Research website of Vyacheslav Gorchilin
2019-09-10
The condenser and the efficiency of the second kind
In this work, we will offer the most common approach to the methods of the transformation efficiency of the second kind with a capacitor and the means of achieving its maximum value from the point of view of radio engineering.
The condenser is the most mysterious element of electronics. Through it cannot pass normal current conduction, however, it can pass-through AC, it can be duroblade and private capacity, and sometimes at the same time may serve as storage and source of charge. The latter should have unique properties and allow to reach high values, the efficiency of the second kind.

Electrical engineering deals with only two kinds of electricity: voltage source and current source, but source charges there. It is unclear how such a source to operate in terms of circuit engineering and mathematics, where this charge is, for example, in the resistance, and, finally, how to measure it in the circuit? This body of knowledge we have yet to learn.

To start, you need to remember, is defined as the potential energy of the capacitor. This formula is derived from a more General $W_C = \int U \Bbb{d} q \qquad (1.1)$ substituting back the classical expression for charge $U = {q \over C} \qquad (1.2)$ Then integrating we get the energy: $W_C = {q^2 \over 2 C} \qquad (1.3)$ In these equations: $$U$$ — voltage across the capacitor, $$q$$ is the charge $$C$$ is the capacitance of the capacitor. If we reduce the capacitance of the capacitor, when the same charge will increase its potential energy. In figures (1a) and (1b) proposes options for such changes by reducing the linear dimensions of a solitary container. Here we will not consider the energy that is needed for such mechanical efforts, because we now what is important is the principle of change.
 Fig.1. Ways to reduce capacity at the same charge (a-b), diagrams of sources of charge (c-e)
In this work we have considered this approach and concluded that reducing linear dimensions you can come to the ultimate value of the electron radius, which will have a maximum potential energy at the minimum size. A set of such electrons will be called e-gas or electronic plasma. By the way, in the same paper we proposed to consider the electron from the point of view of radio engineering and consider it an ideal oscillating circuit, that the further we are going to do.
It is important to withdraw and reverse the principle: placing the electron in the capacitor, linear size (and hence capacity) is much more electron, we proportionally decrease the potential energy (1.3). But without the condenser we will not be able to use a free electron in the actual circuit.
 Fig.2. Part of the patent N.Dedicated to Tesla's "radiant energy". Patent N685957
The objective will, is to minimize the loss of potential energy when converting the electron gas in the charge on the capacitor. Under the electron gas, we mean one or more electrons are uncoupled with each other and with the surrounding matter the condition. Pontyano also that the ideal electron gas in reality is impossible, so we will have in the future, some to idealize. N. Tesla once described this phenomenon as "radiant energy" (Fig. 2).
The simplest solution to this problem is obvious: you must first obtain electron gas, and then convert it and place it in some capacity. This conversion scheme is depicted in figure (1c) and on its basis we will do the further calculation. U1 in it — the high-voltage source, and EGG — generator of the electron gas. The implementation of such a scheme can have many different variants, but we consider only some of them.
Figure (1d) proposed a variant of the ionic or lamp And diode (ID1), which is two plates, the first of which is connected perpendicular needle, a second plate with a smooth surface. Between the plates is air, which is ionized by the first plate and its needle-like structure, entering on the second gives it its charge. With this plate the charge flows into the capacitor C1. The second option shown in (1e), where the capacitor is charging about the same way, but in this case, the electron gas creates discharger FV1. His discharge must have a special structure, which is N.Tesla was described as the "white glow". He achieved this effect by special designs of the arrester, which has devoted many of its patents.
Now we need to calculate how much energy is lost in such transformations. While we assume an idealized scenario under which the loss on the creation and movement of the electron gas, for example, ionization and migration statstool. Then the potential energy of the electron we can take from this work is $W_{e} = \frac {e^{2}} {8\pi \varepsilon _{0} r_{e}} = {e^2 \over 2 C_e} \qquad (1.4)$ and multiply it by the number of electrons $$N$$, are involved in the process: $W_{g} = N W_{e} = {N e^2 \over 2 C_e} \qquad (1.5)$ Here: $$e$$ is the charge of the electron, $$r_{e}$$ is the classic radius of the electron, $$\varepsilon_0$$ is the absolute permeability dielektricheskaya, and $$C_e$$ — self-capacitance of the electron. It is obvious that the total charge equal to the charge of one electron multiplied by the number: $$q = N e$$ then: $W_{g} = {q e \over 2 C_e} \qquad (1.6)$ the Energy generated in the capacitor C1 is found by the formula (1.3). Then losses in converting the potential energy of an electronic gas in the potential energy of the capacitor will be: $\eta_{2} = {W_C \over W_{g}} = {q C_{e} \over eC} \qquad (1.7)$ Substituting here the formula (1.2): $$U_C = q / C$$, we finally obtain: $\eta_{2} = U_C {C_e \over e} = {U_C \over G} \approx {U_C \over 10^6} \qquad (1.8)$ Here we introduce a new constant $$G$$ with which to compare the voltage on the capacitor C1 after conversion. More precisely, this constant is equal to: $G = {e \over C_e} = 1.02\cdot 10^{6} \, (V) \qquad (1.9)$ It can be defined as the voltage of one electron in a state of the electron gas.
Recall that formula (1.8) was derived under the assumption of an idealized version. In reality, it will be necessary to consider the loss of a job And diodes, discharger, or other transducer element, and the approximate math. The fact that in the approximation $$U_C$$ to $$G$$, the dependence will become a non-linear form. But if we are dealing with voltages up to 100 kV, the formula (1.8), taking into account the losses, it is suitable.

The meaning of the formula (1.8) is very simple: for the minimization of energy losses in the transition of the electron gas in condensator, and hence the maximum values of efficiency, you need the capacitor C1 to charge up to as large as possible values.

With capacitor C1 , we can remove the thus obtained energy, for example, via a threshold element, and then to put it on the chain conversion. But the formula (1.8) shows us the absolute values, but in order to calculate a more or less real boost scheme (1d), we need relative values. The only thing we cannot forget is the relative values should always be within the absolute.
Sample calculation
Let's see, what can be a relative gain for the circuit And diode (Fig. 1d). The exact calculation of such a system is quite complicated, so for now we'll make it rough, and in just one cycle. Under the cycle will understand that the time in which the air ions move from one plate ID1 to another. Then the energy cost of the formation of ions between the plates will be such a $W_{D} = {q^2 \over C_{D}} \qquad (1.10)$ and the potential energy on the capacitor C1 will get this: $W_{C} = {q^2 \over 2 C_{1}} \qquad (1.11)$ In these formulas: $$q$$ is the charge between the plates of the ID1, which is completely transferred to the capacitor C1, $$C_{D}$$ is the capacitance between the plates of ID1, and $$C_{1}$$ is the capacitance of the capacitor C1. We assume that the received energy after the charge of ID1 in C1 we fully recycle load. Then the gain per cycle will be considered as $K_{\eta 2} = {W_{C} \over W_{D}} = {C_{D} \over 2 C_{1}} \qquad (1.12)$ it is Clear that here we do not take into account the energy of ionization and heating of ID1, but the visible results of this scheme: for $$K_{\eta 2} \gt 1$$ is needed to the capacitance between the plates in ID1 was greater than the capacitance of capacitor C1 is at least two times.
It remains to calculate the time of flight of ions between the plates And diodes. It is of the well-known formula for velocity of ions in field a relatively small tension [1]: $v = \mu E = \mu {U \over d} \qquad (1.13)$ where: $$v$$ is the velocity of air ions, $$\mu$$ — the mobility of air ions (table value), $$E$$ is the field strength, $$U$$ is a power supply voltage is U1, $$d$$ — the distance between the plates in ID1. Then the time span is defined like this: $t = {d \over v} = {d^2 \over \mu U} \qquad (1.14)$ after this time, the capacitor C1 must be discharged to the load, the discharge time should be much less than $$t$$. The coefficient $$\mu$$ for air is in the range: $$1.4\cdot 10^{-4} - 1.9\cdot 10^{-4}$$.
The materials used
1. A BRIEF PHYSICO-TECHNICAL REFERENCE. 1, - M.: 1960