COMPUTER BASED SIMULATION

Although Tesla coils are relatively basic systems in terms of component count, their operation is often far from simple. In each stage of the Tesla coil system there are quite complex interactions caused by only a few components.

In the charging circuit the connection together of the ballast inductor and tank capacitor creates a resonant circuit. The behaviour of this LC circuit is familiar to many in the frequency domain, and its steady state characteristics are also well defined by mathematics. However, when a spark gap is added to the charging system the analysis becomes more complicated. We are now faced with a system which is resonant and contains a non-linear switching component ! What is more, we are often interested in voltages and currents with respect to time, rather than with respect to frequency. Add to this effects such as inductive-kick and saturation, and it becomes obvious that a mathematical analysis of even the simplest of charging circuits is not so simple at all.

The Primary and Secondary coils present a similar situation. In isolation , the primary and secondary circuit behaviours can be represented by simple differential equations. However, when the two coils are brought together, they interact due to magnetic coupling and the mathematics instantly takes a turn for the worse.

The behaviour of these systems can actually be represented very accurately by mathematics. The problem is that the number and complexity of the calculations makes manual analysis quite difficult. The solution is to use a computer program designed specifically for this purpose.

The PSpice simulator package produced by Microsim is a piece of software which works as follows:

1. You draw an electrical schematic of the system which you want to study,

2. The computer package converts the schematic into a mathematical model,

3. The computer rapidly calculates the complex simultaneous equations that model your circuit,

4. The computer converts the results of the maths back into voltages, and currents which relate to the schematic,

5. Any voltage, current, power waveform etc. can be requested and will be displayed on screen.

A typical Tesla coil system is actually relatively easy for a simulation package such as Microsim to process. Usually the computer will take around 20 seconds to do all of the calculations and present the results !

The advantages of computer based simulation for the Tesla Coil designer are numerous:

1. Simulation allows quick evaluation of different ideas. For example, the effects of different capacitor sizes or different rotary speeds can be evaluated in a few minutes without risk of damaging any real components. Gut feelings are OK, but running something through a simulator first can highlight potentially costly oversights.

2. Simulation allows the system to be optimised by altering parameters until the best performance is achieved. This is often difficult to do in practice due to limited availability of different HV capacitors, inductors etc. After the simulation results are satisfactory, the appropriate parts can be purchased with some degree of confidence in the design.

3. Simulation avoids the need to do maths. It is almost always quicker to simulate than calculate. (The simulation will be right, which is more than can be said for my maths !)

4. Simulation allows any parameter to be measured. For example, you could choose to measure the voltage at the top of the secondary, or the current waveform in the primary circuit of the TC. In practice such measurements are very difficult to perform safely and without affecting the behaviour of the system.

5. Once the simulation is complete, there are a massive range of functions which can be applied to the results. For example RMS currents, average power levels, power factor and even frequency content can be displayed instantly.

Modelling an actual TC

I have found that computer simulations represent Tesla Coil behaviour well and give results which are remarkably close to actual measurements performed on real systems. The key to achieving accurate results is to specify the system as accurately as possible in the initial schematic. You must include winding resistances and stray capacitances etc. If these are not included the simulator cannot take them into account, and the results will be inaccurate.

When simulating a Tesla Coil system I break the system down into two circuits. The first one is the charging circuit, which is simulated with a large step time (100us.) The tank capacitor is charged as normal but discharges into the low resistance of the spark gap model (switch). The large time step can be used here because there is no oscillatory ringdown when the spark gap fires. This allows several seconds of the relatively slow charging cycles to be simulated quite quickly. From this simulation I obtain information about the peak capacitor voltage, power throughput, supply VA and efficiency.

I then simulate one bang of the actual Tesla Coil primary and secondary interaction using a separate schematic with a smaller step time (100ns.) In this simulation a charged tank capacitor is discharged into the primary winding once. This simulation provides information about peak voltages, currents and timing of notches etc. This allows me to experiment with things like coupling coefficient, and quench times.

The two circuits can be combined, but the simulation will run slower, and I prefer to concentrate on one area of the design at a time. I think that the low frequency "charging part" and the high frequency "Tesla Coil part" have little interaction, and occur over such different time scales that they ideally lend themselves to separate simulation runs.

Modelling the HV supply,

 In the charging circuit I usually model the power supply as an ideal AC voltage source, with ballast inductance and winding resistance in series. This contains all the functionality required. It is accurate if done correctly, and runs quickly on the simulator. The example opposite is for a 10kv 100mA neon sign transformer. The 10kv source represents the open circuit voltage of the transformer. The 5000 ohms is the resistance of the secondary winding, and the 318 Henries is the leakage inductance obtained from the equation: L = V / ( 2 x pi x 50 x I)

In cases where a power transformer is used with primary ballasting, the primary ballast inductance is multiplied by the turns ratio squared in order to get the leakage inductance for the simulation.

See section on ballasting for more information.

Note that this approach does not take into account the primary resistance of the neon transformer or the small magnetising current needed to energise the core. In practice these parameters do not have a massive effect on the results. However, a full transformer model could be used if the best possible accuracy is desired.

PITFALLS,

Although simulations are usually fairly accurate, the designer needs to be aware of the areas in which the simulator is not so accurate:

1. Simulators do not include a spark gap model. The spark gap is often modelled by a switch in series with some resistance. Unfortunately the spark gap has a very complex behaviour and is difficult to model accurately. For this reason, the primary waveforms lack the linear decay caused in practice by the incremental resistance of the spark gap. Bursts of VHF noise are also observed at zero crossings in practice but are absent in the simulation results. There is much room for improvement over a simple switch in the area of spark gap modelling.

2. Simulators do not model the behaviour of streamers attached to the toroid. (However, Terry Fritz has done considerable work in this area, and has managed to include the effects of streamer loading in some of his simulations. I recommend including his excellent streamer model if attempting to estimate secondary voltages with any accuracy.)

3. Simulators do not take into account such things as core saturation, or dielectric breakdown. A simulator may say that your tank capacitor has 10MV across it, but in practice it would breakdown long before the voltage gets that high !

4. Simulators do not predict spark length. If only.

During the design of my most recent Tesla Coil I relied heavily on information obtained from simulation in order to optimise the rotary spark gap and charging circuit. I think that the effort was worthwhile. The problems that I had in practice were almost all mechanical in nature. Electrically the system performed as expected, and spark performance was very good for the size of the system.

SIMULATION FILES,

I have included a set of schematic files which can be downloaded and run in the Microsim package. This saves you from having to draw the schematics yourself. You can change component values, voltages, timings etc and re-run in order to observe whatever effects you wish.

The evaluation version of the Microsim 8 package can be downloaded here. (Approx. 16MB so it may take some time over the telephone !)

To download the actual schematics, right-click the animated schematic box and select Save Target As…