As you indicate in your response things don't seem to be straight forward by I have a feeling that at the end we will have a simple way to calculate, build and test these coils. I now have another dilemma. As I indicated before I will build a new extra coil using #13 AWG wire. We were told that the coil's height to diameter ratio should be one. The diameter is given as .4 x secondary coil diameter, therefore, the coil height should be also the same. Since I will use #13 AWG and 124 turns, I can only wind the required turns for the given height if the turns just about touch each other. If I figure with the 62% wire diameter spacing then my overall coil length will increase by 10 cm or to about 36 cm, and the height to diameter ratio to approx. 140 %. The question is then: Should I ignore the wire spacing, should I increase the coil diameter so I can still wound the required length on the proper height or keep the calculated diameter and let the height increased by 40 % above the recommended? By the way I will also provide a tap point at the same length as the secondary, just in case.
Please, Eric and all other active builders make comment(s) if you can.
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#79
08-03-2012, 09:47 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
What's the frequency of your existing extra coil? If it has the same relation to F as my 126 turns coil had then it will be no good, its frequency is too low. In which case you won't need to rewind it with 124 turns so the spacing problem doesn't matter.

If your extra coil has the same relation as mine did then the "tentative" calculations are experimentally updated - Extra coil wire length = λ/4/1.24

I think you should test the existing extra coil to confirm this before trying anything else otherwise maybe you will end up finding out the same thing through a lot of needless work. If you find the existing extra coil frequency as being too low then there's no point in making a new one that's also too low.

The tap won't quite be the same as an extra coil of a different wire length. For example the height to width ratio at the tap won't be 1:1, and the extra wire that's "not being used" won't just be sitting there as if invisible

 Try it like this: First measure the extra coil separately with direct connection and with 10pF or 5pF input and note the peak frequencies.

That should confirm the wire length issue, but if you want to test further, repeat the test you did with the extra coil + secondary, but this time at 1188 kc and the lower peak, note both the secondary meter reading and the extra coil.

If the secondary meter reading is higher than the extra coil at 1188 kc then the wire length is no good, so then make your new extra coil with λ/4/1.24

λ = c/F
c = 299792458
F = 1188000
λ = 252.35055387205387205387205387205

λ/4/1.24 = 50.877127796785054849570978603237 metres
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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

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Last edited by dR-Green; 08-04-2012 at 12:06 AM.
#80
08-05-2012, 10:15 AM
 GSM Silver Member Join Date: Jan 2011 Posts: 688
Quote:
 Originally Posted by dR-Green If the secondary meter reading is higher than the extra coil at 1188 kc then the wire length is no good, so then make your new extra coil with λ/4/1.24 λ = c/F c = 299792458 F = 1188000 λ = 252.35055387205387205387205387205 λ/4/1.24 = 50.877127796785054849570978603237 metres
And if an oscillator ran at 1188kHz, coupled with a 50.8 metre antenna, the antenna system not earthed in the same way it normally is for electromagnetic tuning and radiation ?
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#81
08-05-2012, 08:48 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by GSM And if an oscillator ran at 1188kHz, coupled with a 50.8 metre antenna, the antenna system not earthed in the same way it normally is for electromagnetic tuning and radiation ?
Is that a question?

The extra coil is to be excited/energised from the secondary so the purpose of this is to find out the relative maximum readings with the existing wire length.
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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

"Once men died for Truth, but now Truth dies at the hands of men." - Manly P. Hall
#82
08-06-2012, 07:54 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
I have some tentative data.

Voltage and capacitance readings are not accurate and are for general reference only. All measured frequencies should be within around +/- 5 kc tolerance (namely the extra coil direct measurements with bigger terminal capacitance are most difficult to pinpoint) (at the general system frequency of 3670 kc). Percentages are relative to system F therefore the relations are theoretically scalable. This must be verified.

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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

"Once men died for Truth, but now Truth dies at the hands of men." - Manly P. Hall

Last edited by dR-Green; 08-07-2012 at 12:28 AM.
#83
08-06-2012, 03:09 PM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Extra coil testing

dR Green:
I really appreciate your contribution to my "success?". I have done some more testing on the extra coil and as you suspected the frequencies are too low. Interestingly when I previously published similar results, Eric said the data is fine. Anyway, here are the results:

@ 11 pF can at 5 cm from end of extra coil F=892.1 Kc
can at 40 cm from end of coil F=949 Kc

@ 5 pF can at 5 cm from end of coil F=948.5 Kc
can at 40 cm from end of coil F=990.5 Kc

So next I will wind 50.88 m for the extra coil for my frequency of 1,188 Kc.
I build the frame soon with D/L=1. The 50 turn will give me about 5 mm spacing between turns. I am picking up the #13 AWG wire tomorrow so I will have something soon. I hope from the wilderness Eric will not send a longitudinal wave lightening to strike me down for doing this short version extra coil.
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#84
08-06-2012, 10:53 PM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Quote:
 Originally Posted by Nhopa I hope from the wilderness Eric will not send a longitudinal wave lightening to strike me down for doing this short version extra coil.
Hehe, what, the 50.88 metres or the tapped coil? Eric gave me a wire length to use with a reference to 124% velocity factor, so my reverse mathematics came up with λ/4/1.24 as being the logical calculation that gave an answer 3cm out from Eric's given wire length for 124%. That was the only reference point and no one has confirmed or denied it since so I consider that to be correct for now.

I think what we are always forgetting is that this is all experimental, the design needs to be updated based on the experimental results. From what I can make out I think the "strictness" was mainly down to the fact that Eric wanted specific data on the known coil designs, but now we have that I think from my extra coil and concatenated mode tests, your secondary, and Geometric Algebra's something that hasn't been published (??), all the necessary data has been acquired (and applied to the Colorado Springs setup). So now I think it's down to the experiment and using the collected data to develop something that works.

On a side note in case you haven't seen it I started a coils compendium thread here. The testing is all presented sequentially with Eric's responses etc so the "evolution" is easier to see:

http://www.energeticforum.com/renewa...ompendium.html

Oh yeah, with the new wire length I suspect the extra coil frame doesn't "have" to be the size from the calculations - I think that's just for convenience of not building a new frame. I think it would be ok to make a smaller frame for more turns, perhaps closer to Tesla's CS extra coil? This should also theoretically give a higher potential I would think, which is basically the whole point of the extra coil. As long as it's still 1:1 height to diameter then the only real difference would be the number of turns and the spacing.

 The graphs above are now also updated and compiled into one as I finally figured out how to get Excel to lay it all out properly. What's interesting is that the extra coil direct and secondary cross over when both are tuned to approx 72%, the extra coil 10pF is at 100%. This is also the general area with the highest concatenated mode potential.
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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

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Last edited by dR-Green; 08-07-2012 at 01:55 AM.
#85
08-08-2012, 05:01 AM
 dR-Green Gold Member Join Date: Apr 2008 Location: Wales, UK Posts: 1,557
Some considerations on the tentative tuning relations data. I believe the Tandem mode relation confirms what Eric said. In this mode the condenser rings and extra coil act as one terminal capacitance on the top of the secondary. Therefore as the extra coil terminal capacitance is increased, condenser rings capacitance decreased, the working frequency of the secondary in tandem mode rises, and as the proportions of terminal capacitance vs rings capacitance is not linear or balanced, at a certain point the tandem frequency is unable to go beyond a certain level and then begins to decrease again, as the "secondary terminal capacitance" consisting of the extra coil continues to increase to keep the concatenated mode frequency constant.

Quote:
 Originally Posted by T-rex Two modes of resonance exist, the first is the longitudinal, the second is the transverse. For the first the extra coil input is inductive and thus subtracts from the ring capacitance. For the second mode the extra coil is capacitive and adds to the ring capacitance. The potential meter here is measuring the secondary potential. In the second mode the rings and extra coil all are one terminal capacity so the secondary acts with this as a somewhat lumped LC circuit. In the first mode it is a pair of coupled transmission lines so the magnification factor drops because of travelling waves, and additional losses.
Quote:
 Originally Posted by T-rex Two modes are possible for extra coil in relation with the secondary coil. Both involve quarter wave resonant rise, this the fundamental of resonant transformation. Its also known as constant potential to constant current transformation. A constant potential is a zero impedance (short circuit) a constant current is a zero admittance (open circuit). Departure from these zero values alters the coil distribution to something other than a quarter wave. This quarter wave can exist in a distinct pair of manifestations. The first mode is when the quarter wave is distributed over the length of both extra and secondary windings as a whole, a pair of eighth waves let us say. This is the TANDEM mode. A multiplication in potential is derived hereby since the extra coil exhibits a higher transmission impedance thereby giving rise to a greater EMF between turns and thus a higher termination potential. All photos of my Bolinas and Integratron setups operated in this mode. It is the easy one to achieve. The second mode of the extra coil and secondary coil connection involves two quarter wave distributions, one on each coil. This is not to be considered a half wave however. This mode is the CONCATENATED connection.It compounds the quarter wave resonant rise of the secondary coil with another quarter wave rise in the extra coil, hence a concatenated resonant rise. This is the holy grail of resonant transformer design and unheard of potentials may be gained in this manner. To derive this analytically is extremely difficult, it is an advance transmission line problem. It might not even be possible to calculate or even achieve this mode of resonance, but we are going to give it a try.
The "secondary" measurements could therefore effectively be said to be the tandem mode frequency of the secondary minus its extra terminal capacitance. In this case I think it should be possible to get similar "tandem mode" results simply by replacing the extra coil with a large capacitance. This could be something to try at some point.

As for the concatenated mode, that seems to be a little more tricky

Taking a rounded up/down value of 72% of F as the tuning for the extra coil and secondary

If F = 3670 kc
Luminal wavelength = 81.68 metres

72% tuning = 2642.4 kc
Effective wavelength = 113.454 metres

Both coils tuned to 72% "total effective" wavelength = 226.909 metres
Effective frequency = 1321.2 kc

F to effective frequency ratio = 277%

Effective frequency to F ratio = 36%

This could only be if the coil was operating in 1/2 wave mode.

1/2 wave frequency = 1835 kc

Effective frequency to 1/2 wave frequency ratio = 72% (= tuning factor of F)

Hypothetically, if this was the case then it would be reasonable to think that this is a 1/2 wave situation with the coil operating at 72% the effective luminal frequency due to losses and burdens and what not.

However, while at 1/2 wave it would be operating at 72%, at 1/4 wave it would be operating at 100%. So where did the losses and burdens go?

This "total effective frequency" of 1321.2 kc is not measured, neither is the 72% tuning factor of 2642.4 kc. So this can't be the case.

At 72% tuning, what is measured is:

Concatenated frequency = 3670 kc
Tandem frequency = 1813 kc

3670 kc = 138% effective frequency of 2642.4 kc
1813 kc = 68.6% effective frequency of 2642.4 kc

This seems to confirm "faster than light" when the extra coil is implemented in concatenated mode, and "slower than light" in tandem mode when the extra coil is just a lump of metal. At least theoretically if the coiled wires were lengthened to 72% tuning rather than through additional capacitance.

Bearing in mind that at 72% of F, relative to the wire lengths of the coils:

Secondary luminal frequency = 5730.4 kc
Extra coil luminal frequency = 4550.8 kc

72% F Secondary = 46.11% luminal
72% F Extra coil = 58% luminal

Also, while tuned to 72% of F the extra coil with 10pF input is measured at 100% F.

As I don't believe the coil is operating at 277% as one length of wire, it's not at 72% in 1/2 wave mode, and there is no significance to the 72% frequencies beyond standalone operation, the only other explanation in my mind is that there are two 1/4 wave actions going on. There are two modes of extra coil coupling as explained by Eric which is responsible for this increase in frequency from the 72% tuning factor up to 100% of F. And the tandem mode operation is not a 1/2 wave equivalent as the ratio to F is clearly variable.

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"Knowledge is cosmic. It does not evolve or unfold in man. Man unfolds to an awareness of it. He gradually discovers it." - Walter Russell

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Last edited by dR-Green; 08-08-2012 at 06:54 AM.
#86
08-08-2012, 11:40 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Twelve. (1 of 4)

(1) In the last section it was shown that a Synchronous Machine can synthetically produce reactive power. The practical embodiment of this feature is the regulation of long distance power lines. No stored Energy of Magnetic Induction, nor that of Dielectric Induction, is present to account for this reactive power flow.

In the chapter “Reaction Machines” Steinmetz continues with a more in depth analysis of parametric E.M.F. production. Here Steinmetz presents a situation where a Synchronous Machine can synthesize its own D.C. excitation. This is with no outside source of current to develop the M.M.F., nor any remnant Magnetism.

(2) The chapter “Reaction Machines” gives a more theoretical analysis of Hysteresis. Here the Hysteresis is no longer connected with Saturation, it is independently synthesized by the machine. A pair of Hysteresis Cycles can be formed, one is a forward cycle representing Energy consumption, the other is a reverse cycle representing Energy production; see hysteresis motor.

It is assumed thru the Law of Energy Continuity that the rotating shaft transfers the Energy that is produced or consumed in an Electrical form. The E.M.F. developed in the parametric machine however is unlike that developed by the Motor-Generator. The Motor-Generator is a Constant Magnetism machine and the energy transferred is strictly a function of shaft rotation. The regulation here between mechanical and electrical forms is definitely established by the Law of Energy Continuity.

The parametric E.M.F. is developed by a variation of Magnetism, it is not constant, but pulsates with respect to time. In this situation the machine operates in the constant Current condition and the Energy transferred is a function of Inductance variation via shaft rotation, but not shaft rotation directly. This complicates the Law of Energy Continuity.

(3) In the Synchronous Machine irregularities in pole facings and winding distributions give rise to a pulsation upon the normally constant Magnetism. This constancy is a characteristic of operation as a Motor-Generator. The E.M.F. of rotation and the E.M.F. of variation combines with it to give an effective total E.M.F. at the machine terminals.

Steinmetz suggests no apparatus for developing an E.M.F. by parametric means in his A.C. books, however the Alexanderson Alternator was under development at the time of writing of the Fifth Edition, 1916. In general these parametric variations in rotating machinery are hereby considered parasitic phenomena, just as with Saturation and Hysteresis in magnetic material. These effects are to be minimized not optimized. It is however in this series of writings that the optimization of parametric E.M.F. generation is sought, and its application to the Law of Energy Continuity studied.

(4) In the next chapter, “Distortion of Waveshape and Its Causes”, Steinmetz further develops the analysis of Synchronous Parameter Variation. The material presented in this chapter is minimal. Dimensional in-congruities, irrational units, ambiguous equations, and typo errors render the understanding of this chapter difficult. Also, again Saturation and Hysteresis become merged into a common phenomena, this blurring the true relations between Amplitude and Phase distortions.

In “Distortion of Waveshape and Its Causes” Steinmetz also gives an analysis of the synchronous parameter variation of Resistance, such as in Arc Lighting Systems. Here the remarkable condition exists that a form of reactive power is produced, however with no phase displacement. It is noted by Steinmetz that, where it is Inductance variation gives rise to an effective Resistance of Energy transfer, here the Resistance variation gives rise to an effective Reactance of Energy storage. This reactance is synthetic, no Field of Induction, nor relative mechanical activity, is present to facilitate any reactive power. This synthetic reactance is a result of the particular cause and effect relations in the variant resistance. Again the Law of Energy Continuity is in question. Here the Law of Energy Perpetuity may even be invalidated. This is an important study.

(5) The chapter 25 from “Theory and Calculation of Alternating Current Phenomena” Fifth Edition, 1916, is here re-developed in the following, concentrating of a general equation for the synchronous parameter variation of Inductance and the E.M.F. developed thereby. Symbol standardization, and rationalizing by removal of pi and root two, will be applied to the expressions of Steinmetz.

The parameter variation in this chapter is of the synchronous type. Here the Inductance of a reactance coil with an applied A.C. current is brought into synchronous variation at a harmonic rate in proportion to that of the applied A.C. current. Two E.M.F.'s are developed, that of the reactance opposing the variation of Current, and that of Inductance variation. The E.M.F. of constant Inductance and Current variation is compounded with the E.M.F. of constant Current and Inductance variation. Steinmetz fails to separated these two E.M.F's. Here exists a modulation process, the Inductance variation modulating the reactance current variation. Complex E.M.F.'s result consisting of multiple frequencies and with distorted waveforms.

In chapter 25, expressions are given for the E.M.F. of rotating parameter variation, as in the Synchronous Machine, and the E.M.F. of stationary parameter variation, as in the magnetic material of the static reactance coil. The two are of basically the same mathematical form thus distinction is not a necessity in the development of a General Equation of synchronous parameter variation.

Chapter 25, article 234 begins the analysis, “Lack of Uniformity and Pulsations of the Magnetic Field.” This serves as the basis for the derived General Equation. The sine wave of Magnetism is given by,

Where,

And

Here the Time Angle is the independent variable, this is defined by,

And

Where,

F, frequency in cycles/sec,

and

t, Time variable, seconds.

This time angle is a dimensionless position variable on the A.C. cycle of revolution. Substituting the cyclic period,

Gives the Time Angle as the ratio of the time along the cycle to the time of a complete cycle, that is,

Or in rational form, in radian,

Where,

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#87
08-08-2012, 11:41 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Twelve. (2 of 4)

(6) Let the instantaneous value of Magnetism be given by the relation,

Where,

Substituting the following relation for Magnetic Induction,

Into the general expression segregates the two subjects of parameter variation, that of the Current, i, and that of the Inductance, L. The sine wave of current is given by,

And the pulsating wave of Inductance is given by,

Here in the Inductance the sine wave of variation is offset, and for a modulation depth of one (100%) the sine wave is a pulsating wave in variation with peaks at zero and twice the value of static Inductance. This is expressed as

Where

Is the sine wave of Inductance variation. For a modulation depth of zero the cosine term vanishes and the constant term of static Inductance, L, remains,

Segregating variations the General Equations for Magnetic synchronous parameter variation becomes,

(7) For the condition of Saturation and Hysteresis as exists in magnetic materials the process of saturation is the same for positive and negative half cycles, it is symmetrical. The reduction of Inductance due to saturation in the positive half is the same reduction of Inductance due to the saturation in the negative half. Hence the reduction, or modulation, of Inductance is at Twice the frequency of the A.C. cycle of Magnetism, that is, the Inductance pulsates at Double Frequency. In this situation it is,

n = 2 , numeric,

Where, n, is the harmonic number.
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#88
08-08-2012, 11:42 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Twelve. (3 of 4)

Two factors exist in the characteristics of magnetic material, Hysteresis gives rise to a phase angle, , the angle of hysteresis, and Saturation gives rise to a modulation factor, , the depth of modulation. Hence the sine wave of Inductance variation is expressed by the term,

This for Magnetic material.

(8) The E.M.F. developed by the instantaneous Magnetic Induction, , is the time rate of its variation,

The time rate of variation is expressed as,

Steinmetz substitutes the expression for angular rate of variation,

Where,

And

This angular differential is here given symbolically,

And it is dimensionless. Here gamma represents an infinitesimal Versor Operator, this of an infinite number of divisions, symbolically,

Here the angular frequency, , has become a tensor magnitude, or a Tensor Frequency. The angular rate of variation is thus symbolically expressed by,

Substituting into the relation for E.M.F. gives,

And differentiating, gives the developed E.M.F. of synchronous parameter variation of Inductance as,

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#89
08-08-2012, 11:42 PM
 t-rex Senior Member Join Date: Aug 2011 Location: In the bushes Posts: 422
Law of Electro-Magnetic Induction, Twelve. (4 of 4)

Where it is,

A1 being the Lower Sideband Amplitude, and

A2 being the Upper Sideband Amplitude. Also,

The Lower Sideband Time Angle,

The Upper Sideband Time Angle.

Note here that

Dimensionally establishes the volt.

Hence a pair of new Frequencies are generated by the synchronous parameter variation of Inductance, these given by the relations,

Lower Sideband Frequency,

Upper Sideband Frequency,

Where, , is the “Carrier Frequency”, of current variation via the A.C. cycle of the external current source.

Hence three alternating electric waves exist in the process of synchronous parameter variation, the values are given in Table 1,

Two particular harmonic modulating frequencies are of interest, the second harmonic and the fourth harmonic. For the condition of second harmonic modulation the frequency of the Lower Sideband is equal to the carrier frequency, these two combine in a resultant wave at the carrier frequency. The Upper Sideband is the third harmonic of the carrier frequency and super-imposed upon it creates a regular harmonic waveform. For the condition of fourth harmonic modulation the Lower Sideband gives the Third Harmonic of the carrier wave and the Upper Sideband gives the Fifth Harmonic of the carrier frequency. The odd order series, one, three, five exists here and again super-impose upon each other producing a regular harmonic waveform. All other harmonic modulating frequencies, three, five, etc, give rise to an irregular sequence and thus produce irregular harmonic waveforms. The depth of modulation as well as the Angle of Hysteresis both have a considerable effect on the resulting waveshape. This can give rise to very complex waveforms. It is to be noted that for large depth of modulation, and high orders of modulating harmonics, that the resulting E.M.F. can greatly exceed the E.M.F. of the reactance coil in reaction to the carrier frequency of the external A.C. current source. These processes are worthy of Experimental Research.

(9) Steinmetz does not develop this subject much further. The equations for parameter variation in stationary reactance coils, article 236, are dimensionally invalid,

A weber is not an ohm-second per radian, it is rightly given as

The equations for harmonic summation are not clear and something seems not right. No in depth analysis exists of Resistance parameter variation on a theoretical level, everything is reduced to effective values. E.M.F. is not equated to a co-responding current in many cases making the study of Power Flow difficult in the case of Inductance parameter variation. It is noteworthy in this chapter that Steinmetz gives experimental verification of his parameter variation expressions. It is this feature of Steinmetz's work that makes it of value.

(10) Herewith closes this series of writings, “The Law of Electro-Magnetic Induction”. Three principle conditions for the development of electro-motive force have been presented,

Constant Magnetism,

Constant Current,

Constant Inductance.

While the condition of Constant Magnetism, the Motor-Generator, and the condition of Constant Inductance, the Reactance Coil, are well known engineering realities, it is the special condition of Constant Current that awaits further analysis and experimentation. In this particular condition of E.M.F. development the Law of Energy Continuity may be in need of re-definition. Here the Law of Energy Perpetuity, the holy dictum of modernistic physics, may possibly be invalidated.

73 DE N6KPH SK.....
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#90
08-10-2012, 03:31 PM
 Nhopa Senior Member Join Date: Nov 2011 Posts: 134
Extra coil testing

dR-Green:
I did not make a new "strong" extra coil yet, but took off the 124 turns of wire from the existing frame and put on new winding of 63 1/4 turns of #24 AWG wire. I did 5 runs with 5 pF, 10 pF, 20 pF, 30 pF and 50 pF with can positioned at 1.5 cm and 40 cm from the end of coil. No graphs, but here are the numbers:

can at 1.5 cm can at 40 cm

5 pF 1,721.1 Kc 1,849.5 Kc

10 pF 1,676.1 Kc 1,847.8 Kc

20 pF 1,637.0 Kc 1,815.0 Kc

30 pF 1,593.3 Kc 1,803.5 Kc

50 pF 1,524.4 Kc 1,787.3 Kc

I noticed during testing that the meter readings had a "bump" at lower frequencies, but it was small, that is the meter reading hardly dropped at those points. I did not make note of them, but if they turn out to be important I can easily go back and take note of them. At this point may be I should continue testing the secondary with this "temporary" extra coil before I make a new one with #13 wire. Comments, suggestions from Eric or any other experimenters?
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