**HF Tesla coil
experiments**

Welcome
to Bill's HF tesla coil page. Here I document some of my modeling and
experimental studies of Tesla coils that operate above 2MHz. Please
do not attempt to construct this circuit yourself unless you are
familiar with (and plan to observe) stringent safety procedures for
high power RF and high voltage. This circuit can generate hundreds of
watts of RF power which can cause dangerously severe RF burns as well
as possibly illegal intereference, if operated improperly. It is
** HIGHLY** recommended
to enclose the coil in an RF-tight Faraday cage for your safety as
well as to prevent harmful intereference. Do not, under any
circumstances, allow the spark to contact your body. You will find
yourself in a hospital emergency room with a dangerous and painful RF
burn. (The penetrating nature of these burns are known to cause
gangrene, if left untreated.) So...please be careful....and have fun!

Also, see the related page on Class-E amplifiers as well as this 4HV forum thread.

**Contents
of page:**

Simulation of coupled TC resonator

A better design: the Armstrong oscillator

**First
attempt: 4.5 MHz Royer power oscillator**

As a study of the feasibility of using commonly available power MOSFETS for high-power HF oscillator use with a helical resonator at several MHz, I constructed a Royer power oscillator using a pair of Toshiba 2SK2698s.

The
secondary consists of 86 turns of insulated 1.5mm^{2 }insulated
copper wire on a piece of 90mm diameter PVC drain-pipe. The length of
the winding is about 25m. The primary consists of 4 windings
(center-tapped) of 1.5mm^{2 }insulated copper wound over the
base of the secondary. The gate-drive windings are each a single
small loop inside the base of the secondary resonator, like this:

The completed resonator looks like this (connected to the drive circuit):

The drive circuit is assembled inside of a die-cast aluminium box (which can be mounted with a heat sink)

Notice the red decoupling capacitors and the (black) tape-wrapped choke. Keep the source connections as short as possible. (Here, they are connected directly to the die-cast box.)

To reduce coupling into the power supply and surrounding metal objects, the entire coil is enclosed in a wire mesh Faraday cage. Interestingly, it also seemed to improve the sparks!

It is important that all joints are well soldered. Measurements with the o-scope and a ferrite loop antenna indicate 40-50dB attenuation as a result of the wire-mesh enclosure one meter from the coil.

First light!

Close-up of the sparks...

Using a sensing loop like this

We see the oscillator waveform:

It is very strong and rich in harmonics when the sense loop is near the base of the coil (inside the Faraday cage.) I estimate the peak voltage across the drain-source terminals to be in the range of 100-120V. The single turn sense-loop voltage measured by the o-scope is about 50V. Hence, the two-turn primary voltage is likely more than 100V. I did not have the courage to connect my scope directly to the MOSFET drain (I would not recommend it, unless you use a good 10x or 100x scope probe..).

The power generated by the individual transistors seems to be somewhat unbalanced. The transistor whose drain is connected to the lower primary seems to run hotter than the one connected to the upper primary (and is, of course, susceptible to burn-out..) To find out why, we need to know more about the resonator's behaviour.

**Simulating
the Tesla Coil resonator (with coupling)**

In order to build a proper oscillator circuit model, we need to know how feedback is generated by the resonator and how the power transistors pump power into the oscillations. This calls for a full field model of the Tesla coil resonator.

Here is the geometry of the coil to be simulated in the initial study:

A simulation for the open coil and the enclosed coil will be carried out to

Determine the interwinding coupling coefficients between the two primary windings and the reonator,

Find (confirm) the resonant frequency of the resonator,

Study the effects of the external shield on the resonant frequency.

For this study, we will try NEC (an integral-equation based antenna solver) to generate the modes on the open resonator. this approach should reduce the assumptions needed to correctly model the coil as a proper helical resonator. Note that the simulation will not (initially) account for loading caused by the arc discharge at the top.

**NEC
model of coil geometry**

The driving circuit is modelled using two 50 ohm sources attached to the primary windings of the coil. Given this situation, the so-called S-parameters (scattering parameters) are conveniently computed. To characterise the resonator, first set V2 to zero and V1 to one (see the following figure) and use NEC to compute the currents in the whole system.

The orientation of the primary windings look like this:

When we know the terminal currents, it is possible to deduce the reflection coefficient (S11) and the transmission coefficient (S21) given the source/load resistances and input voltages.

S11 = 1.0 - 100.0 * I1

S21 = 100.0 * I2

To compute S12 and S22, we just swap voltage sources, i.e. make V1=0 and V1=1. This means

S12 = 100.0 * I1

S22 = 1.0 - 100.0 * I2

Be
careful. S11, S21, S12, S22, I1 and I2 are *complex* number
quantities, so use the appropriate arithmetic.

After running our simulation, we can see what the currents look like as a function of position along the resonating helix.

The upper curve is the current on the helix near it's resonant frequency of 4.775 MHz (which turns out to be very close to the measured experimental resonant frequency of 4.828MHz). The lower curve is the current on the helix 75kHz below resonance. We see a sharp decrease in helix current as frequency moves slightly off resonance as a result of its hi-Q properties. (More on this later.) This current profile looks similar to data generated by the Tesla Secondary Simulation Project. However, the NEC simulation generates a current “hump” in the secondary where the primaries overlap. It turns out that this seems to depend on the type of loading used on the primaries. Low-impedance loads/sources cause a depression while higher impedance (50 ohm) loads/sources generate the depression seen in the work of the TSSP. More investigation is of course needed for full characterisation.

A spreadsheet of the primary terminal currents and S parameters was generated from the results. At this point it is important to say that we should be conscious of the limitations of the simulation. In the final three columns labelled “deviation from ideal power conservation and reciprocity” (symmetry of the S-parameter matrix for reciprocal circuits...like our Tesla-coil), a measurement of the error in the simulation is possible. Deviation from ideal for power conservation is indicative of possible radiation from the coil into free space, so it can be difficult to infer true error from this, although we expect not more than a few percent power loss to radiation. Reciprocity is a more stringent test. here we see an error of no more than a few percent relative to the maximum value of S21. Given that the first resonant frequency was well approximated with NEC, it should be possible to build a reliable circuit model for modeling our resonator using the SPICE simulator.

**Plots
of S11, S22 and S21 near the fundamental resonance**

There are several important points to make as a result of these initial simulations:

The phase angle of S21 at 4.775MHz (secondary resonance) is not 180 degrees, i.e. the ideal push-pull coupling that we expected. Instead, it sits at 155 degrees. External circuit elements (or parasitic loading) will evidently make up the difference in phase to achieve stable oscillation.

S11 and S22 have generally the same computed magnitude (as they must, in theory for a reciprocal circuit), but the phase angles are very different, as a result of different levels of coupling (and leakage inductance). The computed input impedance of port 1, lower primary) is less than 50 ohms (real part of S11<0). This could be the origin of the observed transistor overheating.

It could be tricky to get a properly balanced Royer oscillator to work reliably as a result of the different coupling achieved by the two primaries. Other primary configurations or the use of impedance transforming tuning networks may yield better results. In particular, single-sided driver will probably work better.

**A
better, simpler design: The Armstrong Oscillator**

Basically, the conclusion is that a single-sided (single transistor) variation of the Armstrong oscillator. The secondary is coupled to the drain circuit through a four turn primary. A small “tickler” loop provides the feedback that drives the MOSFET gate, as shown in the schematic.

This circuit will exhibit class-E operation with over 90% efficiency by careful choice of the drain capacitor and gate bias. (Technically, the gate bias is very low; just enough to start the oscillator. You will need to adjust the values of the bias resistors to weakly turn on the transistor, i.e. provide about 100-200mA quiescent drain current.)

It turns out that this topology performs better than the original Royer. Operating with 3 amps from a 60V power supply, the transistor will run for some minutes, relying only on the aluminium enclosure for heatsinking. A modest heatsink would allow continuous operation, perhaps at even higher power.

**Simulation
of oscillator**

A spice simulation of the above circuit confirms efficient class-E operation.

Notice
the ringing during the transistor on-time. This is a typical effect
of package parasitics.

Actual experimental operation yields this waveform:

We
see a slight ringing effect. It is less pronounced than the spice
simulation, probably as a result of radiation and other losses which
the Spice model does not take into account.

Frequency op operation is about 4.71 MHz (it wanders over 20KHz or so as a result of varying arc loading).

The complete circuit is disarmingly simple:

The arc is even bigger than the first attempt with the Royer oscillator. Input power is nearly 200 watts.

Notice
the gate coupling loop inside the coil tube. It must be squashed
almost flat to avoid overdriving the gate.