dRGreen420
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quote:
Engineering analysis of the Colorado Springs Tesla Magnifying Transformer
By Eric Dollard
Preface: the following material and calculations are taken from the Tesla Colorado Springs Notebook. An index of important pages is given at the end.
1) The Colorado Transformer consists in part of a basic quarter wave resonant transformer, referred to in the notes as the primary-secondary structure. The primary circuit is of the balanced, open loop break, configuration. This break in the primary loop gives rise to steep transient waves. This in turn gives rise to a multitude of harmonic travelling waves upon the coiled windings which constitute the Tesla Transformer. This is discussed in “Condensed Intro to Tesla Transformers.” Like did Tesla, we will focus on the sinusoidal, single frequency, distributions.
2) Next is the extra coil. This coil here operates with a propagation constant less than an eighth of a wavelength. Therefore the coil is operating as a simple inductance coil, not as a distributed network. The distributed network capacity of this mode can be expressed as a definite terminal capacitance. Hence the inductance of this coil is adequately represented by its static inductance.
3) Finally is the capacity mast. The effective electrostatic capacity of this mast is given. To convert from C.G.S. “centimeters” first divide by the speed of light squared, in centimeters per second, then multiply by ten to the plus ninth. This gives Farads. It works out to 1.1 times C.G.S. gives picoFarads. How easy.
The capacity of the mast consists of two components, one is the self capacity to earth in per Farads, the other is the mutual elastivity K to the ionosphere in per Farads. The measured mast capacity is a resultant, the square root of the ratio of self capacity, C, to the mutual elastivity, K. The actual values of C and K are unknown. The square root of the product of C and K is the propagation constant. The smaller the value of this constant, the greater is the electro-static coupling to the ionosphere.
4) It should be noted that the earth connection at this location was very poor. It was not adequate for the system neutrals. This gives rise to stray mutual inductance between neutral connections. This also led to travelling waves on the two wire 1000 volt power line that powered the Tesla system. Standing waves in the distant generator windings shorted out these coils burning out the town’s generator station.
In conclusion, the Colorado Tesla Transformer is most basic. An extremely high electromotive force is established through the employment of a large lumped series resonant circuit. This series circuit consists of a static inductance coil, the extra coil, and a static capacitance, the capacity mast. This is a basic LC circuit.
This LC circuit is fed by a constant current resonant transformer as a source of low frequency alternating current energy. The operating frequency is near 45 Kilocycles.
5) The propagation constants and the transmission impedances can be derived from the basic physical dimensions of this system. It is fortunate that we have the “RadioTron Designers Handbook”, Tesla did not. He had no frequency counter, no scope, no W.W.V. time standard, Nothing! Think about this.
6) SECONDARY COIL DIMENSIONS AND CONSTANTS
Diameter: 15 meters
Height: 1 meter
Number of Turns: 17 numeric
Mean Length of Turn: 47 meters
Total Length of Turns: 800 meters
Luminal Wavelength: 3200 meters
Self Capacitance: 1500 picoFarad
Self Inductance: 10 milliHenry
Luminal Frequency: 94 Kc/sec
Free Space Frequency: 64 Kc/sec
Actual Frequency: 43 Kc/sec
Free Space Propagation: 68%
Actual Propagation: 46%
Transmission Impedance: 2500 Ohm
Dielectric Burden: 330 picoFarads
7) EXTRA COIL DIMENSIONS AND CONSTANTS
Diameter: 8.4 feet
Height: 8.0 feet
Number of Turns: 100 numeric
Mean Length of Turn: 8 meters
Total Length of Turns: 800 meters
Luminal Wavelength: 3200 meters
Self Capacitance: 112 picoFarad
Self Inductance: 25 milliHenry
Luminal Frequency: 94 Kc/sec
Free Space Frequency: 176 Kc/sec
Actual Frequency: 116 Kc/sec
Free Space Propagation: 187%
Actual Propagation: 123%
Transmission Impedance: 15 Kilo-Ohm
Dielectric Burden: 26 picoFarads
8) MAST CAPACITANCE EFFECTIVE VALUE:
Measured Capacitance is given approximately at 320 picoFarads
The self capacitance of the extra coil is given as 112 picoFarad.
The total capacitance is hence given,
Total End Capacity, 432 picoFarad
This end capacity is series resonant with a 25 milliHenry inductance coil. This gives rise to a propagation constant, (the resonant frequency) and to a transfer impedance.
9) The propagation constant, or frequency, is defined as the inverse of the quantity consisting of the square root of the inductance times the capacitance, this root then multiplied by two Pi. Hence cycles per second.
The product,
25 milliHenry times 432 picoFarad
Results in a frequency of
47 Kilo-cycles
10) The transfer impedance is given as the square root of the ratio of the inductance to the capacitance.
25 milliHenry divided by 432 picoFarad
Results in an impedance of
7600 Ohm
This represents the output impedance of the Tesla Magnifying Transformer.
11) The basic circuit is shown in figure 1:
http://i168.photobucket.com/albums/u200/johnpolakow/Tesla%20Transformer%20Schematic/TeslaTransformerSchematic001.jpg
In basic terms, a 45 Kc/sec 2500 Ohm source of alternating current energy energizes a large series resonant circuit consisting of an inductance coil and elevated capacity structure. At 45 Kilo-cycles per second, every ampere supplied to the extra coil gives rise to 7.6 Kilovolts at the elevated capacity terminal. The effects of higher harmonics and distributed constants can raise this potential by no more than 50% over the base 7.5 KV. Hereby, for a capacity potential of 1000 KV, the input current to the extra coil must be 132 amperes at 45 Kilocycles per second.
12) This derives the total KiloVolt-Ampere reactive activity of the extra coil in 1000 KV operation, hence, the total activity;
132 MegaVolt-Ampere
This is a substantial activity of 174 thousand horsepower, remembering that this is an average value, the peak value is unknown.
13) In conclusion, the Colorado Springs Tesla Magnification Transformer is a very simple system, no more than a giant series resonant circuit with an approximately sinusoidal waveform rendered asymmetrical by a moderate dampening constant. The extra coil is not operating as a transmission network of distributed constants, but only as a basic inductance coil. Hence the length of wire on the coil is somewhat immaterial. The mast capacitance swamps out the extra coil self capacitance, this suppressing transmission modes of higher harmonics.
This transformer is seen to be somewhat disappointing to the theorist. No fancy travelling wave interaction nor any stupendous harmonic conjunctions, only a Big Series Resonant Circuit. It can be surmised that the Colorado Springs Transformer was incapable of full mono-polar operation, due to the suppression of distributed constants. What is fortunate is that with the material hereby provided the Colorado Springs Tesla Transformer can be scaled down to any convenient size for experimentation. This setup is now quantified, and the mystics can remain silent.
73 DE N6KPH
Reference Index (From Colorado Springs Notes)
Page 43 & 58 Primary Circuit
Page 67 Primary Length
Page 203 Primary/Secondary Dimensions
Page 206 Secondary Frequency
Page 211 Secondary Inductance
Page 260 to 267 Capacity Mast
Page 318 Extra Coil Dimensions
Page 357 Extra Coil Ground Frequency
Page 359 Extra Coil Mast Frequency
Page 363 Extra Coil Free Frequency
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