2017-06-06

Some algorithms of switching of two solitary tanks

In this note we show some algorithms of switching of two solitary vessels to increase the efficiency of the second kind. All the equipment of such compounds is based on the model of a charge having a vector character, and differing from it energy model with a scalar expression. In fact, it is the manipulation of different levels of space-time, which can give the system energy gain. As a distant analogy can give an example of energy when a transition of an electron from one atomic orbit to another, lower.

To climb far into the jungle we will not, and only remember these two models of school physics course [1]. \[Q = C\,U, \quad Q_0 = Q_1 + Q_2 + ...\qquad (4.1)\] This model charge. It shows that the charge equals the capacitance voltage. The second property, the charge can be divided into several smaller, but we are not divided, in total, it will still be \(Q_0\). \[W = {Q^2 \over 2\,C} \qquad (4.2)\] Is a model of the potential energy of the capacitor. It shows the quadratic dependence of the energy of the charge and inverse proportional to capacitance. Since then, we apply these models to a secluded capacity [2], the connection of two such capacitors, one of which charged and the other is not, give a simple redistribution of charge between them: \[Q_0 = Q_1 + Q_2 \qquad (4.3)\] where: \(Q_0\) is the initial charge on one of the capacitors to their connections, \(Q_1\), \(Q_2\) — charges of the capacitors after connection. Based on all of the above, move on to the algorithms for joining two containers that are shown in the following figure:

From the figure immediately shows that the energy transfer from the high voltage source HV to the load Rn, compounds isolated capacitances C1 and C2 can have at least two important for us algorithm. First, when the first key SW1 is closed, after its opening — key SW2, and after his opening — closes the key SW3. The second algorithm: initial simultaneously the closure of the keys SW1 and SW2, and after their opening — circuit of the key SW3. These two algorithms we next consider.

The first join algorithm

In this case, after circuit SW1 charges the capacitance C1, and after the circuit SW2, the charge is distributed between C1 and C2. Let this distribution is expressed using the coefficient of \(k = Q_1/Q_2\), where \(Q_1\), \(Q_2\) is the charge on C1 and C2, respectively, after the circuit SW2. Then, the total charge \(Q_0\), transferred to C1 after closing SW1 will be expressed as \[Q_0 = Q_1 + Q_2, \quad Q_0 = Q_1 (1 + 1/k) = Q_2 (1+k) \qquad (4.4)\] After opening SW2 on C2 remains charge with a potential energy \(W_1\), which subsequent the closure of SW3 will be passed to the load Rn: \[W_2 = {Q_2^2 \over 2\,C_2} = {Q_0^2 \over 2\,C_2 (1+k)^2} \qquad (4.5)\] After a full cycle, we need again to charge C1 to a certain charge, which will represent the difference between \(Q_0\) and \(Q_1\): \[\Delta Q = Q_0 - Q_1 = {Q_0 \over 1+k}\qquad (4.6)\] And this, in turn, suggests that recharge will be spent the following energy: \[\Delta W = {\Delta Q^2 \over 2\,C_1} = {Q_0^2 \over 2\,C_1 (1+k)^2}\qquad (4.7)\] To compute the energy saved by this algorithm is now enough to compare the received energy to the C2 after opening SW2 with the energy spent for recharging: \[K_{\eta2} = {W_2 \over \Delta W} = {C_1 \over C_2} \qquad (4.8)\] As you can see, this algorithm gives an increase in efficiency of the second kind by the relation of the two vessels, completely independent of the distribution coefficient \(k\) and other parameters.

The second join algorithm

This algorithm differs from the first in that the keys SW1 and SW2 are closed and open simultaneously. This means that at the same time now recharged and two capacitor hence formula (4.7) will acquire the following form: \[\Delta W = {\Delta Q^2 \over 2\,(C_1+C_2)} = {Q_0^2 \over 2\,(C_1+C_2) (1+k)^2}\qquad (4.9)\] and the energy gain will become: \[K_{\eta2} = {W_2 \over \Delta W} = {C_1+C_2 \over C_2} \qquad (4.10)\] apparently, the second join algorithm is more efficient than the first. And even more enhance the effect by constructing a specific surface of the capacitor C2. You can read about it here.

The implementation of the algorithm

The most obvious implementation of the first algorithm is to replace the switches SW1-SW3 in the gaps. The disadvantages of this device are also immediately visible: the complexity of adjusting the clearances of arresters, their harmful radiation and small life, and also the necessary high resistance and simultaneously a high voltage load.

A more advanced implementation of the algorithm presented on the left. As a high-voltage source to charge capacitor C1, L1 here is a Tesla transformer (TT). The diode VD1 are required to charge separation and may consist of not only a semiconductor pillar, but the vacuum diode; there are also other non-standard variants of its execution. The inductor TT, the optimal strategy is to apply short pulses.

The discharger FV1 here is an analog key and SW2 can be implemented in different ways, directly from the discharger to the ion layer between the capacitors. The capacitor C2 and the coil L2 form a second receiving TT down the winding which is made by removal of energy in the load Rn. It is obvious that the operation time of ion channels in the arrester FV1 must be namogo less than the time constant of the circuit L2C2, i.e. \[t_i \lt \sqrt{L_2\,C_2} \qquad (4.11)\]

__The materials used__