Tesla Transformer
Tesla Transformer is a special type of transformer with air core. Tesla invented and used Tesla Transformer in his laboratory as a generator of high frequency (HF) and high voltage.
The first patent of Tesla Transformer dates back to 1896, although it is similar to the generators used since 1891/92, when he held the famous lectures first in America and then in Europe.
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| Fig. 1: One of Tesla’s patents of HF oscillator from 1896 |
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| Fig. 2: Basic electric shema of Tesla transformer |
The name that is used today has got in the early of 20th century, when many researchers in their laboratories used this transformer for experimentation. It is used to create the high voltages (up to 10 MV and over), generating frequencies of several tens kHz to over MHz.
Tesla Transformer (TT) power ranges from a few tens of watts (for demonstrative purposes) to several tens of kW (special effects). Tesla used it for different experiments with electric lighting with one or without wires, to create phosphorescence effect, for generating X-rays, for showing a variety of high-frequency phenomena in gases, electrotherapy, and wireless power transmission. TT has been used commercially in spark gap radio transmitters until the twenties of the 20th century. TT is now used mainly for educational purposes as well as for special effects in movies and theaters. Small TTs are used as a gas leak detectors in vacuum systems, initiators of the discharge, gas ionization and so on.
The first rigorous mathematical analysis of TT is performed by Oberbeck (Anton Oberbeck) in 1895 and Drude (Paul Drude) in 1904 and 1905. The exact theoretical analysis is only possible in the case of the circuits with no resistance and other effects that lead to losses (skin effect and proximity effect of the turns).
As afore-stated, the TT consists of two galvanic ally separated windings, primary and secondary, which are magnetically loosely coupled, Fig. 1. Tesla's original electric configuration comprises the high-voltage, low frequency transformer T (operating at network frequency inputting the energy in the system) a high-voltage capacitor C1, spark gap SG (stationary or rotary type) and the primary winding L1 (a few of turns) on the primary side. The transformer has a large flux leakage (so to withstand the shorting of the transformer during operation). The secondary side consists of a long coil with a great number of turns. The configuration of these elements is shown in Fig. 1.
The winding L1 (a few turns of thick wire, usually in the form of Archimedes' spiral enabling the maximum distance from the top of the secondary coil E), via the spark gap SG and the capacitor C1 makes the primary circuit of TT. Secondary circuit of TT consists of the secondary winding L2 (one-layer, densely wounded coil) and the secondary capacitance C2) which is formed as the sum of internal capacitance of the coil L2 and capacitance between the toroidal metal cap E on the top and the earth.
Due to the specific way of working, the voltage at the ends of the TT is not proportional to the ratio of numbers of turns of secondary and primary coils. The output voltage can be calculated from the energy conservation low neglecting ohmic losses. Input energy in the capacitor C1 is equal to
The way of working of this resonator transformer differs from ordinary network transformer although the physical law (Faraday's law) which is in the base of their work is the same. The network transformer works at industrial frequency (50 or 60 Hz) and it has well-coupled primary and secondary coils. Actually, one aims to realize the best possibly coupling of coils close to unity and therefore the transformer core is made of iron. As a result, the network transformer continuously transfers the energy from primary to secondary.
The TT works at thousands times higher frequencies compared to network transformer, due to heavy losses the iron core is not used, a coupling of the primary and secondary windings is only 20% or less. This slows down the transfer of energy between the primary and the secondary. The TT does not transfer the energy continuously, the energy being collected in the primary capacitor C1 is transferred to the secondary capacitor C2 in several oscillations. In order to achieve this, the oscillation in the primary and the secondary circuits must be tuned that is the primary and the secondary circuits must have the same resonant frequency. As the natural oscillating frequencies of both circuits are given by
where L1 and L2 are the inductances and C1 and C2 are the capacitances of the primary and the secondary circuits, respectively. It follows the condition for the tuning of the circuits ( f1 = f2)
where V2 is the output voltage on capacitor C2. If one neglects the losses in both coil turns this energy is equal the input energy ( 12EE=). Using already derived condition for resonant circuits, one obtains
Although it can be concluded from the last expression that the voltage on the secondary TT can be increased indefinitely by increasing the capacitance of the capacitor C1 (or decreasing the capacitance of the capacitor C2) this does not happen in the practice. Namely, the TT is usually designed in such a way that before achieving the maximum output voltage V2 the breakdown in the air occurs (depending on the configuration of toroidal top metal caps E). The capacitor C2 is discharged and the whole process of charging the capacitor C2 is repeated closing the spark gap SG.
If the spark gap is static (with a constant distance between the electrodes) it closes (that is the breakdown occurs between the electrodes with the appearance of an arc) when the voltage on the capacitor reaches the breakdown voltage in the air, Fig. 1. The number of breaks is determined by the frequency of the supply voltage (the number of interruptions is two times higher than the frequency).
If the spark gap is of a rotary type, one set of the electrodes are usually placed on rotating disk approaching or moving away from other (stationary) set. The breakdown occurs when the electrodes are close enough and when the voltage is high enough. The number of interruptions is determined by the speed of the rotation of the motor, which carries the electrodes and the number of the electrodes. The number of breaks per second can be significantly greater than the network frequency.
The TT generates the damped quasi-periodic oscillations. It is a simple, inexpensive high-voltage, high-frequency source. The shortcoming of TT is limited possibility of independent changes of the amplitude of the output voltage and the operating frequency because these two parameters are interconnected.
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| Fig. 3 – The TT manufactured at the School of Electrical Engineering in Belgrade in 2006. Output voltage is around 700 kV, working frequency is 100.5 kHz, power 2.5 kVA. |
In Fig. 3, the TT built in 2006 at the School of Electrical Engineering in Belgrade (in honor of the 150th anniversary of Tesla's birth) is shown. The primary coil is in the form of Archimedes’ spiral while the secondary coil is densely wound, number of turns is 970, for 100.5 kHz operating frequency, the length of the secondary wire is 746 m. The coil height is 1m with the diameter of 24.5 cm. The ratio of capacitance in the primary circuit and the total capacitance of the secondary is around 1000. The coefficient of coupling of the coils is around 0.2, the efficiency is 0.83.
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| Fig. 4 – The time dependence of the output voltage on the secondary coil of the TT (discharge without sparks on the secondary capacitance). The amplitude-modulated shape of the secondary voltage can be seen (beating). |
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| Fig. 5 – Spectral analysis of voltage on the secondary TT in accordance with the graphics of secondary voltage in the time domain, in Fig. 4. Three dominant frequencies 100.5 kHz, 116.9 kHz and 8.2 kHz can be observed. The greatest power in the spectrum is achieved at the frequency 100.5 kHz. |
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| Fig. 6 – The TT made at the School of Electrical Engineering in Belgrade for the purpose of the opening ceremony of the 25th Summer Universiade 2009. Project leader Prof. Jovan Cvetić. Installation is attended by academician Prof. A. Marinčić, SANU gallery curator B. Božić and BSc. V.Malić. The total height of TT is 6m, while the length of the secondary coil is about 2m. The output voltage of 1.5 MV, the operating frequency is 52 kHz at input power of 10 kVA. |
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| Fig. 7 – The discharges with the length of over 3m at the top of TT during the ignition of the University torch at the opening ceremony of the 25th Summer Universiade 2009 in Belgrade |
In Figs. 4 and 5 the voltages on the secondary coil in the time and frequency domain are shown. Due to the loose coupling of the primary and the secondary the modulated oscillations occur. In the real case of large output voltages, the discharge occurs at the maximum voltage in the first modulated period of the oscillation, Fig. 4. All the energy of the TT, stored in the secondary capacitance is discharged and spent on electromagnetic radiation and heat. There are three dominant frequencies of oscillations, Fig 5. The calculation of the TT is done in accordance with the dominant frequency, in this case 100.5 kHz.
