Telsa coil operation continued…
The action of the spark gap going open-circuit and ceasing to conduct is referred to as quenching and can only occur when the current through the spark gap falls so low that an arc cannot be sustained, and the air in the gap cools sufficiently so that the gap does not "re-ignite" when the voltage rises again. In a Tesla Coil system, quenching occurs at a primary notch, therefore it is usually referred to as 2nd notch quench etc, depending on which notch the spark gap stops conducting at.
A 1st notch quench is highly desirable because it results in the maximum amount of energy trapped in the secondary. This implies that the spark gap would stop conducting after all of the primary energy is FIRST transferred to the secondary circuit. If this occurs then no energy can be transferred back to the primary. If energy is transferred back to the primary, energy is lost in the spark gap and in heating of the primary components. The graph below shows primary and secondary waveforms from an ideal system which exhibits a first notch quench. Notice that there are no notches in the secondary waveform.
A 1st notch quench is extremely hard to achieve in practice because the overall level of energy in the system is still very high at the1st primary notch, and the time for which the primary current is low at the notch is very short. This does not allow much time for the spark gap to cool and therefore it re-ignites easily as energy is coupled back from the secondary. In an attempt to make a spark gap quench at the first primary notch, several small gaps can be placed in series. However, this is a trade-off as it increases the conduction losses in the spark gap. Any gain in performance from first notch quenching may be lost due to higher gap losses which have been introduced in the initial primary ringdown period. (See section below on "The importance of good quenching".)
Highly useable spark gaps can be made which achieve 2nd or 3rd notch quenching with low conduction losses. Such gaps give excellent results in most applications. The graph below shows the primary and secondary waveforms for a simulated system exhibiting a 3rd notch quench.
Usually, it is not possible for the spark gap to quench in between primary notches. This is because there is either considerable current flow through the spark gap which acts to maintain the arc, or there is considerable voltage in the tank capacitor which would re-ignite the gap if it dared to quench at anywhere other than at a primary notch.
THE IMPORTANCE OF GOOD QUENCHING
So how important is it to built an elaborate spark gap in search of the illusive first notch quench ?
It is accepted that the design of the spark gap does influence its ability to interrupt current (quench). However, my feeling is that trying to design a sophisticated rotary to force a first notch quench under all conditions is not the best use of ones time.
My reasoning for this statement is that the spark gap only has the opportunity to quench at a number of distinct instants in time, (i.e. the primary notches.) If the spark gap does not quench at the first primary notch, then it must wait until the current falls again at the second primary notch before it gets another chance to quench. Likewise if the energy level in the system is still too high at the second notch then it must wait until the third notch occurs, and so on. The conduction time of the spark gap is kind of quantised if you like.
Now let us consider two different operating situations. Firstly, consider a Tesla Coil system in which the toroid is so big as to prevent spark breakout from its surface. In this instance energy is repeatedly transferred back and forth between the primary and secondary coils. This exchange of energy repeats many times because there is no corona to consume energy from the secondary coil. The main loss in the system is the primary spark gap which gradually dissipates energy from the system. The primary spark gap does eventually quench, but only after most of the energy has been lost from the system !
For our second example, lets consider a Tesla Coil which is producing many long streamers from its toroid into the surrounding air. This corona loads the secondary and draws energy out of the system quite quickly. In this case most of the energy is removed from the system after just one transfer to the secondary. This results in little energy left to be transferred back to the primary. As a result, the spark gap quenches at the first available notch !
My point here is that it is not early quenching that produces good sparks, but rather good spark loading that leads to an early quench. If you find this hard to believe, then try observing the voltage field around your Tesla Coil under the two different breakout conditions described. You will notice a huge difference in the spark gap's ability to quench with and without spark breakout.
With this in mind it seems that one of the best ways to achieve good quenching is to ensure there are powerful secondary arcs by way of accurate tuning, and a correctly sized toroid. Long sparks load the secondary winding and remove energy from the system quickly so that the spark gap can quench at the earliest opportunity. An extreme example of this is found when the toroid arcs to a nearby grounded target. The arc to ground presents a low resistance across the secondary. In this case all of the energy is taken out of the system in a very short time. The spark gap has no option but to quench because the system is devoid of energy. See this section containing real oscilloscope waveforms includes a trace showing the effect of an arc to ground.
In summary I believe the key factors in achieving an early quench are as follows:
Ensure accurate tuning.
If the primary and secondary circuits are not tuned to exactly the same frequency the energy transfer is incomplete, and the primary current envelope does not fall to zero. This makes quenching extremely difficult for the spark gap. (Fine tuning should be done at full power so as to include the frequency shift caused by streamer capacitance.)
Ensure heavy spark loading.
This is achieved by using a suitably sized toroid, breakout point, and plenty of power. The more energy you can suck out of the secondary the quicker the plasma in the spark gap will cease.
Use a high impedance tank circuit.
If a very high voltage power supply is used, the tank capacitor can be made smaller, and the primary inductance bigger. This increases the surge impedance and reduces the current flowing in the primary circuit. This lower current reduces heating in the spark gap and gives it a better chance of quenching at a notch.
Use a good gap design.
Finally use a spark gap design which has significant thermal mass, and forced air cooling. This prevents overheating of the electrodes which can act to sustain ionisation in the spark gap.
I mention cooling of the spark gap lastly as I believe this also reduces the tendency for the spark gap to re-fire again at a reduced voltage after quenching. I think this is not technically a quenching issue, but this reduction in breakdown voltage may often be confused with poor quenching. I do not personally subscribe to the idea that high speed rotary gaps, or compound series rotaries promote an earlier quench. It has been my experience that the primary ringdown has finished long before the rotary electrodes have even fully aligned, so the separation velocity does not influence the quenching action. (However, a high separation velocity does act to prevent the spark gap from re-igniting after each bang if the capacitor charges quickly before the electrodes have seperated sufficiently.)
Finally, if early quenching is not a necessity for good spark performance, then why should we be concerned with achieving an early quench at all ?
Well, it is desirable to "put out the fire in the spark gap" as quickly as possible for several reasons. Firstly, whilst the spark gap is conducting there is power being dissipated as heat. This heat errodes the electrodes and reduces the firing voltage of a static gap. Both of these effects are undesirable. Secondly, the average current seen by the components in the tank circuit is proportional to the time that it flows for. If the spark gap can be made to quench at the first notch instead of the third notch, this represents an 80% reduction in the time for which the huge primary current flows. This reduction in RMS current reduces heating in the tank capacitor and extends the life of the components significantly.
As a last thought, each time energy is transferred back to the primary circuit, the spark gap takes its share. This energy is wasted as heat, light and sound. Best get the energy into the streamers quickly before the gap eats it all up !
COUPLING COEFFICIENT (k)
One parameter is key to describing how energy is transferred between the primary and secondary resonant circuits. This parameter is called the Coupling Coefficient and determines how quickly energy is transferred from one coil to the other. Coupling is almost entirely determined by the physical positioning of the two coils relative to each other.
If the primary and secondary are spaced far apart the coupling coefficeint is low, and energy is transferred from primary to secondary (and vice versa) slowly over many cycles of the resonant circuit. This means that the notches which occur are spaced widely apart. With a low coupling coefficient it takes several RF cycles to transfer all of the primary energy into the secondary winding. However, the primary notch is quite wide so the spark gap has plenty of time to cool and gets the best chance of achieving a 1st notch quench. The graph below shows the primary and secondary waveforms of a system with k=0.05. The blue lines indicate the envelope of the primary and secondary oscillations.
If the primary and secondary coils are positioned more closely, the coupling coefficient is medium, and energy is transferred more quickly from one resonant circuit to the other. The primary and secondary notches are now closer together. The graph below shows the primary and secondary waveforms of a system with k=0.1. Notice how there are more notches in the 160us duration of the waveform shown becuase the energy transfers occur quicker.
If the primary and secondary coils are positioned very close to each other, the coupling coefficient is high, and energy is transferred very quickly from one resonant circuit to the other. In practice energy from the primary circuit is transferred into the secondary over a small number of RF cycles, but the spark gap has little chance of quenching, and the energy rapidly sloshes back and forth between primary and secondary. This repeated exchange of energy between the two coils is undesirable because energy is lost in the spark gap during each exchange. The graph below is for a system with k=0.2, and there are now many notches in the 160us simulation period shown.
Practical coupling coefficients exist between 0.05 and 0.2 for conventional Tesla Coils. Performance deteriorates below k=0.05 because much of the energy is lost in the primary circuit before it can be transferred to the secondary. This wasted energy never has chance to contribute to good spark performance. Above k=0.2 voltage breakdown of the secondary winding often results due to the very rapid rate of voltage rise that occurs. There is also some evidence to suggest that high coupling coefficients result in excessive voltage gradients along the length of the secondary resulting in "racing sparks". The exact mechanism by which racing sparks form is still not fully understood.
The coupling together of two resonant circuits results in interaction. Although both resonant circuits are tuned to the same frequency, two different resonant frequencies will be produced when they are magnetically coupled together. This arises because each tuned circuit "sees" more of the capacitance in the other tuned circuit as the primary and secondary are increasingly coupled.
Energy exchange between the two resonant circuits results in "modulation" of the oscillations at the primary and secondary windings. In the above examples, these modulation envelopes are clearly visible (in blue) on both the primary and secondary waveforms. The envelopes produced are the same shape as the beat envelope produced when two dissimilar frequencies interfere constructively and destructively. The modulation envelope is sinusoidal in shape.
In the middle graph with k=0.1 the frequency of the beat envelope is roughly 21kHz. This corresponds to that produced when two frequencies that are 21kHz apart add together. In practice the frequency spectrum consists of two resonant peaks, one at 209kHz and one at 230kHz. (RF engineers will recognise this as the characteristic of a Double-Sideband suppressed carrier radio transmission.)
If the coupling is decreased, the frequency of the beat envelope decreases, and the two resonant peaks in the frequency response move closer together. If the coupling is increased, the frequency of the beat envelope increases, and the two resonant peaks in the frequency response move further apart. This is known as "frequency splitting" and is a natural characteristic of two coupled tuned circuits.
Secondary voltage plotted against time,
Secondary voltage plotted in the frequency spectrum.
The "double-humped" frequency response of the complete system can easily be plotted by doing a frequency sweep of the complete Tesla Coil with everything in place and tuned correctly. In order to do this the HV supply is left off, and the spark gap is shorted. The primary circuit is driven from an RF signal generator and the amplitude of the electric field produced by the secondary is monitored by a remote antenna. The amplitude of the secondary field is then plotted against the frequency, as the signal generator is swept across the frequency range of interest.
The graph above shows such a plot produced by a computer simulation package for a variety of different coupling coefficients. The natural resonant frequency of each of the primary and secondary circuits is 218.7 kHz when they are physically separated. As they are brought physically closer together the coupling coefficient k increases and the two resonant peaks move further apart.
The upper and lower resonant frequencies are mathematically related to the natural resonant frequency and the coupling coefficient k as shown:
Fl = Fn / sqrt ( 1 + k )
Fu = Fn / sqrt ( 1 - k )
Fn is the natural resonant frequency of the primary or secondary circuits in isolation,
Fl is the frequency of the lower peak in the double humped response,
Fu is the frequency of the upper peak in the double humped response,
From this it can be seen that as the coupling approaches unity, the lower peak tends towards 0.707 x Fn and the upper peak tends towards infinity.
In practice this frequency splitting only occurs whilst the spark gap is conducting. Once the spark gap has quenched the secondary tuned circuit rings at its own natural resonant frequency without the influence of the primary circuit. Therefore the frequency spectrum of an operating Telsa Coil consists of the two peaks of the double-humped response plus the natural resonant frequency of the secondary winding. The contribution of the double-humped "sidebands" decreases as the spark gap is made to quench earlier. The graph below was obtained using a Spectrum Analysing RF Receiver to examine the frequency content of the Secondary voltage field.
The main peak around 219kHz is the free resonating frequency of the secondary and appears due to the secondary ringdown after the spark gap quenches. The two peaks either side (approximately 12dB down) are the peaks of the double-humped response. These peaks appear due to the response of the coupled primary and secondary tuned circuits before the spark gap quenches.
In this plot the frequency response appears to decay quite slowly either side of the double-humped response. This "blurring" of the frequency response and also the small ripples are due to the fact that the Tesla coil is repetitive and not a continuous device. The repetitive nature of the Tesla Coil gives rise to this distortion of the frequency plot.
The high frequency noise above 2MHz is believed to be due to stray resonances in the primary circuit and possibly overloading of the receiving antenna system.
The peak at 1MHz is a marker generated by the spectrum analyser, which I forgot to turn off, and has nothing to do with the Tesla Coil operation at all !
The graph below shows the Tesla Coil frequencies in a bit more detail:
In summary the natural resonant frequency and the coupling coefficient of a running Tesla Coil can be estimated from either the secondary voltage waveform or the frequency spectrum of the secondary voltage using the formulae above. Either of these can easily be observed from a safe distance using a simple voltage probe and oscilloscope. Information about the quench of the spark gap can also be gained from examining the secondary voltage field. Alternatively all of the resonant frequencies can be found safely by doing a sweep test with a signal generator.
In the particular case shown above the coupling coefficient was approximately 0.08 and the quench occurred at the 4th primary notch.
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