LOKI: A Self Tuning PLL Based HF Tesla Coil


Update: March 29, 2008: Made some modifications to primary that allow for tuning the primary-secondary coupling.

NEW for January 2007: Go here to get the first release of the technical notes on how I built this class-E audio modulated Tesla coil!

Loki: Mischievous shape-shifting giant from the Norse pantheon who is often associated with fire. While not quite of “god” proportions, this little tesla coil burns hot and can take many forms and put to various uses (e.g. plasma speakers).

First: the usual disclaimer - If you attempt to build HF tesla coils, you do so at your own risk. You need to be aware of the dangers and annoyances that they can produce. Here is a (probably not exhaustive) list of possible hazards and recommendations. Use common sense, please!

  1. Do not, under any circumstances, come into contact with the plasma discharge. It is a high power discharge that is hotter than the surface of the sun and will conduct RF currents into your body. These can cause excruciating, deep burns that will certainly require hospital treatment. It is recommended to enclose the coil in a wire mesh (Faraday) cage to prevent accidental contact.

  2. Be aware that there are potentially lethal high DC voltages present in this circuit.

  3. Do not touch RF output circuit elements when operating this device. Dangerous RF burns can occur.

  4. Use Faraday cage to reduce coupling into surrounding metal building structures. This reduces unintentional radiation (interference) and reduces the risk of burning down your house as a result of induced currents in metal parts of the house structure causing sparks.

  5. Use shielded enclosures and take care to decouple power supply leads from RF (for reducing interference).

  6. Read a bit about good RF practice. You are essentially building a high power radio transmitting circuit. Be aware of good construction practice.

In general, when a tesla coil is first switched on, the resonant frequency is slightly higher than its running frequency. This is because when the coil is running, the plasma at the breakout point behaves like a lossy capacitive/resistive topload. By adding a fraction of a picofarad to the top load capacitance, the frequency shifts by several kilohertz. Since tesla coils which operate above a megahertz of two generally do not have the toroidal or spherical toploads that you find on lower frequency coils, minor variations in capacitance caused by the discharge at the top of the resonator can shift the frequency considerably.

So, on start-up, the signal driving the resonator must have a slightly higher frequency than when the discharge is present in order to guarantee the initiation of the arc. When the discharge is established, the frequency must be reduced a few kilohertz to assure maximum power is delivered to the arc. Furthermore, the frequency will vary as the discharge dimensions change, either as a result of air currents, power level or modulation of the discharge for generating audio (as a plasma speaker).

Fortunately, physics comes to the rescue. When the coil is in resonance, the voltage at the top of the coil will be perfectly 90 degrees out of phase with the current flowing at the bottom of the coil. We can use a phase-locked-loop (PLL) to exploit this phenomenon to auto-tune the coil under a wide range of operating conditions.

The block diagram shows the main subsystems of the coil.

The voltage-controlled oscillator (VCO) runs at 4 times the coil operating frequency (about 19MHz). This allows us to use flip-flops to generate signals at about 4.75MHz with phase of 0, 90, 180 and 270 degrees. The phase comparator is fed directly from the 0 degree output (the reference signal) as well as a phase shifted version of the capacitive pickup signal. The all-pass phase-shifting network can be adjusted for best performance (i.e. when maximum power is tranferred to the coil and with reasonable Class-E amplifier performance). The PLL will always try to keep the phase between the reference signal (0 degree) and the pickup signal at 90 degrees.

This means that the phase shift through the amplifier stage, matching network and capacitive pickup should add up to a total of 360 * N + 180 degrees, where N can be 0, 1, 2,... In practice, the phase delay through these stages is difficult to explicitly state (depends on construction methods, pickup position and matching network tuning, which in trun, depends on the plasma loading of the coil), so some manual “phase tuning” is needed to get good performance.

The first prototype schematic is shown here (click here):

Note the use of an IXDD414 driver chip for the MOSFET. For tuning up this circuit, use 30 volts for the MOSFET Vdd to avoid blowing up your expensive MOSFETS. The series coil in the tuning circuit consists of 12 turns of 1.5 sq. mm enamelled copper wire on a 16mm diameter plastic tube. The coil can be deformed in order to tune for best class-E performance (using an oscilloscope to monitor the drain voltage). Slowly increase Vdd and retune until 100V Vdd is reached. You should be able to achieve 200-250W of spark power with this circuit

A pic of the finished prototype board

The initial test setup. Note the coil in a Faraday cage for safety and interference reduction. The parallel-tuning capacitor is seen on the lower left of the picture.


Scope shot of the drain voltage when everything is well adjusted.

It is very difficult to maintain good class-E operation because it is heavily dependent on the coil loading provided by the top discharge. Serious tweaking of the breakout points and keeping the power level fairly constant seem to be important. More on this soon!

Interesting note: Do not use ferrite core for RF choke on MOSFET drain. Use a good RF powdered iron core like Amidon mix 2 or 7. Ferrite is lossy and will overheat and destabilise amplifier gain as the ferrite loses its magnetic properties as its temperature rises...

Also, applying some of my work in simulating the tesla coil resonator (See this page for the geometry of the coil), I have constructed a model for the single 4 turn primary coil with the aim of studying the input impedance for the unloaded (no arc) coil. This graph shows the input impedance computed by the NEC solver for a lossless coil as well as for a coil where wire losses are present

The black and pink curves are the lossless coil imaginary (reactance) and real (resistance) curves. As we would expect for the lossless coil, the impedance is entirely reactive, since no energy is dissipated. There is a hump in the pink curve at resonance. I am not sure if this a numerical artifact of the NEC model or if we are seeing a minute radiation component to the overall impedance.

The red and blue curves are the resistive and reactive components of the input impedance for the coil where the wire has a finite conductivity (4.7e7S/m: nearly that of copper). The presence of finite conductance wire lowers the resonant frequency a kilohertz or two. The parallel resonance is seen at about 4.705MHz and the series one at about 4.755MHz.

Circuit Models for the resonator

By making educated estimates of equvalent L, C and R we can build a circuit model for the TC resonator that is close to the field model:

The coupling coefficient between the inductors is c=0.19. Be aware that this circuit is for computing the terminal impedance only. Note also that there are other possible circuit models that can be developed (as a parallel resonant circuit, for example). This model does not correctly model the voltage magnification effect of the Tesla coil. For this, a more sophisticated resonator model is needed (like the NEC integral-equation solver used to produce the impedance plots above).

The impedance across the terminals of the 1uH inductor is:

This model can be used in Spice simulations for designing driving circuits. The effects of arc loading can be modeled by using a non-linear capacitance and resistance (derived from empirical arc models) in parallel with the 31.9nF capacitor in the circuit model.

Strongest field at top of coil does not correspond to coupled coil resonance. In fact, by computing the electric field at the top of the coil and comparing the frequencies where the field peak occurs with the points of resonance observed from the feedpoint impedance (input to primary). For the coil with lossy windings:

E-field read on left vertical scale. Impedance is read on the right vertical scale.

The electric field is computed assuming a 50 ohm source impedance and a 1 volt ac source feeding the primary. The electric field peak occurs near 4.715 to 4.720MHz. The parallel resonance (where the resistive part of the feedpoint impedance Re(Z) is maximum and the reactance Im(Z) vanishes) lies at 4.705MHz and the series resonance (where Re(Z) is small and Im(Z) is again zero) is found at 4.755MHz. Hence, the voltage peak at the top does not correspond to the resonant frequencies of the coupled resonator structure! In fact, it lies where the feedpoint reactance nearly takes its minimum value (looks most capacitive). It is for this reason that a matching network is necessary to give optimal power transfer from the final amplifier to the coil.

How do I design a matching network? (This introductory text was presented on the 4HV forum.)

The choice of Lmatch (1.8uH in the schematic) and Cblocking (2700pF) is a bit hit and miss because the it is difficult to calculate the loading from the arc. It generally has to experimentally determined. I started off assuming thet the resonator Q was about 10-20 with arc loading. Assuming that I wanted the real part of the feedpoint impedance to be around 50 ohms (chosen partly for "sentimental" reasons as well as allowing me to use a smaller variable capacitor for tuning). Generally the total inductive reactance of the output circuit should be about 5-8 times the load-line impedance of the transistor. (My case: 100V, 2.2A -> load-line resistance is about 0.5 * 100 / 2.2 = 22 ohms) Including the coil primary and Lmatch, total inductive reactance is about 100 ohms... In practice, my coil Lmatch gives best performance with about 60-70 ohms reactance at my operating frequency. This can be adjusted with the variable cap connected across the primary anyway. The variable cap also assists in transforming the real part of the impedance to a suitable value....when you vary the spark power level, the feedpoint resistance changes.. match can be (almost) restored by adjusting the variable cap. In short, settle on some starting values for Lmatch and Cblocking, Ctune and make an estimate of the primary feedpoint inductance. (I had the benefit of using an advanced simulation to make my estimates.)

The RFC choke is simple... A good rule of thumb is to keep its reactance about 10-20 times the load-line resistance (500 ohms or so). 5 or 6 uH should be enough in your case. Don't overdo it tho'.. You don't want your choke to resonate. Use a powdered iron RF toroid core (no ferrite, Amidon mix 2 or 7 or equivalent should work fine).

I hope to update this page soon with a simple calculator to help in designing a matching network.

Audio Modulation

By using the ubiquitous TL494 chip, a simple and efficient audio modulator can be built. Click here for the schematic.

Similar to the modulation scheme used in the EasternVoltResearch Plasmasonic (found here), I use a “dead-time” pulse width modulation of a 100kHz pulse. Two IRFP460s drive a 1:1:1 trifilar transformer (for isolation and allows transistor drains to be “earthed” easily, i.e. no need for a gate-drive transformer. Ultra fast rectifiers are used on the output. The filter capacitor must not be too large, otherwise you will get too much rolloff of high audio frequencies. (Note: the audio performance is strongly determined by the RF filter elements in the class-E power amplifier stage. In other words, the capacitors and inductors must be sized so the RF is blocked well, but audio rolloff is not significant below 15kHz.)

Here is a photo of the prototype modulator board.

The white cable exiting the left side of the picture is the audio input. Try to keep the audio section well separated from the high-voltage/high frequency sections (the power MOSFETS, etc.) Use double sided boards so a ground plane can be used to reduce EMI and crosstalk. Earthed isolating pads on the component side can also be used for extra interference/crosstalk suppression.

Here is a close up of the transformer.

The two primary windings are easily seen. They are wound in a bifilar configuration to reduce leakage inductance. The primary is wound underneath a layer of electric tape (for extra DC isolation). All windings are with 1.0mm diameter enamelled copper wire.

Here is a movie of the coil in operation!

Things to do:

  1. Nice enclosure

  2. Simulations and theoretical exploration. Ways to optimise the design.

  3. Higher frequencies of operation.

Visit 4HV.org for more details and lots of discussion!

2008-03-29: Finally, I have some time to revisit the design and play with the effects of changing the primary-secondary coupling.

What have I done?

  1. Made a “rotatable” primary coil that fits inside the secondary that allows me to adjust the the coupling between the primary and secondary windings

  2. Made some qualitative measurements of the “sweet spot” that produced large arc power with a minimum of final RF PA transistor heating.

Perhaps some images are the best way to illustrate the modifications.

The thin white rod entering the side of the primary is a fiberglass dowel used to rotate the primary coil inside.

The degree of coupling is greatest when the center axis of the primary coil is aligned with the secondary coil axis. It is minimum when the primary coil axis is perpendicular to the secondary axis. I have not attempted to measure the coupling, but in a relative sense it should depend roughly on the cosine of the angle between the primary and seconadry axis.

Here is a view of the whole resonator structure showing the shunt loading variable capacitor.

By carefully adjusting the coupling and the shunt capacitance, we try to achieve something as close to “zero-voltage-switching” as possible:

Notice that the trace is somewhat ill-defined. This is a result of the arc loading changing the resonant frequency of the resonator. The arc is a flame-like brush discharge that jumps around. The “flame” acts like a top load capacitance that is constantly changing in a chaotic way. The PLL tracks these changes by shifting the VCO frequency to compensate.

Image of the discharge at about 250W of RF power.

Here is a video showing how the modifications were implemented as well as the coil in action. Because of the ability to tune the coupling, I can achieve higher powers with lower final PA drain voltages (which reduces chances of destroying final PA transistor).