Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 69

July 8

From observing the behaviour of his oscillator Tesla came to an interesting conclusion concerning the shape of the conductor of the primary winding, i.e. that a strip conductor was better than a wire of circular cross section because all other conditions being the same it did not get so hot. He believed that there was a special reason for this “not yet satisfactorily explained”. Since the dimensions of the strip conductor are not known we cannot work out the reduction in resistance relative to a circular section conductor due to the skin effect. The surface area of a strip will always be greater than that of a round conductor, the more so the flatter the strip: for a width to thickness ratio of 10:1 a strip will have about 1.8 times more surface area; this could effect a considerable reduction in resistance, which would explain, at least in part, the phenomenon which Tesla discovered.

In connection with coils, a problem to which Tesla often returned was that of the velocity of propagation of phenomena through the circuit. In order to achieve the maximum voltage across the secondary terminals without the addition of capacitance Tesla considered that the length of the windings should be equal to a quarter of the wavelength. This would be perfectly correct in the case of a straight conductor with one end grounded. Such a system, when excited, would certainly have the maximum voltage at the free end, but its magnitude would depend greatly on whether the conductor were horizontal (when radiation is small, so that the Q-factor of the resonant system is high) or vertical (when radiation is efficient so that the damping is high). With a helical conductor as in Tesla’s oscillator, radiation is low as with a horizontal conductor, so that high resonant voltages are possible unless they are reduced by parasitic capacity. In fact, helical winding increases the distributed inductance and capacitance so that the velocity of propagation of current through the coil is reduced, which means that the wire must be made shorter to achieve maximum voltage across the terminals. If the secondary is terminated with a capacitive load (e.g. a metal sphere) the winding length must be still further reduced in order to maintain the same resonance conditions. Tesla took both these effects into account in designing the secondary.

Figures 1 - 8 illustrate several ways of reducing the distributed capacitance of the secondary. The solution of placing the turns far apart (Fig. 6) is still used today when it is necessary to reduce parasitic capacitance.

July 8

Detailed consideration of high frequency transformer is actually a resume of obtained experiences and theoretical thoughts. In order to achieve the goal - the machine of higher power and voltage, Tesla looks for methods to optimize all oscillator details; arcing device, primary and secondary inductances, mutual inductance and distributed secondary capacitance. In the analysis he makes the distinction between the device which would be used for high power transmission at a distance, and that one where small power is required as e.g., for transmission of messages. For the first type a high frequency transformer would be made in a similar way as for low frequencies (therefore with a strong link), and for the other type, high secondary voltage would be achieved by the use of over voltage on the secondary circuit which is poorly linked with primary circuits. In the latter case a maximum validity factor pL/R is required and minimal secondary capacitance.

By considering the oscillator operation, Tesla came to one interesting conclusion on the primary coil conductor shape. He discovered that flat cross-section conductor is better than a circular cross-section conductor, because it gets heated less under the same operating conditions. It is considered that there is some reason for that "which hasn't been satisfactorily explained as yet". As the shape of a flat conductor is not known, it is not possible to calculate the reduction factor of conductor resistance in relation to circular conductor resistance of the same cross-section due to skin effect influence.

The area of a flat conductor is always larger than the area of a circular conductor of the same cross-section and length, and the flatter the conductor is, the more that fact is emphasized. For the ratio between width and thickness of conductor of approximately 10, the conductor has approximately 1.8 times larger area, and therefore considerable resistance reduction could occur which is, if not entirely, then at least, a partial explanation of the event which Tesla discovered experimentally.

The problem Tesla frequently turns back to, related to coils, is the question of event propagation speed through the circuit. Tesla considered that in secondary circuits, where the maximum voltage at coil terminals without additional capacitance has to be produced, it is necessary to wind the coil with wire one quarter of wavelength long. This would be quite correct when a straight conductor one quarter of wavelength would be taken and be grounded at one end. When such a system would be excited, at the open end the maximum voltage would be achieved, but its magnitude, at constant excitation, would strongly depend on whether the conductor is horizontal (when radiation is small, and therefore the resonant system with high validity factor would be achieved) or vertical (when system radiates efficiently, and it behaves as a resonant damped system). When a spiral conductor as at Tesla's oscillator was applied, the radiation is very slight as with a horizontal conductor, and therefore the high overvoltages are possible, unless they are reduced by distributed capacitance. Actually, with a spiral conductor the longitudinal inductance and capacitance are increased, and consequently the current propagation speed in the coil is reduced, which requires the shortening of the wire in order to achieve maximum voltage at the coil's terminal. When a capacitive load is added at the end of the coil (e.g., the metal sphere), the coil length has to be shortened even more in order to maintain the resonant conditions in the system. Both these effects Tesla took in account when designing the secondary.

On figures 1-3 several systems are shown, by which the secondary distributed capacitance reduction is achieved. The solution with separated turns is frequently used even today (Fig. 6) when the distributed capacitance influences the circuit operation in which that coil exists.