Tesla Coils

Tesla coils are among the more exciting physics demonstrations. The presented experiments generally feature wireless energy transfer or sparks of varying length. Because the generated voltage alternates at a high frequency, sparks generally discharge into the air. This effect is often referred to as streamer discharge. I have built many tesla coils over the years. This article will only describe some of my builds and focus on the historic spark gap controlled design.

I built the coil on the right in middle school. It used a blocking oscillator to resonantly drive a small mains transformer. This generated roughly 3kV at a few kilohertz. The transformer output was rectified to feed the classic spark gap tesla coil design. Because the resonant circuits were not matched at all, this build could be more accurately described as an impulse transformer. Still, I don't think this page would be complete without it :).

The other coils were built a few years later. They both feature a neon sign transformer MMC based design with the small coil reaching roughly 0.8m and the big one 1.1m discharge length respectively.

Resonant Circuits

A typical Tesla coil setup consists out of two loosely coupled resonant circuits. A relatively high capacitance and low inductance are used in the primary circuit. In contrast, the secondary circuit employs a low capacitance and large inductance. The secondary inductor is traditionally realized using a large air-core coil, which is the visually defining factor of a tesla coil. Exact frequency matching is required to avoid destructive interference between the two circuits, or, in other words, generate big sparks.

Energy is injected into the primary resonant circuit by pre-charging the capacitor. When the voltage across the capacitor terminals is sufficiently high, a spark gap will break down. The resistance of the spark gap drops drastically and it starts to conduct. The primary LC-circuit is closed and starts to oscillate. Energy is transferred to the secondary side. The voltage quickly rises until the surrounding air's breakdown voltage is reached.

Inductor Design

I have built most of my primary coils as flat spiral type design. The coil is supported using four spacers. I used hvac copper tubing as a conductor. The inductance was calculated using one of Wheeler's formulas. Primary coil taps are adjustable for tuning the primary LC-circuits resonant frequency. A flat inductor is a cost effective design and ensures loose coupling between the resonant circuits. The secondary inductor was wound on a piece of sewage pipe. Since it has many turns, significant parasitic capacitance is formed that has to be considered for frequency matching. In case of the big coil, parasitic effects account for roughly 20% of the total secondary capacitance. Medhurst's formula turned out to provide accurate estimates.

Primary capacitor

I have used Multi-Mini-Cap (MMC) designs in all my Tesla coils. Multiple small capacitors are connected in series to reach the required voltage rating. Several of these capacitor strings are then connected in parallel to match the required capacitance. A parallel resistor is connected to each capacitor for evening out the voltage distribution across the string and discharge any remaining partial charge after operation. The capacitors used must be properly sized for impulse loads or will blow up due to very high surge currents.

Feed Transformer

Typically spark gap tesla coil systems use a primary feed voltage between 5 and 10 Kilovolts. Because the resonance frequency of the LC-circuit is much higher than mains frequency, the capacitor can be connected directly to a mains transformer. The feed transformer needs to be appropriately sized to charge the capacitor such that the spark gap can conduct.

The spark gap was designed to provide constant air flow to aid fast quenching. If the spark gap does not quench fast, energy is repeatedly transferred between primary and secondary circuit.