Nikola Tesla Books
Books written by or about Nikola Tesla
although the capacity is charged up to a much higher potential, but the consideration shows why with a large distributed capacity a very high pressure can not be obtained on the free terminal. All the electrical movement set up in the coil is taken up to fill the condenser and little appears on the free end. This drawback increases, of course, with the frequency and still more with the e.m.f.
In accordance with the preceding, an experimental coil of No. 31 wire (No, 30 not being on hand) was wound on the secondary frame. In the first experiment 14 1/2 turns were coiled up. The results were disappointing and for some time mystifying. The induced e.m.f. ought to have been 14 1/2 times the primary less 40% of total as before stated, but it did not seem so. Finally it was recognized that, as the capacity of the new secondary was very small, the free vibration of the coil was very high hence no good result could be obtained. The capacity in the primary was now reduced until to all evidence resonance was obtained, but the results were much inferior to what might have been expected, probably because $! {pL \over R} $! was small owing to large resistance. One of the reasons was, however, that the capacity in the primary was too small to allow a considerable amount of energy to be transmitted upon the secondary. To better the conditions, one of the balls of 30" diam. was connected to the free terminal; this allowed a greater number of jars in the primary to be used but the capacity of 38.1 cm. was by far too small to secure the best condition of working. The resonating condition in secondary was secured with approximately 7 jars on each side of the primary and when the ball was connected with about 14 jars.
The capacity of the secondary was estimated to be 40cm. and the inductance approx 15 x 106 cm.= $! {15 \over 10^{3}} $! henry.
Note: In these estimates I consider not the actual distributed capacity, but an ideal capacity associated with the coil.
This gave period of secondary roughly:
$! {T = {2 \pi \over 10^{3}} \sqrt{{10 \over 10^{3}} \times {40 \over {9 \times 10^{5}}}} = {{2 \pi \over 10^{7}} \sqrt{600 \over 9}} = {20 \pi \over {3 \times 10^{7}}} \sqrt{6} = {2 \pi \over {3 \times 10^{6}}} \times 2.45 =} $!
$! {= {4.9 \times \pi \over {3 \times 10^{6}}} = {15.4 \over 3 \times 10^{6}}} $! or about $! {{1 \over {195 \times 10^{3}}} = T} $!.
From this n= 195,000 per second. This vibration was far above that of the primary circuit working under favourable conditions, that is with the full number of jars. As the thin secondary did not yield any satisfactory results a coil was now associated with it. It was one used in some experiments before, having 260 turns of cord No. 10 (okonite) wound on a drum 2 feet in diam. and 6 feet long. The total length of wire was 1560 feet and the capacity of the coil (as above) 1530 cm. This coil was connected to the free terminal of the secondary and the free end of the coil was placed vertically on the top of the same and in the prolongation of its axis. Fairly good resonant rise was obtained on the free
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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.
