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.