DC TESLA COIL DESIGN
This page discusses the application of a DC supply to Tesla Coiling. This page covers the simple resistive charging arrangement and contains a link to the more complex DC resonant charging topology. The latter was used by Greg Leyh in his Electrum coil design.
Although the title says "DC Tesla Coil Design", the Tesla Coil itself is still inherently an AC device. The tank capacitor still sees a polarity reversal during ringdown, regardless of the type of supply used to charge it. However, there are several benefits to using a DC supply to charge the tank capacitor.
As with AC charging, a high voltage power supply is used to charge the tank capacitor of the Tesla Coil. However the main difference is that the source of power is a smooth DC supply, rather than an AC supply operating at the mains frequency. This results in some significant differences in behaviour, most of which are advantageous. (See advantages and disadvantages section later.) In particular the removal of the line frequency from the charging circuit can allow the firing rate of the rotary spark gap to be varied over a wide range without encountering any beating or surging problems.
The DC charging arrangement can be broken down into two separate stages:
Both of these stages will be described in detail in the sections that follow…
Click here to go to section covering the HVDC supply.
Click here to go to section covering the resistive charging circuit
Click here to go to section covering the DC resonant charging circuit
Click here to go to section containing design equations
Click here to go to advantages and disadvantages of DC resonant charging
The job of the HVDC supply is to provide a constant high voltage output of fixed polarity to the charging circuit that follows. A perfect supply would provide its rated voltage with no ripple, and its output voltage would not drop when current is drawn from it. In practice this ideal supply can rarely be realised, and a compromise must be made. It is in the areas of ripple and regulation where this compromise is made.
There are many different ways to build a HVDC supply. Possible designs stretch from simple single phase supplies to elaborate 3-phase arrangements. There is a trade-off between simplicity of the design and the performance. Some of the more common alternatives are shown below.
Single phase supply
One of the simplest arrangements for a HVDC supply is shown below:
This design uses a step-up transformer followed by a bridge rectifier and a smoothing capacitor. The rectifier converts the high voltage AC from the transformer into pulsed DC, and the smoothing capacitor acts like a reservoir and holds the peak voltage for the time between peaks.
The DC output voltage from this arrangement is equal to 1.41 times the RMS voltage rating of the transformer. (i.e. It is equal to the peak output voltage from the secondary winding of the transformer.)
Although this circuit is cheap and simple, it exhibits a few shortfalls. The output from the rectifier pulses at twice the supply frequency, (100Hz in the UK), and falls to zero between peaks. This means that the supply would exhibit 100% voltage ripple without the inclusion of the smoothing capacitor. In addition to this the relatively long duration between peaks means that the smoothing capacitor needs to be large to "hold up" the supply and achieve an acceptably low amount of ripple.
We can estimate the size of smoothing capacitor required to obtain a particular percentage of ripple. This is done by assuming that a constant current is drawn from the capacitor over the 10ms time between charging pulses.
A 10kW 10kV supply must supply 1A average current. If we are prepared to accept 10% ripple, then the voltage across the smoothing capacitor is permitted to fall by 1kV over the 10ms duration between charging peaks. We can use the equation:
C = Ix t / V
to find the required smoothing capacitance.
C = 1 x 0.01 / 1000 = 10 uF
This is a big capacitor which implies high cost. The 500 Joules of energy that it stores are also highly dangerous. Clearly a trade-off exists between voltage ripple, and the size and cost of the smoothing capacitor. Fortunately the demands made of the smoothing capacitor and the resulting voltage ripple can both be reduced by choosing a more elaborate supply arrangement.
3-pulse rectifier supply
The circuit below shows a simple 3-phase HVDC supply:
This design uses 3 independent step-up transformers followed by a 3-pulse rectifier and a smoothing capacitor.
This 3-pulse rectifier essentially consists of 3 identical half-wave supplies feeding into one smoothing capacitor.
Since the phases are spaced at 120 degrees relative to each other, then the capacitor sees 3 charging pulses during each cycle of the mains supply.
The DC output voltage from this arrangement is also equal to 1.41 times the RMS voltage rating of the transformer.
There are two advantages of this arrangement compared to the single phase supply described previously. Firstly, the duration between charging pulses is now only 6.67ms instead of 10ms when used on a 50Hz supply. This means that the smoothing capacitor does not need to be as big because it does not need to hold up the voltage for so long. Secondly, the output voltage from this 3-pulse rectifier does not fall right down to zero between pulses. This is because the 3-phases overlap slightly, and the voltage ripple is actually 50% if no smoothing capacitor is used.
Clearly we are heading in the right direction by reducing the time between charging pulses, and by reducing the "un-smoothed" ripple. Both of these things reduce the demands on the smoothing capacitor. This reduces the system cost, and ultimately will give superior performance.
Although the 3-pulse rectifier circuit is superior to a single phase supply, I would not recommend actually building this supply for a number of reasons. The 3-pulse rectifier only uses 3 HV diodes, so it is simple and cheap, but it is not very efficient because it only makes use of the positive half-cycles from each transformer. Secondly, the fact that it only uses the positive cycles from each transformer implies an asymmetric loading on the secondaries of each transformer. This DC current component is undesirable as it can result in saturation of the transformer cores.
A far more efficient supply can be built by using only 3 more diodes…
6-pulse rectifier supply
The circuit below shows a 3-phase supply using a 6-pulse rectifier:
This design uses 3 independent step-up transformers followed by a 6-pulse bridge rectifier and a smoothing capacitor.
This 6-pulse rectifier is like a "full-wave" version of the 3-pulse design shown above.
Since both positive and negative half-cycles are used from all 3 phases, the capacitor now sees 6 charging pulses during each cycle of the mains supply.
The DC output voltage from this arrangement is 73% higher than that obtained from the 3-pulse and single phase designs, because the 6-pulse rectifier extracts the maximum phase-to-phase voltage. A 73% increase in voltage implies a tripling of the energy in the Tesla Coil's primary capacitor, just for the cost of 3 additional HV diodes ! The output voltage for this arrangement is equal to 2.45 times the RMS voltage rating of the transformer.
There are a number of other advantages of this 6-pulse arrangement compared to the two supplies discussed previously. Firstly, the duration between charging pulses is now only 3.33ms with a 50Hz supply. This means that the size of the smoothing capacitor can be reduced again, because it does not need to hold up the voltage for so long. Secondly, the output voltage from this 6-pulse rectifier only falls to 86% between peaks. This is because the 6 pulses overlap considerably, and the ripple is only 14% without any smoothing capacitor. The reduced ripple means that the 6-pulse supply could be used for Tesla Coil purposes without requiring any smoothing capacitor.
Eliminating the smoothing capacitor represents a significant cost reduction in the HVDC supply, and also removes a potentially dangerous source of stored energy from the system. For this reason the author recommends the 6-pulse HVDC supply for DC Tesla Coil use.
12-pulse rectifier supply
The process of using more charging pulses per supply cycle can be taken further in order to reduce the "un-smoothed" ripple at the output of the supply. The circuit below shows a more elaborate supply using a 3-phase supply and a 12-pulse rectifier:
This design uses 6 separate step-up transformers followed by a 12-pulse rectifier and a smoothing capacitor.
The top half of the circuit is the same as the 6-pulse rectifier described above. (The secondary windings of the three transformers are connected in Star Y configuration.)
The bottom half of the circuit is basically another 6-pulse rectifier, however the secondary windings of these transformers are connected in Delta configuration.
This has the effect of shifting the phase of the bottom rectifier pulses by 30 degrees so that they interleave perfectly between the pulses from the top rectifier.
When the outputs from the two 6-pulse rectifiers are combined, the smoothing capacitor sees a total of 12 charging pulses during each cycle of the mains supply !
The DC output voltage from this arrangement is also equal to 2.45 times the RMS voltage rating of the transformer, so there is no voltage gain in moving from the 6-pulse arrangement to the more complex 12-pulse arrangement. However the duration between charging pulses is now only 1.67 ms with a 50Hz supply, making life very easy for any smoothing capacitor, if one is required at all.
The output from the 12-pulse rectifier only falls to 97% of its maximum voltage between peaks. This equates to a ripple of only 3.5% compared to 14% for the 6-pulse design above. Such a low ripple percentage makes this arrangement more than adequate for our application without employing any smoothing capacitor at all.
It should be realised that the lower 3 transformers in the circuit above, need to have their secondary windings rated at 1.73 times the voltage of the upper 3 transformers. This is because the secondary windings of the lower transformers are connected in Delta configuration, and the upper ones are connected in Star (Y) configuration. If the output voltages of the lower transformers are not scaled up accordingly, the 12-pulse rectifier circuit will not function correctly.
Although the 12-pulse rectifier represents a technically elegant HVDC supply, with minimal ripple, and no smoothing capacitor, the Tesla Coil designer must consider whether the added cost, complexity (and weight) can be justified by the low ripple at the DC output. For most applications the moderate ripple from the 6-pulse arrangement is likely acceptable, but if you happen to come across a surplus 12-pulse HVDC supply for the right price...
(Note that dedicated 3-phase transformers could be used instead of three discrete transformers in most of the circuits above. However careful attention must be paid to the way in which the 3 HV secondary windings are connected together. Most of the circuits show here require that they are connected in star configuration as access is required to the neutral for them to work correctly. Whether using separate transformers or a single 3-phase unit, always pay attention to the dots next to the windings in these circuits to ensure correct phasing.)
More HVDC supply configurations
There is an almost endless list of different HVDC supply topologies with different merits, although I have tried to describe the most common ones above.
Other configurations include using more phases to reduce ripple, connecting various rectifiers in series to increase voltage, and "charge-pump" arrangements to obtain higher voltages. Charge-pumps and voltage doublers generally work better at higher frequencies because the capacitors can be made smaller. Therefore they are most effective in 3-phase supplies where the pulse rate is higher.
There are also a range of HVDC supplies using high frequency switching techniques to produce high quality DC with low ripple and excellent regulation. Marco Denicolai's Thor supply is a fine example of this technique.
Inrush current problems !
When the mains power is first switched on the DC smoothing capacitor must be charged from "empty" to its full operating voltage. This requires a lot of energy, and causes the supply to draw a very large current for many milliseconds until the capacitor is fully charged.
This is known as inrush current, and is potentially a big problem. The initial current surge can go into the hundreds of amps if no precautions are taken to limit it. Such a surge would exceed the ratings of rectifiers, transformers, wiring and circuit breakers. Excessive inrush current could even result in damage to the smoothing capacitor due to internal stresses and heating.
Fortunately there are a number of ways to tackle the inrush current problem:
Use a Variac.
A variac can be used to slowly increase the supply voltage so that the smoothing capacitor charges gradually over a period of several seconds. This removes the initial current surge that would occur if the supply was turned on abruptly. However it is still wise to include adequate fusing to protect against the time when you accidentally turn on the power with the variac at its maximum setting !
Use a current limiting resistor.
A current limiting resistor can be inserted in series with the mains supply to the step up transformer. This resistor limits the initial current surge to an acceptable value. It can then be switched out of the circuit to reduce losses and improve regulation when running.
Pre-charge the smoothing capacitor.
A smaller current limited supply, such as a Neon Sign Transformer or Flyback supply can be used to initially charge the smoothing capacitor. Once the capacitor is charged, the main HVDC supply can then be switched on abruptly without incurring a high inrush current.
Do not use a smoothing capacitor.
The smoothing capacitor is the obvious cause of the inrush problem, and can be eliminated provided that the un-smoothed ripple can be tolerated. In the case of a single phase supply this is unlikely since the ripple is 100% of the output voltage without any smoothing capacitor. However for 6-pulse and 12-pulse rectifiers the output ripple will most likely be acceptable without a smoothing capacitor.
The methods described above are applicable to conventional 50Hz (or 60Hz) power supplies. However similar precautions must be taken in solid state HVDC power supplies to limit the inrush current at turn on. Techniques in power electronics such as current mode control and resonant converters allow current limiting to be built into the design with little extra complexity or cost.
THE CHARGING CIRCUIT
Now that we have our HVDC supply, how do we arrange for this to charge our Tesla Coil tank capacitor in between firings of the spark gap ?
It is the job of the charging circuit to charge the tank capacitor from the HVDC supply in a controlled manner during the time between bangs.
At first we might be tempted to connect the tank capacitor directly across the output of the HVDC supply. This would indeed charge the tank capacitor up to the DC supply voltage, but this arrangement is flawed for several reasons:
Firstly, firing of the spark gap would effectively short circuit the DC supply causing a large current surge through the rectifier, spark gap and primary coil. (This current surge would be magnified further if a large DC smoothing capacitor were employed in the supply !)
The second problem exists because the voltage across the tank capacitor must be able to change polarity as the capacitor oscillates with the primary coil. When the capacitor voltage tries to swing negative, the diodes in the bridge rectifier become forward biased and effectively short circuit the tank capacitor ! This shunts the high current away from the primary tank circuit, preventing the proper ringdown from taking place.
Both of these phenomenon lead to rapid destruction of the rectifier diodes. It is clearly necessary to introduce some impedance between the HVDC supply and the Tesla tank capacitor, in order to achieve the following objectives:
Limit the current flow from the HVDC supply when the spark gap fires. Otherwise the HVDC supply is short-circuited.
Control the charging current so that the capacitor charges at a convenient rate between the presentations of the rotary spark gap.
"Decouple" the tank capacitor from the DC supply so that it can resonate freely with the Tesla primary coil during ringdown.
Our first instinct might be to use a high voltage resistor between the DC power supply and the tank capacitor. The inclusion of a simple resistor satisfies the three requirements listed above, however we will see that it still has several disadvantages.
When a capacitor charges from a fixed voltage source through a resistor, the charging current is not constant throughout the charging time. When the capacitor is empty, the full supply voltage is developed across the resistor and maximum current flows. As the capacitor charges, the voltage across the resistor decreases, and therefore the charging current diminishes.
The graph below shows the profile of the capacitor voltage when charging through a resistor from a fixed DC supply:
It can be seen that the quickest rate of charge is at the start of the charging time. The charging of the capacitor becomes progressively slower as it approaches the DC supply voltage. Therefore the majority of the energy is stored early during the charging time, and the later part of the charging time contributes little to the total stored energy.
The graph below shows the profile of the charging current when a capacitor is charged through a resistor from a fixed DC supply:
It can be seen that the highest current flow is at the start of the charging time when the capacitor is "empty". This high current flow through the resistor causes a high power dissipation in the resistor. As the capacitor charges, the current decreases gradually, and the rate of charging therefore decreases as time goes on. From this we can see that it is not possible to put a finite time on how long it takes to fully charge the capacitor. The time taken to fully charge the tank capacitor is infinite. (In theory the capacitor voltage never quite reaches the DC supply voltage, it just gets closer with time.)
If a capacitor is left for a long time to charge to its full potential through a resistor, it can be proven that the same amount of energy has been dissipated in the charging resistor as is finally stored in the capacitor. This implies 50% efficiency if we are prepared to wait "forever" for the capacitor to fully charge. However, in practice we can take advantage of the fact that most of the energy is stored in the early part of the charging time, and choose a finite charging time defined by the rotary firing rate. The penalty for firing before the cap is fully charged, is a decrease in efficiency from the maximum possible 50% value.
As the firing rate is increased the capacitor has less time to charge and it reaches a smaller fraction of the full supply voltage. From the charging equation above, it can be shown that the peak capacitor voltage is related to the firing rate (BPS) as follows:
The energy stored in the capacitor at each bang is therefore as follows:
The power throughput is found by multiplying the bang energy by the repetition rate:
It is not immediately apparent, but differentiation of the above equation reveals a maximum power throughput when:
The power throughput falls either side of this optimum rotary speed.
It should be noted that as the firing rate is increased, the capacitor is less able to charge to a significant voltage in the short time between firings. This limits the useful power throughput, but results in a greater dissipation in the charging resistor !
The graph below shows how the power throughput, power dissipation in the resistor, and total power drawn from the supply vary with rotary BPS.
(This information was obtained from Microsim PSPice simulations carried out over a range of firing rates.)
The graph confirms that maximum power occurs at the speed given by the previous equation. However, it can also be seen that there is almost twice as much power being dissipated in the charging resistor at this BPS. The system is roughly 30% efficient at this rotary speed. Not good.
The efficiency of the system is found by dividing the power throughput by the total power drawn from the supply. The graph below shows the efficiency of the DC resistive charging system at various break rates:
Low speeds give the maximum 50% efficiency by allowing the tank capacitor to charge to its full voltage. The efficiency decreases at higher BPS values as the capacitor is prevented from charging fully, and greater power is dissipated in the charging resistor. Unfortunately the lowest speeds do not give much power throughput either due to the small number of bangs in each second.
It is a sad fact that maximum power throughput and maximum efficiency do not occur at the same BPS.
Disadvantages of charging through a resistor
The list below shows some of the shortfalls of simply using a high voltage resistor in the charging path:
The maximum efficiency is 50%. More than half of the input power will always be dissipated in the resistor. This causes considerable heating and poor spark performance per kilowatt of wall-plug power.
Maximum current flows from the HVDC supply when the spark gap fires. This is bad because high currents heat the spark channel to a high temperature and cause it to resist quenching. This leads to problems such as arc trailing at high powers. Ideally we don't want a high DC current from the HVDC supply at the instant when the spark gap conducts.
The fastest rate of charging is just after the spark gap quenches. This is also bad because the capacitor can quickly charge to a high voltage again, before the rotary electrodes have sufficiently separated. This can cause re-ignition of a rotary spark gap at low speeds.
The power throughput is related to the rotary firing rate (BPS) by a fairly complex equation, (shown above.)
In summary, charging the tank capacitor through a resistor is simple, but inefficient and gives a less than ideal charging profile. For this reason the author does not recommend resistive charging for systems rated at more than a few hundred watts. At higher powers the losses become prohibitive and a more efficient solution becomes desirable.
Fortunately, all of these problems can be improved by replacing the resistor with another familiar current limiting component...
Click here to go to the next section about DC resonant charging.
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