1. How we built Tesla's coil apparatus and why
Faculty of Electrical Engineering
University of Belgrade
How we built Tesla's coil apparatus and why
Jovan Cvetić,
Principal Tesla coil configuration

2. Tesla’s patent Faculty of Electrical Engineering
University of Belgrade
Tesla’s patent

3. Tesla coil general properties:
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 ( )
The maximum energy transferred to the secondary circuit is 50 to 80 percent of the energy initially stored in the primary capacitor.

4. Theory and Model (1) According to Kirchoff laws:
Faculty of Electrical Engineering
University of Belgrade
Theory and Model (1)
According to Kirchoff laws:

5. Theory and Model (2) Analytical solution: Abbreviations
Faculty of Electrical Engineering
University of Belgrade
Theory and Model (2)
Analytical solution:
Abbreviations

6. Faculty of Electrical Engineering
University of Belgrade
Secondary circuit (1)
The secondary coil geometrical parameters used in calculations
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 inductance was measured using RLC meter at 1kHz and compared to semi-empirical Wheeler’s formula:
Wheeler’s formula: mH
Measured:
Ls=45.5mH

7. 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

8. SLIKA KOLA Secondary circuit (3) The total capacitance consists of:
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.
SLIKA KOLA
The secondary self-capacitance:
Medhurst’s formula:
Cs=KD=17.8pF
Measured:
Cs=18pF
The top capacitance:
Semi-empirical formula: pF
The total capacitance:
Formula:
Ctot=56pF
Measured:
Ctot=50pF

9. Faculty of Electrical Engineering
University of Belgrade
Secondary circuit (4)
The secondary resistance is measured by RLC meter at 1kHz giving Rs=15.5W
The summary of secondary coil electrical parameters
Method
Ls[mH]
Cs[pF]
Rs[W]
calculation
44.9
17.8
15.5
Measurement (1kHz)
45.5
18.0

10. Faculty of Electrical Engineering
University of Belgrade
Primary circuit (1)
Capacitance value is usually between 0.05mF and 0.2mF. 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 28mH, respectively.

11. 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 t=2L/R which yields R=0.6W at 100kHz.

12. Faculty of Electrical Engineering University of Belgrade
Rotary spark gap

13. 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.

14. Output - simulation vs. measurement (time domain)
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).

15. Output - simulation vs. measurement (FFT)
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

16. 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.

17. Applications Rotary spark gap tuning
Faculty of Electrical Engineering
University of Belgrade
Applications
Rotary spark gap tuning
Development and simulation of Tesla coil twins
Electro dynamical modeling of rotary spark gap

18. Acknowledgments Professor Radivoje Đurić Professor Milan Savić
Faculty of Electrical Engineering
University of Belgrade
Acknowledgments
Professor Radivoje Đurić
Professor Milan Savić
Professor Acc. Aleksandar Marinčić
Vladimir Malić
Marko Cvejić and Milan Milošević – The Tesla coil EM modeling team
Ivana Milovanović, Uroš Mitrović and Nebojša Malešević –The Rotary spark gap team