Nikola Tesla Books
Books written by or about Nikola Tesla
From this a rough idea of the capacity of the coil may be had, resonance being observed when the primary had T = $! {1 \over {16 \times 10^{4}}} $! as above. From above equation we find
C = $! {10 \over 142,336} $! mfd. or in cm.
C = $! {{9 \times 10^{5} \times 10} \over 142,336} $! = $! {{9 \times 10^{6}} \over 142,336} $! = 63.2cm
This is a much smaller value than would be expected from previous approximate estimates. The correctness of the value found depends, among other things, chiefly on the correct determination of the period, for resonance might have been also obtained with a lower or upper harmonic, but this is not very likely to be the case as the vibration was very intense. There were approximately 5000 volts on primary turn. Resistance of coil was 1.56 ohm. From this ω = $! {2 \pi \times 16 \times 10^{4}} $! = 1,004,800 or 106 approx; ωL = 0.014 x 106 = 14,000, $! {ωL \over R} $! = $! {14,000 \over 1.56} $! = 8910 as factor for magnifying e.m.f. impressed; very large.
Colorado Springs
July 11, 1899
Some considerations on the use of “extra coils”. As has been already pointed out an excellent way of obtaining excessive electromotive forces and great spark lengths is to pass the current from a terminal of an oscillating source into such a coil, properly constructed and proportioned, and having preferably a conducting body - best a sphere - connected to the free terminal. In free air the highest economy is obtained with a well polished sphere, but for the greatest spark length - if this be the chief object - no capacity on the free terminal should be used, but all the wire should be carefully insulated so that streamers can not form except on the very end of the wire which as a rule should be pointed. This, however, is not always true. When the apparatus delivers a notable amount of energy the curvature of the end of wire or terminal attached to it should be such that the streamer breaks out only when the pressure at the terminal is near the maximum. Otherwise, very often, when a finely pointed terminal is employed the streamer begins to break out already at a time when the e.m.f. has a small value and this reduces, of course, the spark length and power of the discharge. By careful experimentation and selection of terminal the most powerful spark display is easily secured which the particular apparatus used is capable of giving. When the conditions are such that for the most powerful discharge a terminal of some, relatively small, curvature is needed, the curvature of the terminal can be beforehand calculated so that the discharge will break out at any point of the wave desired, when the e.m.f. at the terminal has reached any predetermined value. The greater the curvature of the terminal the smaller an electromotive force is required to enable the discharge to break out into the air. In Fact, the curvature of the terminal may serve as an indication of the value of the e.m.f. the apparatus is developing and it is often conve-
78
July 10-11
In order to try and increase the secondary voltage of the HF transformer by keeping down the distributed capacity of the secondary Tesla added a third oscillatory circuit, thus obtaining an oscillator with three resonant circuits of which two are tightly coupled*. The third circuit will not necessarily be most strongly excited when its resonant frequency coincides with that of the primary and secondary (assuming these are the same) and the primary and secondary are tightly coupled. If the spark in the primary circuit lasts long, then the tightly coupled primary-secondary system will produce two distinct oscillations, and the third circuit will be most strongly excited if it is tuned to one (strictly speaking to near one) of these two frequencies. On the other hand, if the spark is of short duration the tightly coupled system may oscillate strongest at the resonant frequency of the secondary, and then the third circuit will be excited the strongest when all three have the same resonant frequency. Tesla believed that his system of coupled circuits was producing a single vibration, which under certain conditions is in fact feasible.
July 10
In distributed capacitance, Tesla sees the main obstacle which limits the voltage in the secondary. His assumption regarding the influence of such capacitance he checks now by calculation of a coil model with evenly distributed voltage and capacitances between windings. In order to calculate the active power (for purpose of simplification) he assumes that all energy received by "capacitors" (they represent distributed capacitance) during one quarter period is used up in the second quarter of a period, and so on. In the second half-period, the event is similar, but only the charging is in opposite direction. He thinks that the number of charges (and discharges) is equal to double the number of high frequency current periods.
After mentioning the damaging effect of distributed capacitance, he continues the description of his thoughts on a secondary with thin wire on the same day. He estimates that the induced secondary voltage will be approximately 40% smaller than the ratio between primary and secondary windings, which corresponds to the induced voltage in an open secondary. In our case, however, a current in the secondary circuit will appear which influences the current in the primary, and therefore the induced voltage will have another value.
By adjusting the capacitance in the primary and secondary circuits, he achieves the maximum secondary voltage. How well Tesla knows the physics of the process could be based on the fact that he doesn't lose sight of the influence of the secondary validity factor, and the magnitude of the primary capacitance which determines the amount of power which the source could provide to the oscillator for conversion into high frequency current.
The voltage increase in the secondary, he achieves by addition of a coil with 260 turns wound with wire 2.6mm in diameter. By addition of this coil the oscillator becomes a system with three oscillating circuits, of which two are well linked*. The third circuit does not have to be the most excited, through a strong link with the primary and secondary circuits, when the resonant frequency of the third circuit is matched with the resonant frequencies of primary and secondary circuits (assuming that both of them are the same). If a spark in the primary circuit lasts for a long time (please see app. Fig., 2P-a) then strongly linked system primary-secondary will produce two emphasized oscillations, and the third circuit will be the most excited if it is adjusted on one of two oscillations (strictly taken in vicinity of one of them). If however, the spark in the primary is of short duration, it could happen that with a strong link, the strongly linked system oscillates the most on its own secondary resonant frequency, and consequently then the third circuit would be the most excited when all three circuits are on the same resonant frequency. Tesla assumes that his linked circuits system produces one vibration, and that is under certain conditions achievable if under the term "one" the most emphasized vibration is understood.
For determination of additional coil inductance, he applies the equation for an indefinitely long coil. The coil's self-capacitance he estimates on the basis of known coil resonant frequency, by assuming that it is equal to the reciprocal period value of the primary circuit which he finds from inductance and capacitance of the primary circuit. When with all the calculation of the additional coil validity factor he makes approximations, because he neglects the coil resistance increase with frequency and consequently he gets an unproportionally high validity factor.
* Similar systems were analyzed in 1906 and 1907 by M. Wien, 1907 by C. Fischer and in 1909 by J. Kaiser(46). From these works it can be seen that the effective value of current in a poorly linked circuit will be at maximum if the resonant frequency of this circuit is the same as the other two better linked circuits only when their link is poor.
July 11
By introducing the additional coil in the oscillator circuit Tesla achieved one modification of his oscillator with resonant transformer. by which means he obtained higher voltages. When these voltages exceeded several hundred thousand volts, he had to carefully lay out the elements, and choose very good insulators. Here the instructions are given how to make the terminals in order to obtain longest and most powerful spark along with delaying the flashover to the instant when maximum voltage is reached (or some desired voltage). He suggests the procedure which enables the voltage measurement by means of metal spheres of various radii. He discusses the disadvantages of this method because the spheres introduce additional capacitance which disturbs the resonance conditions in high frequency circuits.
Tesla considers the additional coil extraordinarily suitable for the achievement of "any" voltage. He gives two wiring schematics of this coil for an oscillator high frequency transformer. He claims that with this coil. considerably higher voltages are achieved than with the secondary in poorer linkage with the primary.
Tesla explains this with the fact that the additional coil is not in an inductive link with the primary, and there is no such reaction in the primary which would dampen the oscillation. He doesn't explain how he imagines this coil to be excited and not to react on the primary transformer secondary to which it is directly connected.
The additional coil description is very detailed. Tesla's wealthy experience in coil design is obvious in its full extent. At the end of his considerations he gives the equation for determination of the number of turns for the additional coil on the basis of operation frequency, wire diameter, separation of windings, and a constant which he determines on the basis of experimental results. He checks the equation on one example and obtains a result very close to the experimental results.
