Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 76

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.

* Similar systems were analyzed in 1906 and 1907 by M. Wien, in 1907 by C. Fischer, and in 1909 by J. Kaiser⁽⁴⁶⁾. From their papers it may be seen that the effective value of the current in the loosely coupled circuit will be a maximum if its resonant frequency is the same as that of the other two coupled circuits but if they were loosely coupled.

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.