'Tesla Tower' — Wireless Power Transmission Station
An electrical charge being conducted through the ground and being returned through the air.
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In principle, without considering specific technical peculiarities, Tesla Tower is helically formed quarter-wave resonator grounded by one tail with distributed parameters, and additional capacity being located in the upper end of the helix.
On the right, you can observe conditional equivalent circuit, where it is especially outlined that the capacity is isolated. According to that drawing, capacity is located between Tower and perpetuity and not between Tower and the Earth as otherwise we would get conventional LC-chain grounded through the Earth).
For the purpose of minimization of stray capacity between the Tower and the Earth, that is, shortcutting LC-chain of the Tower through the Earth, it is necessary to elevate isolated capacity from the ground. Simple assessment demonstrated that it is needed to elevate the capacity to the height, which is equal on its value to several average diameters of such capacity.
At the observation of such condition, capacity between the Tower and the Earth will decrease on its value up to the value, which is comparable with own isolated capacity of the Tower.
It is well known from basics of classic electrical engineering that capacitive and inductive impedance cancel each other in a resonance mode.
Therefore, generator “observes” only active resistance of the resonator. Standing wave with the voltage node in the generator point occurs in the helix. Current loop is located there, as well (at that, voltage loop and current node are located in the resonator’s tail).
More detailed analytical theory of the working principle of such resonator can be found here.
If material located there is too complex to be understood, it is possible to express everything said above in the following way: helically formed resonator of such kind simply represents quarter-wavelength transmission line folded up into helix. That is, standing wave of the current-voltages will exist in such “stretched” transmission line in such resonator at the resonant frequency with the voltage node at the one end of a line and current node on its other end.
Essential different of that from the “stretched” long transmission line is only in amplified inductive and capacitive connection between neighboring segments of such a line due to the their geometrical proximity in helical configuration.
The latter slightly alters resonant frequency and wave propagation speed along the line.
In this Figure, you can see standing waves in long transmissionline.
Waves’ distribution is as follows:
а – of the voltage;
b – that of the current in single-wired transmission line
(figure is taken from the following website)
In other words, the Tower represents current buffer – isolated capacity inside of which reference power generator “brings” charge from the ground.
At that, EM-radiation in terms of radio waves (that is a field in distantly located wave zone of the Tower) is practically absent with regard to our range of working parameters. Let us demonstrate this in details.
There exists such a term as helical antennas in a field of radio physics. Primarily, such term can be related to such helix resonator. However, compared to antennas, electrical length of one turn of the Tower is smaller than wavelength by 1000 to 10 000 times (that is, number of turns can reach up to thousands considering the fact that total length of the coil is approximately equal to the quarter of wavelength).
At that, the greatest part of the currents (current loop) is concentrated in the lower half of the Tower. Hence, such a structure acts as classical conventional concentrated inductivity in terms of external EM-radiation. It is conventional magnetic dipole.
The equation defining radiation resistance of the electrically short magnetic frame (magnetic dipole) with the wavelength denoted as λ is well known (radiation resistance describes the losses of conductor for the radiation of EM-waves, i.e. current power loss for the radiation is considered as formal active resistance losses of which are equal to those spent for the radiation):
(equation 8.148 can be found by checking the link indicated above)
…where d is a diameter of magnetic dipole.
As of the case of N turns, the equation should be multiplied by the factor denoted as N2 (due to the radiation power density being proportional to the quadrate of the amplitude of a frame’s field, i.e. quadrate of the number of the turns in the frame).
Using our parameters such as frequency with the value of 10 kHz,i.e. wavelength of 30 000 m, coil radius being about 2 m, winding length being of 10km, and number of the turns being of 800, we will get the radiation resistance with the value of 0.04 micro ohms.
The latter is insignificantly small in comparison to the losses on the active resistance of a system, which comprises at least 1 ohm.
However, except of tangential constituent of the current in such resonator, there is also axial component (resulting vertical current) because of which the Tower provides radiation of the short electrical dipole for which the radiation resistance is interrelated with the length of dipole denoted as L and wavelength denoted as λ as follows:
(equation 8.81a can be found by checking the link indicated above)
The latter results in the value of about 0.0008 ohm in terms of our parameters and tower’s height being about 30m, which is also insignificantly small in comparison to the losses on the active resistance of a system.
As a result, we can see that both types of radiation emitted from tangential as well as axial constituents of the current are insignificantly small with regard to the losses in active resistances of the Tower’s helix considering that those are upper assessments (as for them, the current value is considered to be constant along all coil turns while in reality the current falls on the sine and there is current node or so-called current zero located at the “hot end” of the coil and real radiation value will be smaller by many times than that of the upper assessments).
So any kind of ideas of the Tower operating as an antenna is absurd (at least, while we adhere the Tesla’s patents and do not exhibit any personal speculations).
The Tower cannot be considered as antenna in its classical understanding. Its radiation, that is, EM-field in the distant wave zone is insignificantly small and the tower can serve only as effective accumulator for charge, which is being brought in and out the ground by the generator at its working frequency.
Therefore, “genial” objections like “you will get conventional helical antenna with very low power transmission efficiency value” as well as any other “objections” based on radiation of such a structure only demonstrate total misunderstanding of the basic principles of radio physics by the opponent.