Research website of Vyacheslav Gorchilin
2019-03-01
Pulse technology. Special cases. Circuitry
Previously we have considered the algorithm of pulse technology on the bias currents and the most common method of calculating the solenoidal and toroidal coils, which are used here as a reactor. Here we will offer engineering formulas for a more specific structures of the coil and some circuit solutions.
 Fig.6. Solenoidal and toroidal coils
Engineering formulas differ from the General minimal number of unknown parameters, have a more simple form and usually approximate. However, they are the most convenient way to quickly count any data.
Solenoid without core
To calculate the inductance of the solenoid (Fig. 6a) without core [2] we take an approximate formula, derived by H. Wheeler $L = 10^{-6} {D\,N^2 \over k + 0.44}, \quad k=\frac{\ell}{D} \qquad (4.1)$ and connected it to (3.9-3.10) of the third part. It: $$D$$ is a diameter of the coil, $$\ell$$ is the length of the winding, $$k$$ — form factor of the coil (the ratio of the length of the winding to the diameter). Then the increase in efficiency will be so: $K_{\eta2}= 1.7\cdot 10^{-7} {D\,C \over (k + 0.44)\,T_0^2} \qquad (4.2)$ and the condition of its sverkhelastichnosti so: $T_0 \lt 4.1\cdot 10^{-4} \sqrt{D\,C \over k + 0.44} \qquad (4.3)$
In works [3-6], you can read about the evolution of formulas to calculate self-capacitance of the coil. We can offer an approximate formula Medhurst, its pretty good timing in a given range: $C = D \left(8 + 11\,k + 27/\sqrt{k} \right) 10^{-12} \qquad (4.4)$ Here again we should recall that in our calculations used the international system of units SI [7].
The solenoid core
Here we assume a ferromagnetic core, which is equal to the length of the winding or more than she did. Then as $$\ell$$ will be the length of this core, and as $$\mu$$ is its relative magnetic permeability. The inductance is considered by the classic formula [1]: $L = 9.9\cdot 10^{-7}\, {\mu\,D^2\,N^2 \over \ell} \qquad (4.5)$ and the formulas (3.9-3.10) are transformed in the following way. Increase efficiency: $K_{\eta2} = 2.9\cdot 10^{-8}\, {\mu\,D^2\,C \over \ell\,T_0^2} \qquad (4.6)$ the Condition of sverkhelastichnosti: $T_0 \lt 1.7\cdot 10^{-4}\,D \sqrt{\mu\,C \over \ell} \qquad (4.7)$
For torroid
In contrast to the solenoid, calculate the self-capacitance of toroidal coils (Fig. 6b) is not possible, it will have to either measure or to pick up empirically. But the calculation of its inductance is quite affordable by the formula [1]: $L = 2\cdot 10^{-7}\,\mu\,h\,N^2 \ln(D_2 / D_1) \qquad (4.8)$ where: $$h$$ — core height, $$D_2, D_1$$ — outer and inner diameters, and $$\mu$$ is its relative permittivity. Then the formulas (3.9-3.10) are transformed in the following way. Increase efficiency: $K_{\eta2} = 3.4\cdot 10^{-8}\, {\mu\,h\,C \over T_0^2} \ln(D_2 / D_1) \qquad (4.9)$ the Condition of sverkhelastichnosti: $T_0 \lt 1.85\cdot 10^{-4} \sqrt{\mu\,h\,C \ln(D_2 / D_1)} \qquad (4.10)$
Power
For a calculation device will be necessary for the calculation of the output power. This can be done, if we know the frequency of oscillator $$f_G$$, which switches the keys SW1 and SW2. Then, the pump power (required power) is how the energy of one pulse from the formula (3.6) multiplied by the frequency $P_1 = f_G\,C\,U_0^2 \qquad (4.11)$ and the output power just damnaged to increase efficiency: $P_2 = K_{\eta2} P_1 \qquad (4.12)$ of Course, such a calculation is appropriate if the observed initial condition, when the conduction current is not allowed. If the pulse length is still large and the conduction current appears, then you need to separately calculate the balance of power in the classical formulas, and then to add them to (4.11-4.12), respectively. In this case the overall efficiency will be different: $K_{\eta} = {P_2 + \mathcal{P}_2 \over P_1 + \mathcal{P}_1} \qquad (4.12)$ where: $$\mathcal{P}_1, \mathcal{P}_2$$ — expended and the output power calculated for the conduction currents.
Circuitry
The simplest device that can make full use of the pulse technology on the bias currents, of course, is quite well-known Tesla coil [8]. To him the primary winding of the inductor consists of several turns of relatively thick wire, periodically connects the capacitor is pre-charged high voltage. The connection is through a spark gap that Tesla has devoted a lot of his patents and gave great value. The secondary winding of the transformer secondary not only in circuit design and structural plan, but in response to the pulse. Its task is to dispose a magnetic field obtained by the displacement current due to the short front of the pulse.
The discharger can generate sufficiently steep pulse edges, and can give odds even to modern electronic keys — its analogs. Therefore, it is still used in their schemes to researchers of free energy. But we should not forget about modern high-speed devices, especially the avalanche processes. Next, we will not dwell on the method of supplying voltage and even on the way of formation of the impulse on the coil-reactor: this is a separate large topic. On future schemes, as before, the momentum will formirovatsya key SW1, which is closed for a short time, preventing the conduction current.
 Fig.7. Some circuit solutions for the pulse technology on the bias currents. In figures 7b and 7c, the left part of the diagram is the same as for 7a
In figure 7a, the capacitor Cq is charged through the inductor Lq from the voltage source B1, and then through the switch SW1 discharges to the reactor L1. Nagoski if the resistance R1 is large, and the voltage B1 is relatively small, the key SW2 is not placed, and the load is connected directly to the reactor. The disadvantage of this scheme is low powered and quite large losses in a closed SW1.
More sophisticated schemes contain elements of SW2. For example, these losses will be less if the gap is load install varistor RV1 (Fig. 7b), which will limit the current through the load when closed the key SW1. But the internal capacitance of the varistor may still be part of the energy in this moment miss. Therefore, the best solution is instead to install high-speed diode VD1 (Fig. 7c) with low capacitance and super fast recovery time. And if you use high voltage and relatively high resistance load, the diodes must be high voltage.
As a reactor you can use the motor winding DP1 (Fig. 7d). Because for normal operation the voltage on the winding has to be supplied constantly, the contacts SW1 almost all the time must be closed, rasikas at short time intervals. The interval should appear in the EMF of self-induction, and then again closes the contact SW1 and the coil of the motor, the rise time of the pulse, is converted in the reactor. Slightly complicating the diagram, you can use the self-induction EMF on the production of useful work; no wonder, Tesla has drawn attention to two-phase motors. If DP1 is powered by AC, the break/close of its circuit need to the maxima of strain. It is obvious that any engine is not suitable, because the design of some of them are made so that with an increase in pulse, most of the energy can go to housing or to offset so necessary self-capacitance of the winding.
One of the experiments on the pulse of technology is offered here: the work of the current transformers on the bias currents.
Of course, that technical solutions can be a great many and here we brought only some of them. The only important thing is observance of principles and conditions-pulse technology for proper operation of its constituent elements. Prior calculation and presented in this work. It is based on well-established mathematical models of Maxwell and other scientists, which allowed the authors to develop simple engineering formulas.

The materials used
1. Wikipedia. Inductance.
2. Wikipedia. Solenoid.
3. The details of the radio contours, calculation and design. V. A. Volkov. 1954
4. A. J. Palermo. Distributed Capacity of Single-Layer Coils.
5. G. Grandi. Stray Capacitances of Single-Layer Solenoid Air-Core Inductors - Grandi, Kazimierczuk, Massarini and Reggiani. 1999
6. David W Knight. The self-resonance and self-capacitance of solenoid coils.
7. Wikipedia. The international system of units.
8. Wikipedia. Tesla Transformer.