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Nikola Tesla Books

Books written by or about Nikola Tesla

Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 59

July 2-3, 1899

Now it is evident that when the relation between p1, Lp and Cp exists, which is here implied, the current passes through the system as if there would be no inductance, hence insofar as the circuit including the break, C1 and L1 is concerned the system LpCp will comport itself as if it consisted of a short wire of inappreciable resistance, the primary being generally made of stout short conductor - therefore, in estimating the quantities of the circuit C1L1b the compound system LpCp may be neglected since it will have little influence upon the period under the conditions assumed, and we may then put C1 = $! {1 \over {p^{2} L_{1}}} $! when resistances are, as always before, negligible.

Since C1 is known we can determine L1 because

L1 = $! {1 \over {p^{2} C_{1}}} $! = $! {1 \over {p^{2} {{8 \pi M} \over {P'^{2} p_{1}}}}} $! = $! {{P'^{2} p_{1}} \over {8 \pi M p^{2}}} $!

Presently then all the quantities are known for determining the constants of circuit LpCp from the two equations:

Lp Cp = Ls Cs
Lp Cp = L1 C1 . . . . . . . . . . III.

Colorado Springs

July 3, 1899

In experiments with the secondary as last described, fairly good resonance was obtained with 15 jars on each side of the primary. A length of wire No. 10 - 170 feet - was covered with intense streamers. The capacity - total - was 7.5x0.003=0.0225 mfd. Lp was approximately estimated 36x7x104 cm. (six primary turns in series). From this T = $! {4.836 \over 10^{5}} $! as calculated. This gives n = $! {1 \over T} $! = 20,7000 per sec. approx. With this vibration λ was nearly 9 miles or $! {λ \over 4} $! = 2.25 miles. Actually, there was only one mile of secondary wire but owing to the large capacity (distributed) in the secondary the vibration was much slower than should be inferred from the length of wire. We may estimate the ideal capacity, which associated with the inductance of the secondary would give a vibration of the above frequency. Since there was resonance we have:

T = $! {4.836 \over 10^{5}} $! = $! {{2 \pi \over 10^{3}} \sqrt{{5 \times 10^{7} \over 10^{9}} C_{s}}} $!

Taking the inductance of the secondary as being 5x107 cm. and from this

Cs = $! {23.34 \over 20,000} $! = roughly $! {1 \over 1000} $! mfd. more exactly 0.0012 mfd. or 1080 cm.

But we may approximately estimate capacity in another way taking the wires in pairs as a condenser. This would give Cs = $! {{A \over 4 \pi d} \times 40} $!, there being 40 pairs since there

59

Source:
by Professor Aleksandar Marinčić

July 2

Here Tesla gives the calculation of values for the spark gap oscillator in the fullest detail so far. However, the analysis does not include all the magnitudes relevant to the functioning of the oscillator, e.g. the primary/secondary coupling of the transformer and the distributed capacitance of the secondary. The power equation is also not fully explained and justified. However, by means of this approximate calculation Tesla did get a valuable rough guide relatively quickly and easily.

Source:
by Professor Aleksandar Marinčić

July 2

From that which has so far been given in segments, he finally formulates completely as a method as to how to perform the approximate calculation on the oscillator in Figure No. 1. For the purpose of clarity we will repeat Tesla's calculation method:

  • the designed oscillator wavelength is chosen;
  • on the basis of wavelength the secondary coil wire length is determined as one quarter of the wavelength;
  • secondary inductance is determined on the basis of known wire length and chosen coil shape;
  • for most efficient operation the capacitance at the open secondary terminal has to be such that Cs= 1/p2Ls, by neglecting the losses;
  • the inductance and capacitance of oscillator primary circuit are determined on the basis that the condition of equal own primary and secondary frequencies is met: LpCp = LsCs. Normally Lp is much smaller than Ls so that the winding ratio of primary and secondary Np/Ns is much smaller than 1.

In procedure we have shown, there is no mention about mutual link between primary and secondary. Secondary distributed capacitance is neglected as well. With the oscillator shown in Figure No. 2, the arcing device is outside of primary circuit LpCp and this according to Tesla enables the achievement of less dampened oscillations in the primary circuit and less current through the arcing device. Under assumption that at the operation frequency circuit LpCp is in resonance, the current 'i' is considerably smaller than current i2. Capacitance C1 (which appears in Figures 3 and 4 as 
well) is determined so that it can accumulate the entire energy which can be transmitted from the network via the supply transformer. At discharge of C1 accumulated energy is converted to energy of high frequency currents. Additional condition for C1 is given by equation II.

Source:
by Professor Aleksandar Marinčić

July 3

The distributed capacitance of the secondary windings is difficult to determine. It depends on the coil diameter, the dimensions of the wire and the insulation and the winding pattern. In a single-layer coil it is due mostly to the capacity between neigh boring turns, and this is the way Tesla calculated it. He considers a greatly simplified model in which it is taken that the parasitic capacity per turn is equal to A/4πd, where A = rπl, half the surface area of the wire in one turn, and d is the distance between turns. The capacitance is calculated as that of a plate condenser of area A and gap d with air between the plates. This model is open to a good many criticisms, but it must not be forgotten that Tesla had to find some solution, whatever its shortcomings. It is also not correct that the total inductance and capacitance of the secondary circuit with the “additional coil” are additive, but Tesla was himself aware that this was guesswork, and often mentions the words “roughly”, “estimate”, etc.

In an earlier calculation (see June 20th) he had started from the primary circuit and worked out the values for the secondary, whereas here he attacks it from the other end: from the resonant frequency of the secondary circuit and the known primary inductance (one turn) he finds the required capacity of the primary circuit. He then checks whether this capacity can be used with an LF transformer of the given power. The formula is approximate, but gives a good rough guide for the power in the mains transformer. The peak power rating of the transformer must be even greater than the value found because the condenser is not charging all the time but only in short pulses.

Source:
by Professor Aleksandar Marinčić

July 3

Secondary distributed capacitance is one of the Tesla oscillator elements which cannot be determined easily. This magnitude depends on coil diameter, wire size and its insulation and coil winding method. At one layer coils it originates mainly due to influence of adjacent windings and Tesla calculates it so. He ultimately simplifies the model and takes that parasitic capacitance per turn is equal A/4πd, where A=rπl - ½ of one turn wire area, and 'd' is distance between turns. According to this model, capacitance is calculated as for a plate type capacitor of area A and distanced between plates with air insulation. There are a number of disadvantages of such a model, but it should not be forgotten that Tesla is looking for the solution. It is not correct also that he considers in the secondary circuit with "additional coil" all inductances and capacitances added together, but Tesla is aware that all this is just guessing and he frequently mentions words as "approximately", "estimate" and "similar".

Contrary to one previous calculation (please see June 20) when Tesla started with primary circuit and calculated the secondary, now he does the opposite; on the basis of secondary circuit resonant frequency and known primary inductance (one turn) he determines the primary circuit capacitance. After that he checks whether the found capacitance is allowed to be used with regards to the transformer power of low frequency. The applied equation is approximate, but it is good for orientational analysis of network transformer energy balance. Maximum transformer power has to be larger than the found one, because the capacitor in the primary is not charged all the time, and then only in short impulses.

Contents

Introduction
June 1 - 30
July 1 - 31
August 1 - 31
September 1 - 30
October 1 - 31
November 1 - 30
December 1 - 31
January 1 - 7
Commentaries

Appendices: I, II

Images

Glossary

Lowercase tau - an irrational constant defined as the ratio of the circumference of a circle to its radius, equal to the radian measure of a full turn; approximately 6.283185307 (equal to 2π, or twice the value of π).
A natural rubber material obtained from Palaquium trees, native to South-east Asia. Gutta-percha made possible practical submarine telegraph cables because it was both waterproof and resistant to seawater as well as being thermoplastic. Gutta-percha's use as an electrical insulator was first suggested by Michael Faraday.
The Habirshaw Electric Cable Company, founded in 1886 by William M. Habirshaw in New York City, New York.
The Brown & Sharpe (B & S) Gauge, also known as the American Wire Gauge (AWG), is the American standard for making/ordering metal sheet and wire sizes.
A traditional general-purpose dry cell battery. Invented by the French engineer Georges Leclanché in 1866.
Refers to Manitou Springs, a small town just six miles west of Colorado Springs, and during Tesla's time there, producer of world-renown bottled water from its natural springs.
A French mineral water bottler.
Lowercase delta letter - used to denote: A change in the value of a variable in calculus. A functional derivative in functional calculus. An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function.
America's oldest existing independent manufacturer of wire and cable, founded in 1878.
Lowercase lambda letter which, in physics and engineering, normally represents wavelength.
The lowercase omega letter, which represents angular velocity in physics.