Tesla coil calculator: coils, topload, coupling, tuning
From the secondary coil to the capacitor bank: the tool calculates inductance, self-capacitance and resonance, the coupling to the primary coil and the matching tuning. The designs are compared by their differences and by components proven in the hobby community.
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Abbreviations and symbols on this page (21)
- SGTC
- Spark Gap Tesla Coil: Tesla coil with a spark gap as the switch.
- SSTC
- Solid State Tesla Coil: Tesla coil with semiconductors (MOSFET or IGBT) instead of a spark gap.
- DRSSTC
- Dual Resonant Solid State Tesla Coil: SSTC with an additionally tuned primary circuit.
- QCW
- Quasi Continuous Wave: DRSSTC with long, ramped pulses for straight sparks.
- VTTC
- Vacuum Tube Tesla Coil: Tesla coil with a transmitting tube as the oscillator.
- NST
- Neon Sign Transformer: current-limited high-voltage transformer for neon tubes, e.g. 10 kV / 30 mA.
- MMC
- Multi Mini Capacitor: capacitor bank made of many identical film capacitors in series and parallel.
- LTR
- Larger Than Resonant: primary capacitor larger than the resonant capacitance of the transformer, usually about 1.5 times.
- OCD
- Over Current Detection: overcurrent shutdown in the driver that protects the semiconductors.
- GDT
- Gate Drive Transformer: small transformer that drives the transistor gates with galvanic isolation.
- IGBT
- Insulated Gate Bipolar Transistor: power transistor for high voltages and currents.
- MOSFET
- Metal-Oxide-Semiconductor Field-Effect Transistor: field-effect transistor switched by the voltage at the gate.
- MIDI
- Musical Instrument Digital Interface: control data for music; a MIDI interrupter makes the sparks play notes.
- UD2
- Universal Driver 2 by Steve Ward: widely used driver board for DRSSTCs.
- RF
- Radio frequency: alternating currents and fields from roughly a few tens of kHz; here mostly 50 kHz to a few MHz.
- k
- Coupling coefficient between two coils, 0 to 1: the share of the magnetic field that passes through both coils.
- Q
- Quality factor of a resonant circuit: 2π f L ÷ R. High = low losses, narrow resonance.
- Lp, Ls
- Inductance of the primary coil (p) and the secondary coil (s).
- Cp
- Capacitance in the primary circuit (primary capacitor or MMC).
- λ/4
- Quarter of the wavelength λ = c ÷ f (c = speed of light). A secondary coil resonates much like a quarter-wave radiator.
- Discharge (bang)
- One firing of the spark gap; the energy per discharge is ½ C U².
1. Design
The five common designs differ in the switch, the tuning and the type of sparks. Select above, compare in the table.
Classic design with a spark gap: a high-voltage transformer charges the capacitor, the spark gap discharges it abruptly into the primary coil. Primary and secondary circuits are tuned to the same frequency and the energy swings across; when the spark breaks off, it stays in the secondary coil.
Neon sign transformer (NST) with safety gap and mains filter; MMC of pulse film capacitors (often CDE 942C, 0.15 µF / 2 kV); primary coil of copper tube; static multi-gap or rotary spark gap; secondary coil of enamelled wire on a plastic tube, aspect ratio 4–6 : 1; toroid of flexible aluminium duct; dedicated RF ground.
| SGTC | SSTC | DRSSTC | QCW | VTTC | |
|---|---|---|---|---|---|
| Switch | spark gap (static or rotary) | MOSFET or IGBT bridge | IGBT bridge | bridge + buck converter | transmitting tube (triode) |
| Tuning | primary and secondary | secondary only | primary and secondary | primary and secondary | primary (tank) and secondary |
| Coupling k | 0.1–0.2 | tighter than SGTC | similar to SGTC, somewhat tighter | above 0.4 | medium |
| Frequency | 50–400 kHz | 100 kHz–1 MHz | usually 40–150 kHz | usually above 400 kHz | a few 100 kHz |
| Sparks | loud, branched; estimate after Freau | continuous or pulsed, shorter | very long, playable via MIDI | straight “swords” | quiet flames, continuous wave |
| Advantages | simple, robust components, long sparks | no spark gap, musical with an interrupter | longest sparks in the hobby field, playable | impressive straight sparks | quiet, continuous wave possible |
| Disadvantages | very loud, ozone, radio interference, spark gap wears | semiconductors are sensitive, sparks shorter than DRSSTC | complex, high currents, faults destroy IGBTs | most demanding design, high stress on the semiconductors | high anode voltage, tubes rare and expensive, heat |
2. Secondary coil and topload
Dimensions of the secondary coil and the topload. The drawing on the right is to scale.
| Turns | 1000 |
| Aspect ratio (length : diameter) | 4.55 : 1 |
| Inductance (Lundin) | 22 mH (Wheeler 21.9 mH) |
| Self-capacitance (Medhurst) | 8 pF |
| Topload capacitance | 21.7 pF |
| Resonance without topload | 379 kHz |
| Resonance with topload | 197 kHz |
| Wire length | 347 m (0.913 × λ/4) |
| Resistance DC / at resonance | 34.4 Ω / 35.8 Ω |
| Quality factor (theoretical) | 761 |
3. Primary coil, coupling and tuning
Flat spiral (0°), cone (e.g. 20–30°) or helix (90°). The coupling is calculated turn by turn from the mutual inductance.
| Primary inductance (Wheeler) | 20.1 µH |
| Outer Ø · height · conductor | Ø 33 cm · 3.47 cm · 6.16 m conductor |
| Coupling coefficient k | 0.156 |
| Required primary capacitance | 32.4 nF |
3.2 cycles until the first complete transfer after 16.2 µs. Tighter coupling = faster transfer, but then the spark gap must quench faster.
4. Supply and capacitor bank
For spark gap coils: neon sign transformer (NST), matching capacitance and MMC of individual capacitors.
| Resonant capacitance (NST) | 9.55 nF |
| LTR capacitance (static spark gap) | 14.3 nF |
| Energy per discharge | 1.43 J · at 14.1 kV peak |
| MMC layout | 15 in series × 1 in parallel = 15 pieces, 10 nF, 30 kV |
| Spark length (estimate after Freau) | ≈ 74.8 cm |
Formula
Secondary: L = µ0 N² A K ÷ l (Nagaoka coefficient K after Lundin), compared with Wheeler L = r² N² ÷ (9 r + 10 l). Self-capacitance after Medhurst C = 0.29 l + 0.41 r + 1.94 √(r³ ÷ l) (inch, pF). Toroid C = 2.8 (1.2781 − d ÷ D) √(π (D − d) d ÷ 4) (inch, pF), sphere 4πε0 r. f = 1 ÷ (2π √(L C)). Primary after Wheeler: spiral r² N² ÷ (8 r + 11 w), cone √((L_helix sin θ)² + (L_spiral cos θ)²). Coupling k = M ÷ √(Lp Ls), M from the mutual inductance of coaxial rings (elliptic integrals). NST: C_res = I ÷ (2π f U), LTR ≈ 1.5 C_res. Spark after Freau ≈ 1.7 √P inch.
Example
Tube 110 mm, 50 cm winding with 0.5 mm enamelled wire: 1000 turns, 22 mH, 379 kHz without topload. With a 120 × 500 mm toroid 197 kHz. Primary coil 8 turns of 6 mm tube, inner diameter 160 mm, 20° cone: 20 µH, k ≈ 0.16, 32 nF for tuning. An NST 10 kV / 30 mA at 50 Hz has 9.5 nF resonant capacitance, LTR about 14 nF.
Notes
- All formulas are approximations for free-standing coils. Walls, floor, primary coil and sparks shift the resonance; final tuning is done with the tap on the primary coil.
- The toroid formula is empirical (±10–20 %). For exact values, measure the frequency: connect a signal generator to the coil and look for the maximum with an oscilloscope or an antenna.
- The quality factor is theoretical (copper and skin effect). Measured values are usually much lower because of the coil form, enamel and surroundings.
- Coupling: SGTC usually 0.1–0.2. Coupling too tightly causes flashovers on the secondary coil and poor quenching of the spark gap.
- Danger to life: mains voltage, high-voltage transformers and charged capacitors kill. Fit capacitors with bleeder resistors and short them before every touch. RF sparks burn and interfere with radio and electronics; operate only with a dedicated RF ground and far away from pacemakers and devices.