How we built Tesla's coil apparatus and why

Faculty of Electrical Engineering

University of Belgrade

Jovan Cvetić, cvetic_j@etf.bg.ac.yu

Principal Tesla coil configuration

Faculty of Electrical Engineering

University of Belgrade

Tesla’s patent

Faculty of Electrical Engineering

University of Belgrade

Tesla coil general properties:

• High-voltage two-coil resonant transformer. • The coil is usually tuned by changing primary circuit inductance (3 to 10 turns) and the spark gap switching frequency.• Coupling between the coils is loose (0.1-0.2)

• The maximum energy transferred to the secondary circuit is 50 to 80 percent of the energy initially stored in the primary capacitor.

Faculty of Electrical Engineering

University of Belgrade

Theory and Model (1)

• According to Kirchoff laws:

Faculty of Electrical Engineering

University of Belgrade

Theory and Model (2)

• Analytical solution:

• Abbreviations

Faculty of Electrical Engineering

University of Belgrade

Secondary circuit (1)

• The secondary coil inductance was measured using RLC meter at 1kHz and compared to semi-empirical Wheeler’s formula:

Height

H [cm]

Diameter D [cm] H/D Wire diameter

(double enameled)

No. of turns

96.5 25.0 3.86 1.0(1.1) 887

The secondary coil geometrical parameters used in calculations

Wheeler’s formula:

Measured: Ls=45.5mH

mH

Faculty of Electrical Engineering

University of Belgrade

Secondary circuit (2)• In order to lower resonant frequency of secondary circuit, the distance between the toroidal terminal and the top of the coil is varied. The following pictures are showing self resonant frequency, and top capacitance versus distance from the secondary coil

• The geometrical parameters are chosen in such way that self-resonant frequency of secondary circuit is 107.8kHz

Faculty of Electrical Engineering

University of Belgrade

Secondary circuit (3)• The total capacitance consists of:

the coil self-capacitance Cs,

and the capacitance of toroidal

top, Ct.• The secondary self-capacitance:Medhurst’s formula:

Measured: Cs=18pFCs=KD=17.8pF

• The top capacitance:Semi-empirical formula:

• The total capacitance:Formula:

Measured:

Ctot=56pF

Ctot=50pF

pF

Faculty of Electrical Engineering

University of Belgrade

Secondary circuit (4)• The secondary resistance is measured by RLC meter at 1kHz giving Rs=15.5

Method Ls[mH] Cs[pF] Rs[]

calculation 44.9 17.8 15.5

Measurement (1kHz)

45.5 18.0 15.5

The summary of secondary coil electrical parameters

Faculty of Electrical Engineering

University of Belgrade

Primary circuit (1)

• Capacitance value is usually between 0.05F and 0.2F. We chose 93.7nF, measured with RLC meter at 1kHz.• The shape of the coil is Archimedes spiral composed of 11 turns of 6mm copper pipe.

• The coil inductance versus number of turns was measured with RLC meter at 1kHz .

• Since the self-resonant frequency of secondary circuit is 107.8kHz, the optimal number and inductance of the primary coil turns are 5.5 and 28H, respectively.

Faculty of Electrical Engineering

University of Belgrade

Primary circuit (2)• The measurement of the primary coil resistance, which varies significantly with frequency, is difficult. • The resistance was measured without secondary circuit using output waveforms of self-resonant dumped oscillations on impulse input. • The decay time is given with =2L/R which yields R=0.6 at 100kHz.

Faculty of Electrical EngineeringUniversity of Belgrade

Rotary spark gap

Faculty of Electrical Engineering

University of Belgrade

Coupling coefficient

• The mutual inductance and coupling coefficient are measured for various positions and number of turns of primary coil. (from 3 to 11).

• For the secondary self-resonant frequency of 107.8kHz and adopted number of turns Np=5.5 of primary coil, one obtains k=0.15 for coupling coefficient.

Faculty of Electrical Engineering

University of Belgrade

Output - simulation vs. measurement (time domain)• PSPICE simulated output voltage (right), compared to the measured signal acquisitioned via GPIB (down).

Faculty of Electrical Engineering

University of Belgrade

Output - simulation vs. measurement (FFT)• PSPICE simulated output voltage (right), compared to the measured signal acquisitioned via GPIB (down).

=100.5kHz

=116.9kHz

Faculty of Electrical Engineering

University of Belgrade

Conclusion

• Although Tesla transformer should be analyzed using model with distributed parameters, this paper shows it can be successfully modeled with lumped element approach.

• The results obtained from PSPICE and MatLab simulations are in good agreement with experimental data.

Faculty of Electrical Engineering

University of Belgrade

Applications

• Rotary spark gap tuning

• Electro dynamical modeling of rotary spark gap

• Development and simulation of Tesla coil twins

Faculty of Electrical Engineering

University of Belgrade

Acknowledgments

Professor Radivoje ĐurićProfessor Milan SavićProfessor Acc. Aleksandar MarinčićVladimir MalićMarko Cvejić and Milan Milošević – The Tesla coil EM modeling teamIvana Milovanović, Uroš Mitrović and Nebojša Malešević –The Rotary spark gap team