Flat Coil Design – Part 1

The flat, spiral, or pancake coil, applied to the transmission of electric energy was presented in a patent by Tesla[1] in 1900, subsequently investigated by Dollard et al.[2], Mackay et al.[3], and no doubt by others. The design, implementation, and measurement of a flat coil is presented in the following sequence of posts. This coil has then been used in a range of experiments including single wire effects, wireless transmission of power, and investigations into the properties of displacement and transference of electric power. These experiments, and there results so far, will be reported in a subsequent sequence of posts.

Tesla’s original design of the coil is shown in Fig. 1. Designing a flat coil empirically from scratch starts with choosing the required fundamental resonant frequency of the secondary coil. For the purposes of the intended experiments large voltage magnification is not required, and hence the flat coil comprises only Tesla’s secondary coil (λ/4) as a continuous spiral. If additional voltage magnification were required then Tesla’s extra coil[4] (λ/2) could also be added at the top-end or central-end of the coil to make a complete tuned coil (3λ/4 or nλ/4 where n is an odd positive integer). The outer turns of the secondary coil are more closely coupled by induction to the primary coil by virtue of their closer proximity to the primary. The secondary coil, (with or without the extra coil), and in combination with the top-load or termination, accumulates energy induced from the primary and forms a resonant cavity at the designed frequency.

The properties of this resonant cavity are critical to the correct formation of the Longitudinal Magneto Dielectric (LMD) wave (standing-wave) in the coil, which may also be conjectured to be a significant pre-condition for the generation of a displacement event. The properties of the resonant cavity thus formed in a coupled free resonator, and their relationship to the displacement of electric power, will be considered in more detail in Part 2, and further at the experimental stage.

It is important to note that experiments that may include the radiation of electromagnetic energy need to comply with international radio regulation and standards, and so the fundamental operating resonant frequency of the secondary coil is to be set in the 160m amateur radio band (UK standard) in the range 1.810 – 2.000 MHz. As per Tesla’s original design, the coil is to be primarily used in a quarter-wave (λ/4) mode where the top-end or central-end of the coil is a high impedance (in this case open-circuit or connected to a top-load), and the bottom-end or outer-end of the coil is connected to a low impedance (ground, load, or other impedance lowering receptacle).

In this mode the fundamental resonant frequency of the secondary coil is firstly determined by the wire length combined with coil geometry, dimensions, and materials, all which lead to an inductive element in parallel with a capacitive element, or in electrical terms a parallel self-resonant circuit. This will set the free self-resonant frequency at which a 180o phase change will occur in the impedance of the coil. In an ideal parallel resonant circuit this would also be the frequency at which the impedance reaches a maximum. In the practical (non-ideal) case the impedance maximum does not correspond to the frequency of phase change, but is rather reduced due to a range of factors, including:

1. The inter-winding mutual capacitance.

2. The internal series resistance of the coil.

3. Additional capacitive and other circuit loading directly to either end of the secondary coil.

4. The geometry, dimensions, materials and proximity of other conductive/insulating mediums.

5. Conducting extensions to the central and/or outer ends of the secondary coil e.g. adding an additional length of wire to either end of the coil, or a conductive ground plane.

6. The resonant frequency of other closely coupled coils e.g. the primary coil.

7. The wire type used for the secondary e.g. magnet wire, insulated multi-stranded, stranded coaxial sheath etc.

According to the purpose of the experiments to be undertaken using this coil, that is, the exploration of displacement and transference of electric power, the coil geometry will be designed to optimise inter-winding capacitance (coupling). Inter-winding capacitance has been suggested to make a significant contribution[2,3] in the formation of the Longitudinal Magneto Dielectric (LMD) wave in the coil.

With this in mind the geometry of the coil is arranged with two inter-leaved layers of the coil where the number and spacing of the wire turns is arranged in order to maximise the inter-winding capacitive network, whilst keeping the fundamental resonant frequency within the required band. Arrangement of this network is by empirical methods and should ensure that the mutual inter-winding capacitance is not too high, and hence presenting too much of a capacitive load on the coil and reducing the Q, and also not too low and leading to deterioration of the required LMD wave. In other words, the magnetic field of induction and the electric field of induction must be as closely and mutually balanced in the coil as possible. This will be further considered in part 2 as an important pre-condition for the generation of a displacement event.

When the final coil(s) are incorporated into each experimental arrangement fine-tuning of the operating frequency is to be primarily affected by adjustment of the primary coil variable capacitance, and via an adjustable wire extension at the central end of the secondary coil e.g. using a short length of wire,  whip antenna, or telescopic aerial. In a parallel resonant circuit, and when the internal series resistance of the coil is significant, the minimum current at resonance occurs at a frequency lower than that expected from the ideal resonant case[5]. In our coil design this series resistance is significant (changing with wire type and geometry) and so also contributes to a reduction in frequency of the parallel resonant impedance maximum.

It is also intended that the resonant frequency of the primary circuit will be used to tune the overall frequency characteristics of the complete coil. This will make it possible to optimise the performance of the coil in a wide range of different experimental conditions including being driven by different types of electric generators (driving the primary coil), as well as attached to a range of different loads (driven from the secondary coil). Adjustment of the resonant frequency of the primary coil causes a corresponding change in the resonant frequency of the secondary coil, and most especially when the fundamental resonant frequency is close for the two coils. The primary coil is intended to be loaded with a variable capacitance in the range 100pF – 1500pF which is suitable for tuning the coil within the desired frequency band, and additionally at frequencies above and below this band.

The accurate prediction by calculation of the self-resonant frequency of a coil is a research topic in itself, and has received considerable investigation, modelling, and experimentation over the years. A detailed theoretical and modelled study of helical resonators has been presented by Corum et al.[6]. An experimental investigation into the properties of coil resonators has been presented by Knight[7], and who introduces a system of analysis and testing that is closely related to the work being undertaken here. In the coil design being considered the required fundamental resonant frequency of the coil is to be established by empirical methods, and combined with fine adjustment when the coil is to be constructed and operated.

Taking into account the described considerations, and when the impedance of the coil bottom-end is lowered by an external length of wire (~2m in length) to establish the correct quarter wave coil mode of operation, the frequency at which the 180o phase change occurs in the impedance of the coil was found to be 2400kc/s. When tuned and loaded with the methods described above this has been found to yield a fundamental resonant frequency within the stated required 160m band. With this point established the required wire length of the secondary was determined to be ~25m in length, arising from 2 layers of 10 turns inter-leaved in close coupling to form a 20 turn secondary coil, and with the following calculated dimensions. A spiral calculator tool[8] was used to confirm these dimensions and wire length before final design and construction of the secondary coil as shown in Fig. 2.

From Fig. 2. two layers of the secondary coil result in a wire length of 25.132m and a secondary conductor wire to spacing ratio of 1:3.2, a ratio that has been empirically found to benefit the formation of the Longitudinal Magneto Dielectric (LMD) wave in this geometry of coil.

The number of turns in the secondary is kept low, in this case 20 turns, in order to minimise excess voltage magnification and step-up which can cause the breakout of discharge streamers from the top load. For the purposes of the investigation of electric displacement of power it is preferred to maximise the generation of the Longitudinal Magneto Dielectric (LMD) wave, and for the case of transference the Transverse Electromagnetic (TEM) wave, by containing as much energy within the secondary as possible, and so avoiding the dissipation of energy by discharge to the surrounding environment.

This concludes the first part of the design of a suitable flat coil, and to be continued in part 2 where the properties of the secondary coil are used to consider the design requirements of a suitable primary coil.

Click here to continue to part 2 of the flat coil design.


1. Tesla, N., System of transmission of electrical energy, US Patent US645576A, March 20, 1900.

2. Dollard, E. & Lindemann, P. & Brown, T., Tesla’s Longitudinal Electricity, Borderland Sciences Video, 1987.

3. Mackay, M. & Dollard, E., Tesla’s Radiant Matter Replication, 2013, Gestalt Reality

4. Tesla, N., Colorado Springs Notes 1899-1900, Nikola Tesla Museum Beograd, 1978.

5. Resonance in Series-Parallel Circuits, Chapter 6 – Resonance, All About Circuits

6. Corum, K. & Corum, J., RF Coils, Helical Resonators and Voltage Magnification by Coherent Spatial Modes, TELSIKS University of Nis, Sept. 19-21, 2001.

7. Knight, D., The self-resonance and self-capacitance of solenoid coils, July 12, 2013, G3YNH

8. Bell, S., Flat Spiral Coil Calculator, DeepFriedNeon


 

Flat Coil Design – Part 2

The final coil required for the purpose of experiments to be undertaken in the displacement and transference of electric power, is a loosely coupled air core resonant transformer, or what has become known as a “Tesla Magnifying Transmitter” (TMT), sometimes also referred to as a “Magnifying Transformer” (MT), and described in more detail by Tesla[1,2], and notably through subsequent investigations by Dollard[3], amongst others.

In the TMT the properties of both the secondary and primary have been carefully arranged empirically to be beneficial to the overall transmission of electrical energy, both in conveying power between the primary and the secondary, and most importantly in the formation of an electrical cavity between the extra coil top-load, (secondary in the case of our flat coil), and any connected transmission and/or load elements. It is to be considered that the formation of an electrical cavity constitutes one of the key important pre-conditions for the generation of a displacement event.

With the basic secondary geometric specification defined in part 1, the design of the primary can now be considered. The overall electrical characteristics and performance of the final coil are defined by first, the individual properties of both the primary and the secondary, and secondly, on their combined electrical coupling together.

Accordingly the design of the primary coil needs to take into account a wide range of factors, including:

1. The continuity and coherence of the electric and magnetic fields of induction between the primary and the secondary.

2. The inductance and series resistance of the primary coil, and hence the magnitude of current in the primary from the generator.

3. The self-capacitance of the primary, and hence its fundamental self-resonant frequency.

4. Additional parallel loading capacitance, and hence tuning of the final flat coil.

5. The number of primary turns, and in specific relation to the number of secondary turns coupled together to form a transformer.

6. The coupling factor and the fundamental resonant frequency of both the primary and secondary together.

7. The magnitude of the electric power to be passed from the primary to the secondary.

8. The geometry and materials used in construction of the primary.

9. The wire type used for the primary e.g. magnet wire, insulated multi-stranded, copper tubing, copper strip etc.

The continuity and coherence of the electric and magnetic fields of induction between the primary and secondary coils is a critical factor in generating suitable currents, (oscillating and impulse), which are required for the effective generation of significant and measurable displacement events. It is suggested that a displacement event requires the electric field of induction to be spatially in phase with the magnetic field of induction, which is not a condition that normally occurs with these two fields in processes involving transmission of electric power through transference. In relation to the purpose of the work being undertaken in this research suitable further understanding to the detail pertaining to this field can be found in the work of Steinmetz[4,5], and Dollard[6-9].

Transference gives rise to the normal process of electromagnetic propagation and induction, a process involving the transformation though induction of one field to another though time. This process leads to the transmission of electric power between two or multiple points where the electric and magnetic fields of induction are spatially separated at right-angles and whose magnitude will decay over time in normal processes that lead to dissipation of the two fields through the medium, system, or circuit of interest. The perceived properties of transference result in the qualities widely observed in electromagnetic propagation (e.g. through Hertzian waves), in transmission lines, and through induction and conduction of electric power (electricity) in suitable electric and electronic circuits. This field is of course vast, greatly investigated and documented, with established theory at both the macroscopic and microscopic levels which can easily be corroborated and confirmed both by practical experiments, and the vast implementation of electric and electronic devices within industry.

In stark relation to this the displacement of electric power stands in its infancy, is generally not well investigated, understood, or even carefully and systematically investigated. This would appear to result both from the practical difficulties in generating and then measuring the properties of this state, and also from the lack of development and interest from industry, and since early postulation and investigation by the such notable figures such as Maxwell[10], Heaviside[11], Steinmetz[4,5], and Tesla[12].

It is suggested that the displacement of electric power results from a coherent relationship between the electric and magnetic fields of induction, in such a way that they cannot easily be distinguished as separate fields by conventional measurement means. If this were the case then both these fields would appear undifferentiated from one another, or rather in a cooperative relationship where both are in phase spatially and temporally. In this way the displacement of this “combined” field could occur over any distance without either constituent field dissipating, as there is no required transformation from one field to another in order to “propagate” or “transmit” from one position to another. The properties arising from this coherent and cooperative relationship between the two fields should be observable, under the correct and necessary pre-conditions, as displacement events which give rise to unusual and yet to be explored electrical phenomena that are not explainable by normal modes of transference.

It is conjectured that the displacement of electric power results from the impact of a non-linear event on the coherent relationship between the two fields of induction. At its very root where there is no distinct differentiation between these two fields, they are undifferentiated, a state that we cannot observe electrically by normal perceptual or measurement means. As the process of differentiation occurs between the fields there is as yet a coherent and cooperative inter-dependent relationship between the two forming fields, and they are taking a path of becoming less non-linear and more linear to our perceptual observation. This inter-dependent state should be observable when the correct pre-conditions have been established and a non-linear change is introduced to the system. This non-linear change initiates a displacement event where the resulting change to the energetic dynamics of the system give rise to electrical phenomena that can be measured through the linear process of transference, that is, with normal voltage and currents. The process of transference results from the full and linear separation between the electric and magnetic fields of induction as a response to the displacement event.

The process of displacement is often likened to establishing a longitudinal wave, (a condition between the two fields of induction), often referred to as a standing wave within an electrical system bounded in a specifically terminated cavity e.g. two joined TMTs either by a conducting medium such as a wire or through the earth. It is suspected, and to be determined, that the longitudinal wave, or standing wave case, is actually a pre-condition to a displacement event rather than the event itself. Establishing a standing-wave in a TMT cavity results in a different set of properties from displacement, where the electric and magnetic fields of induction are not spatially or temporally in phase and hence no power is dissipated, but where the two fields of induction are balanced but still in the fully linear state of transference. This means that a longitudinal wave, or an LMD standing wave, must first be established as a pre-condition within the system, and then a non-linear change introduced to this system as a trigger for the generation of a displacement wave. The generation of a displacement wave changes the energetic dynamics in the system to re-establish the balance of the magnetic and electric fields of induction, and hence re-establish the “harmonious” steady-state of the system having addressed the change or “need” of this system.

With all this said regarding displacement and transference it is critically important in the design of our MT, for the purpose of investigating displacement events, to ensure that we create a system which is best suited to sustain for as long as possible the coherent balance and continuity between the electric and magnetic fields of induction. In this way we so arrange our design to ensure that any generated displacement events occurring from or within the generator, from or within the medium conveying the electric power, and from or within any load thus designed to receive or utilise this power, will sustain the event for as long as possible and with amplitude such that it can be investigated and measured. Tesla[12] suggested and established this requirement clearly, in that the conducting boundary conditions for the electric and magnetic fields of induction must ensure the maximum balance, continuity, and coherence for these two inter-dependent fields when moving from one section of an electrical system to another. In this way he established the requirement between the primary and secondary of an MT should be made from equal weights of conductor.

From further investigation by others, notably Dollard[3,6], where the density of the conductor in the primary and secondary is the same, (e.g. for a primary and secondary both with copper as the conductor), equal volumes of the conductors can be considered equivalent to equal weights of the conductors, and has been found to apply best when working at lower frequencies where the skin effect does not have a significant effect on the impedance of the conductor, e.g. when working with normal copper or aluminium conductors at a frequency < 3000kc/s. At higher frequencies where the skin-effect can dominate the impedance of the conductor, balancing the bounding conditions for the two fields of induction can be better accomplished by equal surface area of the conductors.

Fig 2. below shows the effects of the skin-effect on the penetration depth with frequency for a range of common conductors.

In the case of the current flat coil design operating at nominally the loaded fundamental resonant frequency in the range 1810 – 2000kc/s, with both copper in the primary and secondary, equal weights calculations have been used to design the primary using multi-stranded wires, braided coaxial shields, copper tubing, and copper strip.

The design of the current flat coil primary is concluded in part 3 with consideration to these different types of primary conductor, and the calculations as to size and length of the conductor to be used for equal weights of conductor in the secondary and primary coils.

Click here to continue to part 3 of the flat coil design.


1. Tesla, N., Apparatus for Transmitting Electrical Energy, US Patent US1119732A, January 18, 1902.

2. Tesla, N., Rare Notes from Tesla on Wardenclyffe, Electric Spacecraft, 26, Apr/May/Jun 1997.

3. Dollard, E., Condensed Intro to Tesla Transformers, Borderland Sciences Publication, 1986.

4. Steinmetz, C., Theory and Calculation of Transient Electric Phenomena and Oscillations, McGraw-Hill Publication, 1909.

5. Steinmetz, C., Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients, McGraw-Hill Publication, 1911.

6. Dollard, E., The Oscillating Current Transformer, JBR, May-June 1986.

7. Dollard, E., Theory of Wireless Power, Borderland Sciences Publication, 1986.

8. Dollard, E., Symbolic Representation of Alternating Electric Waves, Borderland Sciences Publication, 1986.

9. Dollard, E., Symbolic Representation of the Generalized Electric Wave, Borderland Sciences Publication, 1986.

10. Maxwell, J., A Dynamical Theory of the Electromagnetic Field, Phil. Trans. Royal Society, pg459-pg512, January 1865.

11. Heaviside, O., Electrical Papers, Vol I & II Macmillan and Co., 1892.

12. Tesla, N., Colorado Springs Notes 1899-1900, Nikola Tesla Museum Beograd, 1978.


 

Flat Coil Design – Part 3

Following on from part 2 it has been establised that the primary and secondary coils will be so arranged to contain equal weights of conductor, dependent on the geometry of the specific conductors being used, and so to ensure the continuity of conductor boundary conditions and hence the balance, continuity and coherence of the electric and magnetic fields of induction between the primary and the secondary coils.

It is important in the primary to maximise the current carrying capability of the coil, which will allow the generator or tank circuit to provide strong oscillations, bursts, and impulses, according to the type of experiment to be undertaken. This means that the inductive reactance of the primary should be as low as possible within the band of frequencies required, allowing a large current to flow, and whilst also allowing for a practical value of tank capacitor with sufficient adjustment to tune above and below the frequencies of interest. In this case it is intended to use a variable high voltage vacuum capacitor in the range 100pF – 1500pF, with the desired fundamental resonant frequency change at 2400kc/s occurring at a tank capacitance in the range 900pF – 1100pF which allows for good adjustment for the variable vacuum capacitor, but also for the ease of use of a fixed high voltage capacitance of 1000pF (1nF). For the tank capacitance to be 1000pF, and in the ideal theoretical case, the  inductance of the primary would be 4.4uH.

Accordingly, and in consideration of the 20 turns in the secondary designed in part 1, the number of turns in the primary will be fixed at nominally 2, and with the ability to tap the primary, (for use with bare metal primary materials only e.g. copper tube or strip), slightly above or below the exact 2 turns mark should a finer resolution of tuning be required. This gives a voltage magnification in the magnifying transformer according to the secondary-primary turns ratio of 10, which is high enough to magnify the generator voltages to a more usable level in the observation and measurement of displacement events, and yet still low enough to allow high voltage generators to be used in the tank circuit without causing excessive breakout and discharge, and hence dissipation of energy to the surrounding environment, from the secondary.

Wire spacing between the turns of the primary is to be arranged to avoid any possibility of electric discharge through sparking when the primary is driven at resonance from a high voltage generator such as a vacuum tube oscillator or linear amplifier, a static or rotary spark gap generator, or other high voltage generator such as a vintage diathermy machine or electro-therapy generator. This means that the wire spacing in the primary should be safe for potentials up to 20kV applied across the primary terminals by a generator, and contacts to the primary and the primary conductor size should be able to support total input powers up to 2.5kW. With this considered the nominal distance between the start of the outer turn and the end of the second inner turn was set at 25mm, which gives a turn spacing of 12.5mm. The generally accepted dielectric strength of air at normal temperature, pressure, and humidity is 30kV/cm. When using a bare copper 3/16″ or 4.8mm tube this leaves the gap between conductors in the primary of 7.7mm which would have a nominal breakdown voltage in air of ~ 23kV, which is considered adequate for the highest voltage generators currently used in this research. The centre diameter of the primary coil was determined empirically by adjustment in relation to the secondary where the Q of the final coil was maximised, and a coupling factor between the primary and most outer turns of the secondary of ~ 0.15 was achieved.

With these characteristics defined the primary wire length could be defined to best match the required characteristics. Again the spiral coil calculator was used to assist in this calculation:

From Fig. 1. the required primary coil wire length is 3.455m, which theoretically yields a coil inductance of 4.8uH. At 2400kc/s for the desired fundamental resonant frequency phase change this yields a tank capacitance of 914pF, which is within the range required in the flat coil design.

Conductors to be used / tested in the secondary coil include:

1S. PTFE / Teflon coated, silver plated, multi-stranded wire. The strong PTFE coating prevents spark or streamer breakouts from running along the length of the wire, and the silver coating bonds the jacket firmly to the inner wire conductor. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: Awg16, 19/0.3 (19/29), ID ~ 1.35mm, OD ~ 2.5mm, white PTFE jacket.

2S. Silicone coated, flexible high density micro-stranded wire. The high number of conductor strands make this wire suitable for a higher frequency, lower-loss winding, and the silicone coating makes the wire very flexible with good high voltage and temperature properties. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: Awg16, 252 strands, ID ~ 1.5mm, OD ~ 3.0mm, black silicone jacket.

3S. Braided shield coaxial cable. The outer shield to be used as the conductor with many strands maximising the inter-turn capacitance, and the conductor surface area, and with the inner coaxial conductor non-connected. Given the secondary coil properties, dimensions, and turn spacing required the wire selected as the most suitable was: RG316 Coaxial cable OD ~ 2.50mm, transparent Teflon jacket.

Conductors to be used / tested in the primary coil include:

1P. Silicone coated, flexible high density micro-stranded wire. The high number of conductor strands make this wire suitable for a higher frequency, lower-loss winding, and the silicone coating makes the wire very flexible with good high voltage and temperature properties.

2P. Flexible copper tubing, with good high current capability and easy primary tapping to the bare conductor surface.

3P. Copper strip, with high surface area, high current capability, and highest Q for the high frequency experiments.

The early versions of the flat coil used wire combination 1S-1P for both the generator and load coil, providing an easy to use coil structure suitable for a wide range of preliminary investigations into the displacement and transference of electric power. This was later replaced by 1S-3P as the best measured for both the generator and load coil for experiments with displacement events. Later experiments in telluric transmission of electric power used the 1S-3P combination as the best measured generator coil, and with 3S-1P as the best measured load coil. The details of these measurements and there results will be reported in the experimental posts.

For calculations of copper weight, volume, and other useful data with respect to solid and stranded wires, and where either exact specification data, or measured data, is not available for the actual wire used, the following wire and cable data from Calmot can be used.

Click here to view or download the Calmot wire and cable data.

1. For coil 1S-1P the equal weight of copper calculation:

Secondary wire length (from part 2): 25.132 m

Specification unit weight of actual wire used: 11.120 kg/km

Secondary wire weight = 11.120 x 25.132 / 1000 = 0.279 kg

Calmot data for 8 AWG 1666 / 40: 81.1 kg/km

Actual primary wire 1P 8 AWG 1600 / 40 = 1600 / 1666 x 81.1 = 77.887 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.279 x 1000 / 77.887 = 3.582 m

Calculated primary wire length from flat spiral coil calculator in Fig. 1: 3.455 m

1P Primary wire length of silicone coated micro-stranded 8 AWG 1600 / 40 = 3.58 m

2. For coil 1S-2P the equal volume of copper calculation:

Secondary wire weight (as above) = 0.279 kg

Measured unit weight of pure copper pipe OD 4.75mm (3/16″), wall thickness 0.8mm: 77.420 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.279 x 1000 / 77.420 = 3.603 m

2P Primary length of 4.75mm (3/16″) pure copper pipe = 3.60  m

3. For coil 1S-3P the equal weight of copper calculation:

Secondary wire weight (as above) = 0.279 kg

Specification unit weight of pure copper strip 30mm wide and 0.3mm thick (standard strip available): 80.450 kg/km

Required primary strip length for exact equal secondary and primary weights = 0.279 x 1000 / 80.450 = 3.467 m

3P Primary length of 30mm x 0.3mm pure copper strip = 3.47  m

4. For coil 3S-1P the equal volume of copper calculation:

Measured unit weight of RG316 outer braid only: 6.150 kg/km

Secondary wire weight = 6.150 x 25.132 / 1000 = 0.155 kg

Actual primary wire 1P 10 AWG 1050 / 40 = 45.150 kg/km

Required primary wire length for exact equal secondary and primary weights = 0.155 x 1000 / 45.150 = 3.433 m

1P Primary wire length of silicone coated micro-stranded 10 AWG 1050 / 40 = 3.50 m (2% error to allow for 2 complete turns and connection)

All required primary lengths, (other than case 4 where the primary must be extended for 2 complete turns), are longer than the flat spiral coil calculation of 3.455m, which allows for 2 full turns of the primary and connections to be made to the primary capacitor. Connections to the primary capacitor are arranged at the point where the primary length is equal to that required to equal the weights of the secondary and primary coils.

It must also be noted that the primary capacitor introduces a weight of conductor into the primary circuit calculation which has not been accounted for above. In the experimental stage different capacitor sizes and weights will be used to determine the overall induction field mismatch caused by this circuit element and/or other elements in the generator or load. In the case of diminished displacement and transference of electric power results, the primary weight of copper will need to be adjusted through reduced AWG size (P1), reduced tube diameter (P2), and reduced strip width (P3), in order to get the best equal conductor weight match.

This concludes the three design parts for the flat coil with all the necessary parameters for construction of the final coil.

Click here to continue to the flat coil construction post.


1. A & P Electronic Media, AMInnovations by Adrian Marsh, 2019,  EMediaPress


 

Flat Coil Construction

The flat coil design has provided the necessary dimensions and materials for the secondary and primary coil to be constructed. This post will outline construction of the 3S-1P flat coil described in Part 3 of the design. The complete constructed flat coil is shown in Figures 1. below, and gives an overall impression of how the coil has been mechanically designed to accommodate the required electrical coil design for a range of different experimental scenarios.

The overall required specification from the design process is summarised as follows, and can then be considered for the mechanical design and construction:

Secondary specification (3S):

Geometry: 2 spiral coils interleaved per turn

Number of turns: 20

Coil Inner diameter: 345mm

Coil Outer diameter: 455mm

Wire length: 25.132m

Wire type: RG316 braided coax with the outer braid connected only

Calculated inductance (assuming solid wire): 142.8µH

Primary specification (1P):

Geometry: spiral turns in same plane and outside the secondary

Number of turns: 2

Coil inner diameter: 525mm

Coil outer diameter: 575mm

Calculated wire length: 3.455m

Wire type: AWG10 1050 / 40 Silicone coated micro-stranded wire

Calculated wire length to equal primary and secondary conductor weight: 3.50m (2% error from calculated wire length to allow for 2 complete turns and connection)

Calculated inductance (assuming solid wire): 4.8µH

Frequency specification:

Secondary resonant frequency 180° phase change: 2400kc/s

Secondary tuned fundamental resonant frequency: 1810 – 2000kc/s

Calculated parallel primary tuning capacitance to match the secondary 180° phase change frequency: 916pF (assuming 4.8µH primary inductance)

Ideal parallel primary tuning capacitance: 100pF – 1200pF 4kV vacuum capacitor

Fig. 2. below shows the plan for the flat coil mechanical design with the key supports, secondary, and primary coil positions and dimensions indicated.

The back board uses 12mm thick finished interior plywood, and has four quarter circle cut-outs to remove the excess material from around the secondary coil. The back board is supported on a plywood or nylon base with a support pillar in the back to prevent warping of the plywood back board over time.  It is useful to varnish the back board if the coil is to be used outside, to afford some protection against moisture absorption into the wood.

The coils are supported on the back board by 16 PTFE or Neutral Nylon 66 supports and have the dimensions 190mm x 50mm x 12mm (LxHxW). These supports have 2.5mm wide grooves cut 9.0mm deep from the top edge to retain the windings of the secondary coil. Three grooves where also cut outside of the secondary ID and OD to allow for rewinding adjustments during experimentation. In total 17 grooves (11 for the secondary and 3 either side) were cut to accommodate the windings of the secondary coil. The windings of the secondary coil are retained in the slots by sprung nylon straps screwed to the coil supports using tapped M3 nylon screws. This method of retaining the secondary was used rather than a more permanent gluing approach, to allow the windings to be adjusted, rewound, or even changed in specification or wire type if required. The coil supports were mounted to the back board using M6 countersunk nylon screws. No metal screws or attachments were used in close proximity to the coils.

The outer top ends of the coil supports have an additional 3 x 6.0mm grooves cut 8mm deep to accommodate the windings of the primary wire. In addition each of the primary grooves was cut with a thin narrow slot (1mm wide) and 20mm deep to accommodate the flat copper strip primary (3P) if required. The bottom most coil support has a nylon mount for a high voltage output terminal connected to the outer end of the secondary coil. The inner end of the secondary conductor can be fed to a range of different mounts including a BNC connector for a telescopic aerial, a ceramic bulb-holder mounted on a nylon support for a neon bulb, or other high voltage terminal, feed, or top-load. The primary coil ends are fed through the back board, (via insulated conduits if necessary), and then attached directly to the primary capacitor at the primary length established in the equal weight of copper calculations in the part 3 of the design.

The early versions of the flat coil used solid nylon coil supports fixing the secondary and primary onto the back board. A later version of the flat coil, (as shown in the Figures 1. and 3.), used two-part coil supports arranged in such a way that the complete secondary unit can be removed from the primary and back board. This mechanical design greatly assists measurements of the secondary and primary independently whilst still in-situ to the experiment or circuit being measured. In the frequency measurements it is desirable to remove the secondary coil from the system and test the primary properties before adding the secondary, which then provides a much clearer understanding of how the two coils interact in the electrical system.

The secondary windings and the primary windings are normally wound in the same rotation direction on a single flat coil. A clockwise wound secondary will have a corresponding clockwise wound primary. For experiments involving displacement and transference of electric power between two flat coils the coil winding direction would ordinarily be in counter-rotation between the two flat coils, so as to define a clear boundary for the electric and magnetic fields of induction between the two coils. For example, if the flat coil attached to the generator has its windings wound clockwise, then the flat coil attached to the load will have its windings wound anti-clockwise. The flat coil winding possibilities have been measured, and the differences noted, for first, two flat coils counter wound, then secondly two flat coils wound in the same direction, and thirdly even with a single flat coil with counter-wound secondary and primary coils. These differences and their effects on the boundary conditions for the electric and magnetic fields of induction will be reported and considered in the measurement and experimental posts.

The secondary winding was wound onto the coil supports to create two inter-leaved coils as suggested and demonstrated by Dollard[1]. The lower turn is wound into the bottom of the coil support groove starting from the required secondary OD position. After the first complete turn nylon supports, fashioned from trimmed nylon M3 screws, were inserted into the groove to provide the correct spacing between the upper and lower coils. The depth of the groove and the spacer were so arranged so that the spacing between the two coils was ~60-65% of the conductor winding pitch. It has been suggested by Dollard[2] that this winding space is optimal for the inter-winding capacitive network and hence advantageous in generating the Longitudinal Magneto Dielectric (LMD) wave or standing wave.  The formation of the LMD wave is conjectured as a necessary pre-condition for the generation of a displacement event when combined with a non-linear element, load, or event in the system.

To investigate and confirm the 60-65% spacing, a flat coil has also been assembled where the upper and lower coils are wound directly on top of each other with no nylon spacer, and only spaced by twice the thickness of the insulating jacket around the conductor of the winding. In the case of the 3S coax braid coil the conductors are spaced by 0.5mm without the nylon spacer, and by 3.0mm with the spacer. In the case of the 1S PTFE coated stranded wire the conductors are spaced by 1.0mm without the nylon spacer, and by 3.5mm with the spacer.

With the spacer in place above the lower winding the upper turn is now added to the coil. When one complete turn has been wound the wire in the upper coil will move to the lower coil in the next adjacent groove of the coil support. This continues until 10 complete grooves have been wound, which corresponds to an inter-leaved upper and lower flat coil of 10 turns each, and 20 turns in total. After the 10 complete grooves have been wound the coil length can be fine adjusted by a fraction of a turn (e.g. 0.5) before being terminated at the conductor centre mount.

In later versions of the flat coil the back-board was modified to provide mounts for using the coil vertically, horizontally, or with nylon threaded mounts to attach legs so that the coil can be used horizontally outside or on the bench. This combination of fixtures allow for a wide range of experimental conditions including outside as well as inside in the lab or workshop.

Detailed pictures of the mechanical construction are shown in Figures 3. below.

Click here to continue to the flat coil frequency measurements part 1.


1. Dollard, E. & Lindemann, P. & Brown, T., Tesla’s Longitudinal Electricity, Borderland Sciences Video, 1987.

2. Dollard, E., Theory of Wireless Power, Borderland Sciences Publication, 1986.

3. A & P Electronic Media, AMInnovations by Adrian Marsh, 2019,  EMediaPress


 

Tesla Coil Geometry and Cylindrical Coil Design

Tesla used a range of different coil geometries throughout his experimental work, including flat[1], cylindrical[2], conical[3] , and separated cylindrical secondary with an extra coil[4]. Each of these different geometries present different advantages and different limitations, and hence it is important for any experiment using a Tesla coil or TMT system to choose a coil geometry best suited to the type of experiment at hand. Different experiments are designed to study different aspects of electrical phenomena and qualities including, displacement and transference of electric power, radiant energy and matter, wireless, single wire, and low-loss transmission, longitudinal modes and cavity effects, plasma and dielectric effects etc.

The electrical dynamics and properties of different Tesla coil geometries is a complex and involved field, and has been much explored both theoretically and practically in the prior art, and notably including Dollard[5,6] and Corum et al.[7,8]. In the first part of this post we review some of the most important experimental considerations for coil geometry that I have observed and encountered throughout my research so far. In the second part we take a look at a cylindrical coil design suitable for plasma effects and other discharge phenomena when combined with an extra coil, and similar to a design by Eric Dollard for his cosmic induction generator.

Figures 1 below show the final cylindrical coil design in a variety of configurations, including a TMT system for transference of electric power experiments, induction generator plasma experiments, and both driven using the Quad 811A tube board. The detail of these experiments, phenomena and measurements will be reported in subsequent posts.

Coupling and Free Resonance

A Tesla coil can be considered to be a resonant air-cored transformer when excited by a linear sinusoidal drive to the primary coil. As such it is fundamentally important to ensure that as much energy as possible from the generator, is transferred from the primary coil to the secondary coil as quickly as possible, so the coupling between the two coils is maximised. At the same time, at least the secondary coil must be able to freely resonate according to the nature of its design and geometry, and with maximised quality factor and minimised resistive losses, requiring minimised coupling between the two coils. In some cases both the primary and secondary coils are arranged to resonate in tune with each other whilst maximising the resonant properties of the secondary. These two fundamental requirements of Tesla coils present a trade-off or balance that must be optimally struck in any TC design, and according to the intended application.

Maximising coupling of the primary and secondary implies tightly coupled coils which are in close proximity to each other, and that maximise the enclosed area of intersection of the magnetic field of induction, Φ. Increased coupling reduces the ability of the secondary coil to freely resonate at its fundamental resonant frequency, as it becomes increasingly driven by the primary, quenching the Q of the coil system, and tending towards a standard, magnetically coupled, non-resonant transformer.

The secondary coil on its own will freely resonate with maximum Q and impedance at the fundamental resonant frequency according to its design, geometry, and the materials used in its construction. As a primary coil is brought into proximity with the secondary the coupling starts to increase from zero and the properties of the two coils start to interact. With a non-zero coupling coefficient energy can now be transferred between the two coils, but the freely resonant properties of the secondary also start to change, influenced by the impedance characteristics of the primary, resonant or not.

The most optimum balance between these two requirements can be established in a separated secondary induction and extra coil arrangement, where tightly coupled induction can occur between the primary and secondary, whilst the free resonator properties of the coil system are maintained by the extra coil. This coil geometry is considered in more detail later in this post.

Field Distribution. Magnification and Compression

Magnification of the dielectric field of induction, Ψ, occurs from turn-to-turn of the secondary, starting from those turns most tightly coupled to the primary and enclosing the largest area of intersection with Φ from the primary. This magnification of Ψ is influenced by the geometry of the secondary through compression of the field distribution. In a cylindrical coil each turn moving away from the coupling region describes the same area and path length, which in principle leads to a uniform exponential increase in the magnification of Ψ.

In contrast, in a flat coil geometry each turn becomes smaller than the last as the turns move away from the outer coupling region. In this case Ψ is progressively compressed towards the centre of the coil increasing the magnification non-linearly towards the centre high-end of the coil, and leading to a highly non-linear dielectric induction field distribution. For the same number of turns Ψ is measurably higher towards the high-end in a flat coil, than for the same turn measurement in a cylindrical coil.

For coils designed to explore phenomena related to the imbalanced magnification of the dielectric field of induction Ψ e.g. attractive and repulsive forces, low temperature light emission and “cold” electricity, charge accumulation and storage, and “fern” effect discharges, then compression is particularly important in the geometry of the required coil. In this case a flat coil with many smaller turns to the centre, or a conical coil with turns concentrated towards the cone tip, are more suited to investigation of these kinds of phenomena.

Cylindrical coils, or separated secondary induction and extra coils, are better suited for experiments requiring a balance between Ψ and Φ e.g. for experiments in the displacement of electric power with a non-linear impetus, telluric and single wire transference of electric power in a TMT system, and plasma phenomena.

Charge Distribution, Conductor Volume and Surface Area, and boundary Conditions

If we consider the secondary coil to be a continuous metal conductor, at a typical resonant frequency between 10kc – 10Mc, then geometry effects considerably the charge storage and distribution across its surface. In the case of a flat coil the largest proportion of conductor is closer to the outer coupling region, and hence the distribution of charge on the conductor is biased towards the outer perimeter of the coil with less towards the centre. The effect of this is to electrically damp the resonant properties of the secondary towards the centre, so less energy can be stored and released in each resonant cycle, which in turn effects the amount of energy that can be coupled to the longitudinal mode within the cavity described by the secondary coil system.

In my own research I have found it to be critically important in coil design, for the purpose of investigating displacement events and their related phenomena e.g. radiant energy emissions, to ensure that we create a system which is best suited to sustain for as long as possible the coherent balance and continuity between the dielectric and magnetic fields of induction. In this way we so arrange our design to ensure that any generated displacement events occurring from or within the generator, from or within the medium conveying the electric power, and from or within any load thus designed to receive or utilise this power, will sustain the event for as long as possible and with amplitude such that it can be investigated and measured. Tesla[9] suggested and established this requirement clearly, in that the conducting boundary conditions for Ψ and Φ must ensure the maximum balance, continuity, and coherence for these two inter-dependent fields when moving from one section of an electrical system to another. In this way he established that the requirement between the primary and secondary of a magnifying transformer should be made from equal volumes of conductor.

From further investigation by others, notably Dollard[5,10], where the density of the conductor in the primary and secondary is the same, (e.g. for a primary and secondary both with copper as the conductor), equal volumes of the conductors can be considered equivalent to equal weights of the conductors, and has been found to apply best when working at lower frequencies where the skin effect does not have a significant effect on the impedance of the conductor, e.g. when working with normal copper or aluminium conductors at a frequency < 3000kc. At higher frequencies where the skin-effect can dominate the impedance of the conductor, balancing the bounding conditions for the two fields of induction can be better accomplished by equal surface area of the conductors.

In any calculation of equal weights or surface areas of the system conductors it is necessary to consider the overall resonant system of both the primary and secondary. For example, if the primary is tuned by a vacuum variable capacitor then this and the inter-connection conductors must be added to the calculation. If the secondary coil includes a top-load e.g. metal toroid, multi-wave oscillator resonator, or other conductive arrangement this must also be added to the calculation for the secondary. Empirically any conductor that contributes to the resonant circuit of the coil needs to be factored into the equation.

It is also empirically suggested that this calculation is adequate for the dielectric field of induction Ψ, and that for complete continuity there must be a balance in magnetic materials as well. Normally magnetic materials are to be avoided or eliminated in the design of a TC in order to prevent reduction and/or distortion of the magnetic coupling between the primary and secondary, and parasitic inductive losses. If magnetic materials are deliberately placed in the design e.g. when using a magnetic disruptor to quench the primary spark gap, which also forms part of the primary resonant system, then this should be balanced out magnetically in the secondary load circuit.

Geometry and the Longitudinal Mode Cavity

One of the unique qualities of any TC geometry is that a longitudinal cavity is established between the outer boundary conditions of the secondary coil. The Longitudinal Magneto-Dielectric (LMD) mode has been considered both theoretically and experimentally in the prior art[10-12], and appears to develop within the secondary coil primarily as a result of the geometrical inter-action between the distributed inter-turn mutual inductance, and the inter-turn mutual capacitance. It is conjectured that the ratio and balance of this distributed inductance and capacitance determines the cavity properties, and hence the formation of a pressure wavefront, where Ψ and Φ establish and maintain a phase alignment to each other. The outer boundary conditions of the longitudinal cavity are dynamically defined, where significant electrical reflections from impedance mismatch will collapse the phase alignment between Ψ and Φ, and lead to dissipation of the LMD mode.

In a typical TC the boundary conditions of this longitudinal cavity usually occur at the top-load at the high or inner-end of the coil, and the low or outer-end plus any single wire extension, load in the single wire extension, and termination load at the end of the wire extension, whether this be open-circuit, ground, or other defined load. In a matched TMT system, as in my transference of electric power experiments, the longitudinal cavity can be extended all the way from the “transmitter” cavity through the transmission medium to the “receiver” cavity. In principle when the longitudinal mode is established stably in this cavity, electric power can be passed between the source and load over very great distances, (in the far field condition), and is considered to be a key principle in Tesla’s telluric transmission of wireless power.

The LMD mode of transmission forms as a standing wave between the transmitter and receiver coils of a TMT system. In successive cycles of the generator oscillations, electrical energy is coupled from the generator into the cavity. The pressure of the wavefront in the longitudinal mode moves backwards and forwards as it traverses the cavity from the transmitter to the receiver, reflected from the top load of the receiver and back again towards the transmitter where it is amplified or suppressed by coupling from subsequent cycles from the generator. Whether the longitudinal wavefront is amplified or suppressed depends on the tuning of the system and hence the longitudinal wavelength in the cavity.

At the correct point of tuning the amplitude of the wavefront is reinforced by successive cycles from the generator. The magnitude of this longitudinal wavefront reaches an equilibrium in the cavity based on the impedance characteristics of the cavity medium, its tuning, and dissipation of the stored power to both the transmission medium, and to the surrounding environment. The longitudinal wavelength within the medium is longer than that of the generator excitations, which represents a lower frequency of oscillation for the longitudinal mode. This puts the phase aligned Ψ and Φ wavefront at different phase relationships to any transverse components throughout the length of the cavity, a property of the longitudinal mode that can be measured in the cavity region.

At the correct point of tuning Ψ and Φ in the LMD mode form a standing wave in the cavity which results from the longitudinal wavelength, where the boundaries of the cavity are defined by the high impedance, high potential, points at the top-loads of the coils, and one or more null points form inside the cavity. At the fundamental frequency of the LMD mode, (not the same frequency as the fundamental resonance of the secondary coils or the generator oscillations), only a single null will exist in the centre of the cavity, and when the coils are closely spaced in the near-field. At higher order harmonics, and dependent on spacing between the coils multiple null points can form.

Empirically through observation and measurement in the various experiments in my research, and particularly in Transference of Electric Power, and Tesla’s Radiant Energy and Matter, a trade-off exists in the geometry of the coil, and the LMD mode. With tight and closely wound turns in a coil with significant magnification, and where height to width ratio > ~ 2, e.g. a conventional tall and narrow streamer coil, the LMD mode can easily be established within the secondary coil, but appears to diminish and tend quickly to zero in any single wire extension from the low end, even when the extension is left open-circuit, (complete wavefront reflection). In this case this type of coil geometry is unsuitable for transference of electric power experiments even in the near-field case. In the close mid-field region, (the boundary of which starts at approximately twice the secondary coil diameter), a TMT with reciprocal and transverse tuned transmitter and receiver coils, the power transferred through to the receiver load would be very low e.g. for 500W of power supplied from the generator only a few watts of power is available at the final load. In the far-field region the coils appear as unconnected from each other, even with a lower impedance single wire extension connected between both low ends of the transmitter and receiver secondary coils. In this geometry case telluric transference of electric power does not appear possible, even when the transmission medium is a relatively low impedance, (less than the combined impedance of the secondary coils at the transverse resonant frequency).

With loosely wound turns where the turn spacing is equal to or greater than the wire diameter, when the magnification secondary to primary turns ratio is lower e.g. 10-15 : 1, and where the height to width ratio is <~ 1, the LMD mode appears to have a lower intensity in the secondary coil, but can extend over very large distances and easily into the far field. In this case, and using a suitable flat or cylindrical coil TMT system the longitudinal mode can be extended across the entire cavity in any extent, near, mid or far-field. Substantial electric power can be transferred from the generator to the receiver load through a low impedance single wire extension, through a telluric channel, or other suitably arranged low impedance or resonant transmission medium, and as demonstrated in transference of electric power experiments.

Hybrid Coils and Turn layering

In some cases a combination of coil geometry, or hybrid coil, has proven to be the best choice for the experiment in hand. An example of this would be the flat coil originally demonstrated by Dollard et al.[11], and used extensively in my own research and particularly in experiments on the transference of electric power, and telluric transference of electric power. In this flat coil geometry turn layering is used to produce two flat coil spirals closely spaced to each other, and providing a combination of properties from the flat and cylindrical designs. In particular the magnification of the coil can be increased, without damping the free resonant properties of the coil, and emphasising the compression properties that accentuate dielectric induction field phenomena.

Flat coils with turn layering up to as many as 5 layers can demonstrate excellent magnification and compression whilst retaining loosely wound turns and hence a good longitudinal cavity mode. Such a multi-layered coil is well suited to intense dielectric phenomena, such as Eric Dollard’s “fern” discharge experiment. The disadvantage of progressive turn layering is in the imbalance created between Ψ and Φ, and with each additional turn the rapidly increasing risk of breakdown at the winding return point. Whilst the longitudinal cavity in a TMT system appears to remain well established where a typical null point can be measured in transmission medium, the amount of power that can be transferred between generator and receiver load appears greatly diminished.

This reduction in transferred electric power is most likely as a result of the geometry imposed imbalance between Ψ and Φ, where Ψ has been significantly accentuated, and Φ has been suppressed by the hybrid and turn layered geometry. Maximum power transfer in a TMT system appears to occur when Ψ and Φ are maintained in dynamic balance, through optimal geometry of the TMT coils, transverse tuning to match the resonant frequencies of transmitter and receiver, and longitudinal mode tuning through obtaining a clearly defined standing wave within the cavity, (accomplished primarily through adjusting the electrical path length of the transmission medium to obtain a strong simultaneous null point for Ψ and Φ at the cavity centre).

Secondary Coil Induction and Extra Coil Resonance

This coil geometry and arrangement is probably the best for resolving the fundamental trade-off between coupling and free resonance, and appears to be Tesla’s[4] own choice of system arrangement for large scale transmission of electric power. In this coil arrangement the induction between primary and secondary is separated from the free resonator or extra coil. This allows the primary and secondary to be tightly coupled and designed to maximise transfer of energy between the generator and primary coil and the secondary coil. The air-core of this primary-secondary induction transformer allows it to operate at a higher frequency than a conventional iron-cored power transformer, whilst retaining resonant properties that improve impedance matching to the generator. The tuned high or low input impedance presented to the generator through correctly matching this arrangement, allows optimal generator drive from a wide range of different source types, including linear sinusoidal oscillators, spark-gap discharges, and other transient and impulse generators.

In Tesla’s case this was driven through very powerful uni-directional disruptive discharges from energy stored in large tank capacitors, and charged by high voltage DC dynamos. In this case the primary-secondary induction transformer requires a very low input impedance, maximising impulse primary currents, which in turn produces very strong magnetic induction field coupling between the primary and secondary. In this case the secondary is arranged in close proximity to the primary, of the same diameter to maximise intersection of the magnetic field of induction, and the number of turns kept minimal to prevent magnification and compression of the dielectric induction field, whilst minimising electrical losses in the secondary, and preventing premature leakage of energy through discharges from the secondary high-end.

The high-end of the secondary induction coil is directly connected to the low-end of the extra coil. The extra coil can be considered in this arrangement as a free resonator, often physically displaced from, or orthogonal to the secondary coil, but can also be driven centrally on axis to the secondary as in Tesla’s Colorado Springs apparatus[5,9]. The extra coil in this arrangement has an optimal electrical length of λ/4, and when combined with the primary – secondary induction transformer, the complete Tesla coil geometry is a tuned system with length 3λ/4, or generally nλ/4 where n is an odd positive integer. When arranged in this fashion the extra coil produces considerable magnification as a free resonator whilst maintaining a good balance between Ψ and Φ. Interesting variations on the standard high aspect ratio, (tall and narrow for high magnification), cylindrical extra coil geometry, include conical and golden ratio designed coils.

Ultimately the optimal design of this geometry as a resonant magnifying transformer is resolved by impedance matching the various stages of the system from generator to primary, primary to secondary, secondary to extra, and extra to extension and top-load. If a cavity is to be generated at the low end of the secondary coil, then impedance matching from the secondary to the cavity, and any additional circuit elements in the cavity, is also important. This approach to Tesla transformer design is notably explored in the prior art by Dollard[5,12], and within my own research through looking at TC and TMT system impedance, tuning, and matching using a vector network analyser.

An interesting alternative consideration arises regarding Tesla’s intended purpose for the extra coil, when we take into account that the Colorado Springs apparatus was designed around 1900, and specifically to be driven by powerful impulse disruptive discharges. When the extra coil is arranged to resonate at the third harmonic of the secondary induction system, and where the quality factor (Q) of the extra coil is very high, the output from the top-end of the extra coil will be a very powerful, low distortion, sinusoidal oscillation at a single frequency. This form of output is ideally suited to radio transmission as the carrier wave, and has been selected from a wide spectral bandwidth discharge.

The multitude of frequencies contained within a disruptive discharge are highly unsuitable for radio transmission due to the interference created across bands, and the large amount of energy dispersed across the spectral bandwidth, as demonstrated by the early spark-gap radio transmitters used in the very early 20th century. High power single frequency oscillators for radio transmitters became standard with the development of the vacuum tube in the early 20th century, but before this, and at the time of the Colorado Springs research, Tesla had found a unique way to create a powerful single frequency carrier wave from a wide-band disruptive discharge generator. As an alternative interpretation of his work at this time, the extra coil was ideally suited to both select and tune the output of a very high power transmitter to a single frequency.

Coil Geometry Comparison Summary

Flat Coil (loosely wound with 2 layers): Good compression and magnification of the dielectric field of induction, generally suitable for transference of electric power experiments as a TMT system with a secondary to primary turns ratio around 20:2. Shows moderate dielectric induction field phenomena such as attractive and repulsive forces and capacitor charging. Maintains a good longitudinal cavity for LMD experiments when correctly tuned, and the efficiency for the transference of electric power appears moderate around 60%+ when carefully tuned in the transverse modes, and balanced to maintain a longitudinal null point at the centre of the single wire transmission medium.

This coil geometry gives a good general purpose experimental base, the imbalance in Ψ and Φ due to the compression of Ψ limits the efficiency in power transfer, but yields a range of interesting phenomena. Can be readily matched in the primary circuit to either a linear sinusoidal oscillator or a spark discharge generator.

Cylindrical Coil (loosely wound): Best geometry to maintain the balance between Ψ and Φ, and hence highest efficiency in the transference of electric power experiments. In the near to mid-field with correct tuning and balancing efficiency can be > 90%. In a coherent arrangement where the longitudinal mode is established across the entire TMT system from generator to load it may, in principle, be possible to establish 100% displacement of electric power from source to load, although this remains a work in progress to demonstrate and validate.

When combined with an extra coil into the Colorado Springs experimental arrangement, and with suitable Telluric tuning and matching, then far-field longitudinal transference of electric power may also be possible, and appears to remain one of the ultimate goals of this field of energy research. In my research so far I have measured far-field Telluric power transfer, (at ~ 3 miles between transmitter and receiver), of around 10dBm in the 80m amateur band from the upper resonant frequency of a carefully tuned TMT system.

The cylindrical coil geometry, again due to its well balanced Ψ and Φ, and with a secondary to primary turns ratio between 20:2 and 20:3 also appears best suited to plasma based experiments, such as Dollard’s cosmic induction generator design. This geometry also forms a good induction pump for a wide range of extra coils. A conical extra coil added to a cylindrical coil induction generator greatly improves the compression and magnification of this geometry, accentuating Ψ, and yielding good dielectric induction field phenomena.

When mounted on separate support structures the primary and secondary can be moved and positioned relative to each other, which gives free and variable adjustment over the coupling between the primary and secondary coils. In a TMT system where the coupling can be adjusted in both transmitter and receiver, very fine balancing can be accomplished between coupling and primary tuning, and hence the possibility for increased transference of electric power efficiency.

Streamer Coil (tightly wound): A high aspect ratio tall and narrow cylindrical coil which is usually more tightly coupled to the primary. This geometry has excellent voltage magnification, and when combined with an accumulator at the high or top-end of the secondary coil can achieve considerable energy storage at very high potentials. Most often used for discharge streamer entertainment, or as a high frequency, high voltage power supply in research, this TC geometry can reach many MVs of voltage magnification and deliver many kWs of power continuously.

Due to the tight coupling and huge magnification, dielectric induction field phenomena can be very strong in this arrangement. Longitudinal cavity phenomena and the LMD mode appear to be small in this arrangement, that is, they can be so small as to easily go undetected. This coil geometry is unsuitable for transference of electric power, and experiments where a balance and tuning needs to be maintained between Ψ and Φ.

Golden Ratio Geometry

This is a particularly interesting geometry and could lead to a wide range of interesting phenomena yet to be explored. The golden ratio (GR) is very widely treated in the prior art and the following references constitute further reading on this subject[13-15]. From the perspective of TC and TMT systems the golden ratio can be conceived in a variety of different ways, including the aspect ratio for any of the coil geometries, and in particular the cylindrical and/or extra coils that can have there height to width ratios according to GR, the wire diameter to turn period according to GR, the primary coil as a spiral defined on GR proportions, and the electrical length of the primary, secondary, and extra coils according to GR, and even the ratio between the longitudinal  and transverse modes (including the cavity ratio) according to the GR.

It is conjectured that perhaps the most interesting GR relationship would exist directly between Ψ and Φ, which could be arranged through geometry, tuning, and generator and load characteristics. This area of research and investigation requires considerable further work, and remains work in progress at this time, and to be reported at a future point.

Displacement, Non-linear Dynamics, and Geometry

There is a very important distinction to be made in this area, which for me results from the sum total of my research so far, and all the experiments, observations, and measurements that have accompanied this journey. I would assert that Displacement and the observable phenomena that are emitted through the principle and mechanism of displacement e.g. Tesla’s Radiant Energy and Matter, do NOT originate as a result of the coil geometry of the experimental system. To clarify, I conjecture that displacement is an underlying coherent principle and mechanism within the inner workings of electricity, and that it is a displacement event that gives rise to the emission of various phenomena, including radiant energy. Displacement seems to be most effectively revealed by driving the experiment in a non-linear or transient fashion e.g. from a cylindrical TC with moderate coupling, driven by an impulse or disruptive discharge generator of at least a moderate power e.g. > 500W.

Therefore I am discriminating between displacement events and their associated phenomena, and the different properties of Tesla coils and TMT systems that result from the difference in balance between the differentiated dielectric and magnetic fields of induction, that are brought about by varying coil geometries. Said in yet another way, Tesla’s Radiant Energy and Matter, and other coherent electrical phenomena are not the product of coil geometry, but rather underlying coherent processes that constitute the inner, and as yet unexplored, workings of electricity. Whilst this conjecture may be difficult for some to acknowledge without considerable additional supporting evidence and results, something my research is actively engaged in acquiring, it would appear to me completely as common sense that there are underlying processes of a coherent nature that emit coherent forms of phenomena. These coherent phenomena are as yet manifestly unexplained by even the best current understanding of transference, which arises from the differentiated dielectric and magnetic fields of induction, and which constitutes electrical properties relating to common circuit characteristics and transmission.

This said, coil geometry and careful design are most important in balancing or preferentially accentuating Ψ and Φ. The relative balance or imbalance of Ψ and Φ, which results from a particular coil geometry and experimental system arrangement, results in a specific coil geometry being better suited to different types of experiment e.g. a flat coil for dielectric induction phenomena, a cylindrical coil based TMT system for maximum transference of electric power and plasma effects, Tesla’s Colorado Springs TMT system for far-field telluric transference of electric power etc.

The distinction between geometry based phenomena, and displacement based phenomena can be directly compared and contrasted when the TC or TMT system is driven by a linear sinusoidal source, or a non-linear transient impetus. The non-linear transient impetus will reveal displacement based phenomena related to the undifferentiated coherent induction field. The linear sinusoidal drive will reveal phenomena related to the balance of the differentiated induction fields Ψ and Φ, through the balance between the transverse and longitudinal modes, and the tuning and boundary conditions of the longitudinal cavity established in the system. Transverse tuning is about selectively coupling as much energy as possible from the generator to the transmitter, and from the receiver to the load, whereas tuning of the longitudinal cavity and its properties, is about transferring as much energy as possible between the transmitter and receiver.

In summary, this is a vast, and probably one of the most fascinating areas of electrical phenomena, that arise from Tesla coil based systems, and warrants considerable further research, observation, and measurement. Suffice to say for now, I would conjecture that the distinction between the undifferentiated and differentiated induction fields, is in my view key to discriminating between phenomena that relate to displacement (coherent and inner), and those that relate to transference (incoherent and outer). For me the purpose of the Tesla coil is very much as a fine tunable instrument with which to experiment, observe, and measure qualities that will progressively reveal the inner nature and workings of electricity.

For further exploration and discussion on what is presented on this page, please see the Energetic Forum[16].

Cylindrical Coil Design and Construction

This cylindrical coil was designed to be suitable for plasma experiments including induction generator arrangements, transference of electric power, and as a suitable induction pump for various extra coil configurations. The secondary coil was intended to have its fundamental resonant frequency, the lower frequency when coupled with the primary coil, in the 160m amateur band between 1.8-2.0Mc, and the upper frequency as close to, or tunable into, the 80m amateur band at 3.5-4.0Mc. For induction generator experiments it was decided to keep the diameter of the secondary coil close to that originally designed by Dollard.

The period of the turns in the secondary was kept at the empirical boundary of 2 x the outer conductor diameter of the secondary wire, which appears to maximise the Q of the secondary coil, whilst maintaining good coil longitudinal cavity properties by not excessively loading the inter-turn mutual capacitance of the windings. The wire for the secondary is the many stranded outer shield of RG316 coax, in order to minimise losses in the secondary coil through the skin effect, whilst maximising secondary conductor surface area. The outer diameter of RG316 is 2.5mm, and turn period of 5mm was empirically set as optimal for the intended experimental applications.

When driven by a primary with coupling coefficient to the secondary of ~ 0.1-0.3 the lower resonant frequency can become shifted down from the resonant phase change, set by the wire length, by as much as 500kc, and the upper resonant frequency shifted up by as much as 1500kc. This being the case then the resonant phase change of the secondary, from the wire length, would be set at around 2.2 – 2.3Mc. This will arrange with primary tuning, and adjustment of the coupling coefficient, for the lower resonant frequency to be well within the desired 160m band, and the upper to be close to and tunable into the 80m band.

Tccad 2.0 was used for a rapid and approximate indication of the electrical and resonant characteristics of the secondary coil, the detailed results of which are shown below in figure 2. The parameter “Winding Height of Secondary Coil” on the turn period of 5mm, (“Wire Diameter” 2.5mm +  “Spacing Between Windings” 2.5mm), was used to adjust the number of turns in the secondary until the “Approximate Resonant Frequency” and “Secondary Quarter Wavelength Resonant Frequency” were closest to the desired 2.2Mc.

The secondary was arranged to be 24 turns in total, 23 RG316 coax turns + 1 1/8” copper tube shield and capacity turn. This turn is spaced further away from the end of the coax turns to reduce the possibility of high-end discharge to lower turns, and is also intended to shield distortions to the dielectric field of induction at the high-end of the secondary, and particularly when operated in close proximity to another cylindrical coil or extra coil. The shield turn presents a uniform continuous metal conductor surface at the high-end of the coil, with a more uniform charge distribution, and to a limited degree providing some accumulation at the top-end without excessively loading the resonant frequency of the secondary. This capacity turn is included in the resonant frequency calculation on Tccad as it directly impacts the wire length and hence the resonant phase change of the secondary coil.

The primary design was intended to fully fit inside the secondary for maximum coupling experiments, reducing the outer diameter of the primary to 390mm. This does introduce a distortion in the magnetic field of induction as compared with a primary the same diameter as the secondary, and standing-off a physical distance below the secondary bottom-end winding. For the intended experiments the primary was set as a fixed 4 turns of  1/8” copper tube on a turn period of 9mm, and which have 4 fixed taps, and of course a variable tap can be used on the bare copper tube for very accurate tuning adjustments if needed. The fixed taps allow the primary coil to be electrically varied between 1 and 4 turns.

In this case where the intended experiments are firstly plasma phenomena, it was more important to have easily adjustable taps to flexibly change the primary characteristics, than maintain the need for equal weights of conductor in the primary and secondary coils. Even if the copper turn is not electrically used in the current path of the primary, the electrically unused copper places boundary conditions on the fields of induction, and hence must be factored in for experiments that require this balanced boundary condition from equal weights or volumes of conductor e.g. in achieving very high efficiency in the transference of electric power, and for establishing a strong and extended longitudinal LMD mode in the secondary cavity.

For reference, the equal weights of copper (< 3.0Mc) from primary to secondary calculation is as follows:

Secondary wire length for the 23 turns of RG316 coax = 32.52m

Measured unit weight of RG316 outer braid only: 6.150 kg/km

Secondary RG316 wire weight = 6.150 x 32.52 / 1000 = 0.200 kg

Secondary wire length for the 1/8” copper tube single turn = 1.41m

Measured unit weight of 1/8” copper tube: 50.3 kg/km

Secondary 1/8” copper tube weight = 50.3 x 1.41 / 1000 = 0.071 kg

Total conductor weight of secondary coil = 0.271 kg

Primary wire length per turn @ 390mm diameter = 1.23m

Primary turn 1/8” copper tube weight = 50.3 x 1.23 / 1000 = 0.062 kg

Number of turns in the primary required to equal the secondary coil weight: 0.271 / 0.062 ~ 4.4 turns

If we now factor in the weight of the vacuum variable capacitor copper plates and interconnection of the primary to this capacitor, which constitute the parallel resonant circuit of the primary:

Total approximated weight of copper in the capacitor plates and interconnections ~ 0.125 kg

Number of turns in the primary required to equal the secondary coil weight, (including primary resonant circuit):

(0.271 – 0.125) / 0.062 ~ 2.4 turns

Two to three turns of the primary is considered an optimum match to the mid-range tuned position of the vacuum variable capacitor at ~ 600pF, and with a coupling coefficient between primary and secondary of ~ 0.2. The primary inter-connections are made from copper plate, and 8 AWG (1600/0.08) micro-stranded silicone coated wire. The same wire is used to connect both primary coils to the generator for push-push, push-pull, and quadrature drive, and forms a good low impedance, low inductance connection for power transfer between the generator and the primary coils.

Figures 3 below show some of the construction features of the cylindrical coil design, including the support frame interleave arrangement, the secondary coil windings, the primary coil taps and tuning capacitor mounting, and the primary circuit inter-connections.

The overall design and construction of this cylindrical coil provides a simple yet versatile Tesla coil which can be used in a range of different experiments, including plasma phenomena and as an induction generator, and transference of electric power in a TMT system. By extending with extra coils, or by specifically designed primary coils e.g. equal weights of copper, or a Golden Ratio spiral, the useful range of experimental phenomena can be extended to include high efficiency transference of electric power, and telluric transference of electric power in the far-field. The detail of these experiments, phenomena and measurements will be reported in subsequent posts.

Click here to continue to cylindrical coil input impedance – TC and TMT Z11 measurements.


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16. Forum Members, Eric Dollard Official Forum -> Eric Dollard, Post #2819 onwards, Energetic Forum, 2020.