I'm trying to understand the secondary coil design. It sounds like Nhopa is saying that Tesla's colorado springs notes describe a long thin secondary, yet Eric's notes in intro to tesla coils describe the secondary as a spiral or short fat coil. Anyone want to weigh in on which is correct? The picture on the front of Eric's intro to tesla coils looks like a long thin coil, so I'm confused on what is correct.

The Colorado Springs coil (the one in most pictures) secondary is 15 metres diameter and about 2m high. Or short and fat.

A flat spiral coil is another coil altogether. In context it means you can either build one or the other.

May I recommend going to the source of the information rather than interpreting interpretations

[edit] I suppose the simple answer to your original question if you don't want to have to make an extra coil is to make a flat spiral coil instead.

WOW!

That mega post by Mr. Dollard answered quite a few complex and downright perplexing issues that I was trying to resolve when doing the math on impulse discharges (of L or C or both one into the other)! Also the concept of the battery as having characteristics of both a capacitor and inductor rings true with me, I have been trying to resolve how to analyze the storage battery (in the electrical sense, or non-chemical sense) for quite some time and came to similar but not quite as refined results. I think one word would sum up my opinion of what was recently posted, Hallelujah! I feel as if that post filled in a fair bit of what I was unsure about in my post "Question On Plank, Q with Respect to an Impulse Discharge of L or C into r".

Furthermore, we now have new insight into the whole negative resistance / negative conductance situation, I personally HATE the term NEGATIVE RESISTANCE -r (generally this is actually a non-linear/non-ohmic resistance and has nothing to do with excess energy), negative ohms is acceptable by my standards though. With whats presented by Mr. Dollard we at least can now call negative ohms & siemens, Receptance H & Acceptance S, something that makes me very happy indeed. This should elucidate, if the concept is fully understood and used properly, interesting phenomena in an electrical circuit whereby there is an excess of energy (or the "load" acts as a "source").

Finally we see some use of a versor operator and its application and (inferred) theory of its use mathematically in electrical situations! I think there's a lot yet to be said or done with this mathematical tool. Hopefully we will get another post with its usage soon from Mr. Dollard.

In conclusion I feel everyone should read that post a few times over, it has some gold nuggets that are sure to give new insight and potential use in future "practical" real life situations.

Garrett M

Thank you dR-Green for the help with my questions. I guess no.:2, the "well as a ground" still needs to be resolved. It seems to me from the foregoing discussions, that the best answers to questions is experimenting. After all Tesla's Colorado Springs Notes are about experimenting. Tesla did'n have all the answers but deducted many from the various experiments. I also apologize for my mistake about the diameter to lenght ratios of the secondery coil. Most of the "extra" coils have a D to L ratio of larger than 1. For example from the Notes on p.110: 2' dia to 6' lg, p.160: 6' dia to 12' lg. However the cage type "extra" coil shown on a few pages in the Notes are indeed close to the 1:1 ratio.
I agree for first hand information one must be going to the source. In our case the real McCoys are the Colorado Spring Notes and Eric Dollard's publications on the subject.
@skaght: Things can be confusing and that is the reason why I have lots of questions. I would recommend obtaining a copy of the Notes as an onhand reference together with Eric's various publications on the subject.

In Eric's notes, intro to tesla coils, he states that for plasma work you need an "image coil" between the secondary and ground to provide 180 degree phase shift. I would prefer not to build two tesla coils as he seems to suggest later on for plasma work, since I'm not positive of all the design parameters. Would a simple coil with 1/2 wavelength resonance work as an image coil? Or does "image coil" literally mean that the coil is a "mirror image" of the secondary and extra coil? I've been searching for a definition of an image coil and I'm not finding much.

Does anyone know the definition of the term "image coil"?

Thanks!

Hi,
He mentioned AFC - automatic frequency and phase control.Probably need to keep resonance all the time or need to check phase between 2 coils, even load changed. to do that he have 2 same secondary coils. He is measuring phase of 2 secondary coils and based on that is controlling a voltage controled oscillator - VCO.VCO is generating a main fequency and as well a synchronization pulses for pulse modulation of main frequency.Phase discriminator is checking a difference in phase and frequency of 2 signals.It is used in nearly all RF receivers.

On Page 13 of that book is :

"To confine the energy an image coil
(180 degree shift) must be connected to the earth terminal. Making this
arrangement in a horseshoe configuration produces intense dielectric
flux and displacement current that is quite usefull for plasma work."

The electrical length is 360 degrees at the fundamental of oscillation.
I think that image coil is to keep total electrical lenght in 360 degree. then need to control a phase of that 2 coils to get strongest effect.

Foreword:

I thought I would share what I understand about the DC & AC versor operators of Mr. Dollard and while I can’t speak for Mr. Dollard or say that I am 100% right, this post is intended to assist anyone who would like a “beginner’s guide” on the subject (sadly this is all I am capable of at the moment). I feel that Mr. Dollard takes for granted, his understanding of exponentiation and use of versors in relation to degrees of rotation, much like breathing or walking most people don’t even have to think to do these things. Thus this is written for your “common man”, who like myself (I’m a high school dropout), were never given a good education and lack the fundamentals of more advanced math principles. This is by no means a formal study, but instead, can be looked at as a primer on the subject, at least until a better treatment by Mr. Dollard is available.

If you already have a good grasp of the Dollard type versos then this whole post can be skipped over.

Roots & Powers; Exponentiation Cliff Notes:

To fully understand the machinery of a versor operator of the type used by Mr. Dollard, one must first understand the subject of “exponentiation” (also known less formally as roots and powers of a number) or at least have available a basic reference sheet of what each degree of power or root does.

So as not to be confused with the versor operators used latter on, we will use the letter b as our variable and n as our root or power. This exercise requires only basic high school algebra, and will be found to give good insight into the workings of a versor operator.


Here we have b, or some “arbitrary number”, to the nth power, n being another “arbitrary number”. Where b & n are assumed to be whole real numbers and where b is not equal to zero.

Depending upon what “arbitrary number” n represents, changes a whole host of things with how b is treated. Shown below are some simple common numbers that n could represent, and from understanding these seven different powers of b we can start to gain some insight into versors and also what to do when confronted by these in other mathematical situations.


Here we have a few arbitrary values of n, some of which may seem familiar and others very foreign.

Let’s start off with the case of b^1

Here it is understood algebraically that any number raised to the exponent 1 is simply the same number. (In the case of Mr. Dollard’s DC Versor, h=-1 and AC versor k=+j)

Next, we have the case of b^0

Here it is understood algebraically that any nonzero number raised to the exponent 0 will ALWAYS equal POSITIVE UNITY +1. As was shown above for b^1, and referenced with b^0, any number (aside from zero) be it negative or positive divided into itself will always be a positive one.

Moving on to b^(1/2) and b^(1/n)

Here it is understood algebraically that any number raised to the exponent (1/n) represents the root of that number, where n=2 is the “square root”, n=3 the “cube root”, n=4 the forth root etc. This relation b^(1/n) has use with both the DC & AC versor operators, h & k, which will be discussed further on.

Continuing to b^-1

Here it is understood algebraically that any number raised to the exponent -1 is simply the reciprocal of the number itself.

Taking this concept further b^-(1/2) and b^-(1/n)

Here it is understood algebraically that any number raised to the exponent –(1/n) is simply the reciprocal of the root of that number.

It can be seen that these less common “powers” of b can save quite a bit of space when writing an equation and are generally used in calculus for this very reason. Also it can be seen that when using “fractional” powers (1/n) instead of roots (numbers inside a radical), you gain a greater understanding of what is going on mathematically and are less likely to be confused when in unfamiliar circumstances, i.e. fractional powers are roots and negative powers are reciprocals. The cases of b^n where n>2 or b^-n where b<-2 and where b is not equal 0, are very simple cases, which I don’t think need even the slightest explanation, as they are the most commonly understood form of powers (at least for positive powers equal to or greater than 2 this is the case). This topic could be taken much further but I don’t feel there is anything to gain with respect to understanding of the versor operators used by Mr. Dollard in doing so. The most vaguely understood cases of n have been shown and given proper, albeit very simple, explanations with some minor references to the DC & AC versor operators h & k for use further on in this post.

The Roots of Unity; Negative & Imaginary Numbers Cliff Notes:

It turns out the subject “roots of unity” has a lot to do with a Dollard type versor operator and a whole host of other branches of science. With what we just covered on exponentiation we can now briefly cover this primer before finally getting to the versors.


In a nut shell, any number that equals 1 when raised to some power of n is a so called “root of unity”.

When we go to solve for b we get

Here things start to get interesting with regards to Mr. Dollard’s work and his versors.

For the purpose of this post, we will limit the values of n, in the above, to only 2 & 4, as these have the most relevance to the Dollard DC & AC versors.

In the case of n=2 we have

Here we are confronted with the “square root” of unity. From this problem, we get two possible solutions or roots, b=1 & b=-1.

As we all blink our eyes and breathe without giving a second thought, we also take for granted the concept of negative numbers. If we represent positive numbers extending to the right of zero, we can represent negative numbers extending to the left all of which is along a single axis where the angle of measure between both sides is always 180°, as shown below.



The above expression and diagram give some general insight into the DC versor h. The base value of h in the case of Mr. Dollard’s DC versor is always -1, h^1=h=-1. In this special case h^-1, h, h^1, … etc. (all odd non-fractional powers of h^n where n=1+x2) equal -1, or 180° rotation (from +1) and for h^-2, h^0, h^2, … etc. (all even non-fractional powers of h^n where n=0+x2) equal +1 or 0° rotation (from +1).

In the case of n=4 we have

Here we are confronted with the “fourth root” of unity. From this problem, we get four possible solutions or roots, b=+1, b=-1, b=+j=(sqrt-1) & b=-j=-(sqrt-1).

It turns out that a mathematician named Gauss extended the concept of the real axis by placing j or (sqrt-1) as halfway between +1 and -1, having an angle of 90° from the line -1 and +1. If the division of unity into plus and minus is 180°, a second division leads to an axis which intersects this line at an angle of 90°. We now have two axes, the horizontal representing positive and negative real numbers, and the vertical representing positive and negative imaginary numbers. These two axes form the complex coordinate system, any number inside this plane, is a number having a real and an imaginary part.



The above expression and diagram give some general insight into the AC versor k. The base value of k in the case of Mr. Dollards AC versor is always +j, k^1=k=+j, also the diagram above would need to be turned 90° to the left so that the positive real axis is on top. In this special case, k, k^1, k^5, … etc. (all odd non-fractional powers of k^n where n= 1+x4) equal +j, or 90°, rotation (from +1), for k^0, k^4, k^8 … etc. (all even non-fractional powers of k^n where n= 0+x4) equal +1 or 0° rotation (from +1), for k^2, k^6, k^10… etc. (all even non-fractional powers of k^n where n= 2+x4) equal -1 or 180° rotation (from +1), for k^3, k^7, k^11… etc. (all odd non-fractional powers of k^n where n= 3+x4) equal -j or 90° rotation (from +1). Note that negative values for exponents are not shown, but would follow the same pattern, if I’m not mistaken, as for the positive values as they are only reciprocals, i.e. 1/j=j & 1/-1=-1.

Continued in Part 2

Continuing with Part 2

Versor Operators; Rotation about an Axis:

With the above cliff notes on exponentiation and roots of unity we can now perform a more advanced and elucidated study of a Dollard type versor operator, but first, we should cover a few basic concepts of what a versor is and historically where it came from.

For this purpose, one needs go no further than a quick study of William Rowan Hamilton, the discoverer of quaternions. Hamilton during the year 1843, discovered a new mathematical entity which he called a quaternion and from which formed a new branch of mathematical thought that extended the complex numbers, with new imaginary axes “j” & “k” (“i” is the familiar imaginary axis from high school). This expanded the usual Argand diagram with two new axes that have a 90° separation to the Re and Im axes while also having a 90° separation between themselves, j & k. New terms were spawned from the mind of Hamilton to describe the unique concepts and entities contained in this seemingly odd branch of mathematics. Notably the most important, for our discussion, are “scalar”, “tensor” “vector” & “versor”. Without going too deep into this topic, we will only cover the versor and a few of its associated relations.

Hamilton’s Versor

In Hamilton’s branch of math, each Quaternion has a Tensor, which is a measure of its magnitude; this being similar to the length of a Vector is a measure of a Vectors' magnitude. The Versor is a Quaternion having a Tensor of 1, Tensors by Hamilton’s definition are “signless numbers” or more simply a positive number. The term Versor was derived by Hamilton from the Latin vertere, "to turn".

In general a Versor can be associated with a plane, an axis and an angle. When a versor and a vector which lies in the plane of the versor are multiplied, the result is a new vector of the same length but turned by the angle of the versor. When the arc of a versor has the magnitude of a right angle (π/2), it is then called a Right Versor. Right Versors have a zero Scalar part, and thus, are Vectors of length one, or Unit Vectors.

Outside the context of quaternion theory, in normal algebra and geometry, the term Versor is often used for a Right Versor. In this case, a Versor is defined as a Unit Vector indicating the orientation of a directed axis in a Cartesian coordinate system.

Dollard type Versors

It can be seen that the Dollard DC & AC versors share many commonalties with Hamilton’s Quaternion Versor, but despite this, they generally have little to no relation to one another. The Dollard versors, from what I understand, are used to indicate the orientation of (or rotate) a vector magnitude’s position in a Cartesian coordinate system, and possibly polar or spherical coordinate systems as well. These versors form what could be called a Unit Vector, where the vector magnitude is always equal to unity.

In the case of both the DC & AC versors, their associated Unit Vector always equals a magnitude of one, also, the possible “directions” of travel are associated with the number of axes present. This is where we get the accompanying roots of the Unit Vector. The number of possible directions become the exponent n of the unit vector and the corresponding roots derived, are from the number of potential positions, these derived roots represent the angle of rotation.

The DC Versor h, 180° Rotation (or Mirror Image Operator)

Thus, if there are only two possible directions on the real axis, as seen from the origin (+1 & -1), such as in the DC circuit (consumption and production of active power) we have:

With the real axis as the only number system used, we have only two directions of travel, thus the versor operator h has only two possible positions with corresponding values +1 & -1. Despite any arbitrary power of h (-1), there is a periodicity or repeating nature of the values for h, which can be seen as a cycling through or rotation of the positions that h can have. For simplicity, only h^1 (or h) & h^0 are needed to describe -1, 180° rotation (from +1) & +1, 0° rotation (from +1). The pattern of periodicity for h was discussed earlier under the topic “roots of unity”.

The AC Versor k, 90° Rotation (or Quadrant Operator)

Note: When dealing with Mr Dollard's AC versor k, the usual Argand diagram would need to be turned 90° to the left so that the positive real axis is on top. Everything I have written in this post, related to versor k, is in direct reference to this subtle change of perspective! i.e. the horizontal or "x" axis is now the imaginary axis and the corresponding vertical or "y" axis is now the real axis.

Similarly, if there are four possible directions along the real & imaginary axes, as seen from the origin (+1, -1, +j & -j), such as in the AC circuit (production of active & reactive power and consumption of active & reactive power) we have:

With the real & imaginary axes, as the number systems used, we have four directions of travel, thus the versor operator k has four possible positions with corresponding values +1, -1, +j & -j. Despite any arbitrary power of k (+j), there is a periodicity or repeating nature of the values for k, which can be seen as a cycling through or rotation of the positions that k can have. For simplicity, only k^1, k^0, k^2 & k^3 are needed to describe +j, 90° rotation (from +1), +1, 0° rotation (from +1), -1, 180° rotation (from +1) and –j, 90° rotation (from +1). The pattern of periodicity for k was discussed earlier under the topic “roots of unity”.

Something of great interest to this concept, is the fact that if an arbitrary vector is multiplied by k^1, the rotation is always equal to one -90° (or +270°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^1, it would be rotated -90°, or now positioned at (j,-1). When a vector is multiplied by k^0, the rotation always equals 0°, or no rotation (even if it were 360°, there was no apparent change of position), where a vector of (j,1) is multiplied by k^0, it would still be positioned at (j,1). When a vector is multiplied by k^2, the rotation is always equal to one +180° (or -180°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^2, it would now be positioned at (-j,-1). When a vector is multiplied by k^3, the rotation is always equal to one -270° (or +90°) rotation (relative to where it was), where a vector of (j,1) is multiplied by k^3, it would now be positioned at (-j,1).

Note: The coordinates used for the above arbitrary vectors, is in the standard format where (x,y) denotes the exact position on the grid, and where the length or MAGNITUDE of the vector is determined as the distance from the origin (0,0) to that point.

The notion of whether the RESULTANT rotation, by k^n, is NEGATIVE (-) or POSITIVE (+), has strictly to do with the "NORMAL" direction of rotation of the arbitrary vector. In the special case of vectors E & I, the INDUCTIONS of the Magnetic & Dielectric fields, we find that they counter rotate, and thus form a pair of counter rotating vectors, having a double frequency PRODUCT (EI=P) called Power. E is said to rotate Clock-Wise (CW) and I is said to rotate Counter-Clock-Wise (CCW) with this distinction made, a rotation by versor k can now be found to have produced a forward (leading) or backward (lagging) effect on the vector's arbitrary position, with respect to its normal direction of rotation.

I hope this helps anyone who was a bit unsure as to what Mr. Dollard’s versors were all about, granted there is quite a lot of regurgitation of various other concepts I feel that they were necessary to cover before a good grasp of the versor (as a unit vector) concept could be had.

Continued in Part 3, The subtopic of "AC Power" is discussed in minor detail, which shows the relevant "cause & effect" brought about by a rotation by versor k.

Garrett M

Could this be what tesla had in mind?


the earth as a spherical capacitor inside the air as an outer spherical capacitor with the coils connecting the whole thing as a gigantic resonant tank?

What is the big deal? Eric Dollard has done this demonstration almost 30 yars-ago, and the first time before anyone else.

@garretm4:
For some simple feedback on your extensive efforts on Vensor Operator decoding of AC & DC circuits, yes I have found it useful in helping to better understand some of Mr Dollard’s maths. Unfortunately I do not quite grasp all of the advanced maths principles, so yes, it does help. Thank you.

@KokomojO
As for the LMD experiment tests first done by Mr Dollard, and reproduced by Naudin: I am unsure about the power output shown by Naudin.
Having said that, I would suggest you just give it a go yourself, even just for experiment sake!

I have played around with these of recent times and also going back a few years ago too. My setup at the moment consists of 300watt audio amp, fed by an audio generator. Two inductors of 4mH and of about 7ohms each. Wound on 3.5 inch PVC pipe in the conventional way with 0.5mm wire. – (Eric would not approve). Two caps of 0.005uF at 10,000 Volts, oil filled, (oil caps seem to work the best but are $$). (I will soon complete two more coils and two more caps). This setup resonates at around 50kcps. Basically, I think it ends up as being (two) single wire transmissions. Each output will easily light two large fluro tubes. If they are kept open circuit the fluro’s radiate well. Bringing another fluro, (just holding it) near, it also lights up.
Using a single fluro’s on each end (output) one can feel tingles through the glass of the fluro tube. If a single fluro tube is put right across the output (closed circuit) one can feel a charge coming off of the fluro and if I’m not dreaming one can also feel a delicate pressure given off too. (?) It feels “nice”. Rectifying the output to DC and then charging caps is another area of interest. (I’ll say no more at this time).
Basically many of the effects from normally seen with a Tesla coil can be seen with this setup. - Mostly when the system runs in open circuit mode. The amplifier sees a resonant series circuit as a short circuit, so the ohms of resistance of the coils is the only impedance the amp works with, so the ohms are about 3.5ohms, but the amp transistors still get hot! As for power in and out, I have not measured as I don’t have high frequency meters at the moment so I have not measured. Voltage is high! However I have only just observed the “effects” only. - Give it ago yourself.

Continuing with Part 3

Note: While this portion of my post is not paramount for the understanding of the AC versor k, I do feel the subject of AC Power is quite mysterious for most people and thought I would attempt to shed some light on the matter.

AC Power; Complex, Absolute, Real & Imaginary:

Whether the current I or voltage E of the AC circuit is leading or lagging, by any arbitrary value (in degrees or radians), the resultant QUADRANT in which the vector of Power is located changes as a direct result. There exist four quadrants in the Cartesian coordinate system, which form the complex plane as seen on an Argand diagram, each quadrant can be thought to represent a specific condition or state of the electric circuit. These specific states are CONSTANT for ANY circuit whose PARAMETERS (L, C, M, K, g & r) DO NOT CHANGE in TIME. If the load of an AC motor increases or decreases a change in the MAGNETUDE of transferred magnetic energy from L1 to L2 via M causes a STATE CHANGE, thus a corresponding change in the POSITION of the Power vector. For the very SPECIAL condition of of a storage parameter (L or C) whose value changes PERIODICALLY in time, we will find that the Power vector will have two or more PERIODIC positions in TIME. Determined by the state of affairs present, this special condition has the possibility to REMOVE energy from the circuit (with out associated loss as heat) while also having the possibility of INTRODUCING energy into the circuit (from the fields of induction OUTSIDE the guiding wires).

As is shown in Mr. Dollards (excellent) book Symbolic Representation of Alternating Electric Waves (Pages 28-29)

The Real & Imaginary, two Axes having Four Directions:
(+1) 0, Consumption of Active Energy
(+j) 1, Consumption of Reactive Energy
(-1) 2, Production of Active Energy
(-j) 3, Production of Reactive Energy

If the vector of Power is found to be on one of the axes, it is seen to have a 100% condition of any one state, dependent upon its direction. i.e. 100% consumption of active energy or 100% production of active energy.

If the vector of Power is found to lie outside the vertical and horizontal axes, such as between axes (which is the usual case), it will be found inside only one of four quadrants.

The Corresponding Quadrants:
(+j,+1) I Consumption of Active & Consumption of Reactive Energy
(+j,-1) II Production of Active & Consumption of Reactive Energy
(-j,-1) III Production of Active & Production of Reactive Energy
(-j,+1) IV Consumption of Active & Production of Reactive Energy

The exact placement of the Power vector inside any one quadrant will yield any arbitrary GRADIENT of the above listed states. This causes the complex problems associated with MEASURING the MAGNITUDE of the Power vector. This is because we have EIGHT possible conditions in which the state of "Power" can be in (four single states, on an axis & four dual states, between axes), thus no single measurement will suffice in giving the total measurement of Power.

Hence the four Measurements of AC Power:
1 Apparent Power..(Watt Meter + VAR Meter)..(Complex, Real + Imaginary Axes Value)
2 Vector Power.....(Volt Meter * Amp Meter)...(Absolute, sqrt(Real^2 + Imaginary^2) Axes Value)
3 Active Power.....(Watt Meter)....................(Real Axis Value)
4 Reactive Power..(VAR Meter).....................(Imaginary Axis Value)

The length or MAGNITUDE of the Power vector is determined by the distance from the origin (0,0) to its location (x,y), this length is what we "MEASURE" when using our watt, var, volt & amp meters. In the case of Apparent Power we add the length of the active power (0,0) to (0,y) to that of the reactive power (0,0) to (x,0), this forms a complex number which cannot be found with only one measurement. This geometrically analyzed, would be seen as a corner of a square or rectangle. For the measurement of Vector Power we take the actual length of the Power vector, or its distance from (0,0) to (x,y). Geometrically this forms the hypotenuse of a right triangle, whereby the length can be solved with use of the Pythagorean Theorem, or a^2+b^2=c^2. Hence the associated (Vector Power)=sqrt((real axis length)^2 + (imaginary axis length)^2) formula. Finally for both the Reactive & Active Power, the measure of the vectors length or magnitude is simply from the origin (0,0) to the associated location along the real (0,y) or imaginary (x,0) axes.

The material written above, should assist in the understanding of the affects a rotation by versor k can have on the double frequency Power vector, or its source vectors E & I. While only generalities are used, they do serve to guide you to the right solution when doing calculations and measurements of a specific circuit arrangement.

Note: If any errors or unintelligible sections are found, send me a PM and I will correct them ASAP.

Garrett M

Notes on the Crystal Set

When measuring the velocity difference between underground and our ground, the two seperate receivers can be brought into phase unison by the use of a test oscillator. Both receivers must have a primary tank circuit, here you can place your measurement equipment.

The detected AM output, audio frequency, signal is immune to receiver phase shift. This is a property of A.M. detection. Use the audio to measure propagation delay.

Wind all coils in the same direction, this is a must! Brass is a very good primary material, good depth of penetration at broadcast frequencies. Wires and clip lead interconnection are the "Road to Absolute Defeat." Coils and Condensers must be merged into each other in broad surfaces. Stacked metal plates on insulators makes good condensers. Transmitter air condensers are good, vacuum condensers are the best. A number of small condensers are better than one big one, less stray inductance. Stray inductance is fatal to success! For smaller units silver mica condensers are the only way, use no others. Paralell them on a low inductance bus.

Do not get sidetracked, experimental and auxilliary coils as well as patent diagrams will get you stuck in the sand forever. The finished Colorado unit dimensions are all in the notebook. It is all there, look at it, not the diversions, and remember everything you thought was Tesla is the exact opposite. It is there; one or two turn primary; a 20% height/width secondary; and a 100% height/width extra coil, all there, wire size, turns, all there, can you find it? It then can be scaled to any frequency and any KVAR capacity within wavelength conditions.

As your unit gets perfected the signal gets stronger and stronger, then diodes start burning out. We then are reaching the engineering objective, that is to light a number 327 pilot lamp. Not much power but too bright for Einstein.

Thank you! I've been trying to resolve the inductance, capacitance and resonance of a coil and it's dimensions to the wavelength. I have not till now read thru the springs notes. Tesla's notes are quite clear on the relations and how it's derived. First time I've seen the relationship explained.

Thank you Eric,

599 - Loud and clear on the engineering details & tips provided!


Colorado unit dimensions:
(Taken from C.S. Notes* & Leland Anderson’s publication).

Primary coil: 51’ diameter Two turns – (further details to follow)**
Secondary coil: 51’ diameter 9’ high, 29 turns, heavy cable.
Extra coil: 8’3’’ diameter, 8’ in length, 100 turns No.6 wire.

*C.S.N. (page numbers to edit in here later).
**More reading required for correct answer on this, (Feel free to help and add an answer you E.F. mob)!

My Radio “receiver” is under consideration, parts acquisition & construction..

The design of the Tesla Transformer starts with the secondary resonant coil. In its resonant mode it is a quadrapolar resonator. Two constants exist in the construction of this solenoidal resonator, one is that the height to length ratio must be 20%, the other is that the side by side spacing of the cylindrical conductor turns is 62% the diameter of the cylindrical conductor. The optimum number of turns is 20 on the secondary, with 2 on the primary. This gives the physical size of the coil for a given frequency. Increasing the number of turns reduces the size of the secondary coil in proportion to the increase in turns. Accordingly the conductor diameter also decreases as the copper is spread out over more windings. The ratio of secondary turns to primary turns must equal a constraint of 10 to 1. For a given number of turns the operating frequency becomes the sole independent variable in coil design.

The primary coil is the same diameter as the secondary coil. The ratio of conductor width to coil diameter is 18%. The sheet conductor is closely spiralled into two turns, for a secondary of twenty turns. For a conductor thickness as given by the maximum thickness vs frequency the volume of the primary metal must equal the volume of the secondary metal, based upon equal weights for primary and secondary metals. Brass can be 1.7 times thicker than copper, and bronze can be 2.8 times thicker than copper, for a given maximum thickness and frequency.

The primary condenser should be made of the same amount of metal as the primary coil. Their weights should be about the same. The connecting leads must be short and the same width as the primary conductor. Large, multiplate air condensers are good, so are metal sheets and glass.

The secondary capacitance is best a copper tubing ring around the outside of the H end of the coil. This ring must be open in one spot along its loop so as not to be a shorted turn. The end of the secondary wire connects to this capacity ring. Beer cans make the best elevated capacitors.

The finished transformer must operate on a directly connected ground plane. A large plywood table with aluminum foil glued on to it, this covered with a plastic or glass sheet is the minimum required ground plane. Obviously the aluminum plane must be solidly earthed with special attention to minimizing ground lead inductance. In order to light a lamp a more broadcast station style of ground plane is required, but for testing purposes the metallized plywood "ten by" sheet is just fine. Good luck and good crystal set DX ing.



73 DE N6KPH

shouldn't the self capacitance and inductance be calculated to insure that the secondary coil does not resonate at a slower frequency from the primary and also to insure that LsCs = LpCp ? and from this then the resonance should be easier to maintain.

Eric, thanks for the additional design information. The initial approach that I have taken with physical construction has centered around copper weight balancing of the coils, but designing around the resonant frequency makes the most sense now doesn't it? It's a bit of a chicken and egg problem, do I start with the materials available or do I start with the number crunching. I started somewhere in between and it's been a pretty fun learning process to iterate as the equations become more clear and the manufacturing skills improve.
Electrical measurements are still an issue to be dealt with.

Maybe a simple c-program to crunch the numbers as a design aid would be useful.

Attached Images

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In order to get the weight you need to start with the frequency, from that it'll determine the wire length and then the weight based on wire gauge or in the case of the primary flat wire strip. capacitance and inductance will also cause a change in the number of turns based on wire gauge. it does seem a bit of push-pull but if one is pinned down then the rest follow.

Eric is right that all the needed calcs are in the notes, I personally have been fascinated by the calculations and how Tesla is utilizing them for design and implementation. I do enjoy his reference to and use of other equations as a secondary check against his calcs.

Too much inductance slows down the natural fq so capacitance needs to annul it, however if self capacitance is too high it will also slow the fq while increase the Q, If it's to small then it doesn't transmit the power and the fq will be to high. it's a balance act of just the right capacitance to annul the mutual inductance of the primary and secondary, hence utilization of the 'extra' coil for capacitance. along with all that resistance needs to be as negligible as possible. A balancing act for sure.

I have thought of a simple program to crunch the numbers as the equations are not that complex. difficulty though is that there are a fair number of variables and one needs to grasp how each impacts the other or the calculations will not work. it's not a simple flow diagram from A~B. still should be possible, I've written complex calcs for thermodynamic flow that had numerous variables.

No promises as I still want to spend more time crunching the numbers and seeing the ratios. Eric has posted a great start that will enable anyone to build an antenna that will work as described, all that's needed is the frequency and L and C calcs.

interesting.....

just from observation I would not expect a 2 turn primary to really couple in the same sense we normally think of a tank?

Again by observation, I get the impression the primary is to transfer a very fast impulse in a very broad band low q arrangement to the secondary by means of a magnetic pulse, not exactly sure how that would relate to the electric field transfer.

So it seems the 2 turn primary would function more so as an exciter and be sort of freq independent to the system because I presume it would have very low q and not really tunable as such.

It seems to me that the goal of the primary is ideally infinitely high current with infinitely short pulse width causing infinitely high spike impulses would best be achieved as Eric is saying with the use of flat strap and vacuum caps etc. The resonance of a 2 turn coil would be several orders above the fundamental of the secondary or the extra coils.

That said it would create a corresponding magnetic flux setting the secondary in motion which I believe is a 180 degree tank giving the joule ringer effect and a tendency to store and build up energy if you will.

Then the extra coil appears to be needed to get that open ended 1/4 wave length which will cause it to transfer with that vacuum cleaner effect that Eric was talking about.

If I understand what is going on here correctly, while everything is important, if the secondary is in fact a 180 degree coil that to me would be the most important coil to have properly tuned to prevent leakage then tune the extra to it.

So at first blush I would consider winding the secondary then put it in parallel with a non reactive load resistor and build 2 little z matched strip line swr meters, one for each coil lead and use those measurements to adjust for a perfect known 180 degrees, and that would also work to match the extra coil.

I have been busy to the extreme with barely enough time to read the posts, so I have not run any math, just what I gather from combining what has been said and my past antenna building experience.

If this turns out to be incorrect I will redact this to keep the thread clean.

Calculated values for a Tesla Transformer Secondary Coil.

Calculated of from Eric’s GIVEN conditions.
(See Tesla Type Crystal Radio formulas above).

My Calculated values are based on an AM receiving frequency of 1395Kcps.

1. Total Length of Coiled Wire lo (for Frequency of 1395kcps)

lo = 34.244 Meters or lo = 3424.4 Centimeters.


2. Total Number of Turns GIVEN 20, Length of Each Turn:

l = 1.7122 Meters or 171.22 Centimeters.


3. Coil Height to Width Ratio GIVEN 20%:

W = 0.5449 Meters or 54.49 Centimeters

H = 0.10898 Meters or 10.898 Centimeters.

4. Side By Side Wire Spacing GIVEN 62% of Wire Diameter for 20 Turns, A Wire Diameter of:

d = 0.03322 Centimeters or d = 3.322 Millimeters.

5. Maximum Conductor Thickness is GIVEN by 10 / sqrt F:

Thickness of Copper = 0.008466 Centimeters or 0.084 Millimeters
Thickness of Brass = 0.1439 Millimeters.
Thickness of Bronze = 0.2370 Millimeters.


(6). Primary Coil Width GIVEN 18% Ratio to Coil Diameter:

Primary Coil Width = 9.808 Centimeters.

Primary Coil Length = Two turns of ~ 171.22 Centimeters
Primary Coil Length = ~ 342.44 Centimeters. Or 3.4244 Meters.

Please correct and or check me if my values are off, please compare them to yours figures.

I am yet to calculate weight of copper contained in primary to weight contained in Secondary, I will try on a per volume calculation next. I will also measure these by weight (per meter) on an accurate balance to help determine this. More later.. Of course for lower frequencies the coil's overall physical size becomes larger.

The important calculation factors here have been GIVEN from Eric, for which I must say thank you! - Too bright for Einstein.

I'm currently only 1/4 of the way thru the Colorado spring notes. while the above posted construction details by Eric are useful there is still the matter of inductance and capacitance to be accounted for. I have also noted that Tesla's Eq for such vary from the current ones today. I would err to Tesla's Equations for such calculations over the commonly available ones on the net as the ones in the notes will derive a period of oscillation for various capacitance and mutual ratios in the circuit.

the period of oscillations need to be in harmony between the primary and secondary to give the best resonance.

As I said I'm only 1/4 the way into the notes, if any of this changes I'll correct my post, however I don't think it will as these points are a common thread in the notes and Tesla is so far only tweaking or tuning the accuracy of the setup, the equations are boiler plate in this regard.

Hi,
I am a noob and recently been trying to replicate this slowly. So far I have a manual by IEEE Steve Jackson which replicates an example based on Prof. Meyl's kit on one-wire transmission.

I heard that Mr. Dollard is not happy with Professor Meyl's way of doing it and find it difficult to reason why. Professor Meyl says the same things as achieving 1.5 times of the speed of light and he mentions the longitudinal waves, I guess his approach uses neutrinos or something to that effect to connect with particle theory.

Why is Mr. Dollard against some of Mr. Meyl's notes? In what areas?

I am really sorry if I have asked a similar question again and look forward to concrete reasons as to why and what ways exist to cope with the uncertainty around research. Like to know what to know from where.

Hi all:
Reading the notes, the name of two items often come up , the "sensitive device" and the "mercury break" or "Thomas clockwork with wheel". The sensitive device looks very similar to a Reed switch, so the question is, can one use the Reed switch, inserted into a coil, in lieu of the sensitive device's glass tube with the two wires?
The question about the break is what kind of mechanical device, if any, can be used instead of the mercury break or the Thomas clockwork? Is there anything commercially available out there? If not, are there plans available to build one of these devices at home?
For use with lower voltages I have seen an electronic "break" circuit that employes a 555 IC timer. It was published in the Borderland Sciences 4th edition of the "The Lakhovsky Multiple Wave Oscillator Handbook", pages 45and 125. This circuit has a variable frequency range between 130-1,300 Cps.
I am currently getting the required components to build this circuit and if it works as advertised then I will publish it on this forum.

Eric what about distributed capacitance on the secondary? the version and I'll call them that because I have no idea how accurate they are of the Colorado notes I have, have a final revision of the 2nd coil @ 15m dia, with 18 turns, 4 lower @ 1" spacing and the remainder of 2.625" for a total height of 42"

Wire length, the eq l=c/w would be for a straight horizontal length. However in a coil the inductance and capacitance would change that as Tesla notes in the use of inductance and distributed capacitance equations to calculate the free resonance of the coil. The frequency of charge impressed into the primary was 1600Hz per the notes and the resonance was based on inductance and capacitance at that fq in the length of the primary, it was then calculated to have the length of the secondary match that resonant wavelength based again on the inductance and capacitance.

I have another question, in previous posts you mention the wavelengths of the primary,2nd and extra as:
Primary: 1/2
Secondary: 3/4
Extra: 1/4

The notes have these relations:
Primary: 1/4 or 1/2 depending on series of both turns
Secondary: Sep 4th 1/4
Extra: Sep 4th 1/16 ; Sep 19th 1/2 per diagram #4

there seems to be an issue with the 'notes', apparently various translations are edited and most likely incorrect. does anyone have any idea as to which one is most accurate and where to procure them?

thanks,

My above posts are based on the notes I have by
ALEKSANDAR MARINCIC, D.Sc.
ASSOCIATE PROFEsSOR OF ELEClltICAL ENGINEERING a£OGRAD UNIVERSITY
SCIENTIFIC ADVISER TO TtlE NlkOLA TESLA MUSeUM

note sure how accurate these are...

I don't understand the quadripolar resonance equations. The only practical value that I can see that would satisfy the equations are when L=C=M=K=1, which seems extremely limiting. I can't see how a tesla coil could satisfy this. It's been a while since I've done my college math courses, so if I'm missing something, please point it out.