What Exactly is a Tesla Coil

So what exactly is a Tesla Coil?

So what exactly is a Tesla Coil?

"But Captain! Ye cannae change the laws o' physics!" Chief Engineer Scott, USS Enterprise

There remains nagging away in the back of the mind the idea that the exact mechanism of operation of a Tesla coil has still not been fully disclosed. This bothered me not at all to begin with, as my interest lay with the spark transmitter and the Tesla coil was a mere dummy load and nothing more. Eventually, however, I had to concede that the blasted thing would not leave me in peace until I had got to the bottom of it. I pondered for an excessive amount of time over this, until gradually the concept began to emerge from the murk. All this Tesla coil stuff seems vaguely familiar from somewhere . . . I can remember from 25 years ago, one of my chemistry teachers asking the class "What would happen if you put a bottle of electrons in the middle of the lab?" He then proceeded to give the wrong answer, that everything in the lab would immediately rush towards the bottle because of its net charge. Actually, you and I know the right answer to that question. The electrons have so much less inertia than everything else in the lab that it is the electrons which do the moving, bursting out of their bottle and rushing in all directions towards the induced positive charges on the surface of each earthed object in the vicinity. The important thing of course is the charge q, i.e. the number of electrons stuffed into that bottle. There are 96500 coulombs in one faraday of electricity, and each coulomb is equal to 6,24 x 1018 electrons. The more electrons in the bottle, the greater the repulsive force developed between them, the greater the induced charges in the surroundings, and the greater the attractive forces between the electrons and their surroundings.

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So what exactly is a Tesla Coil?

The Tesla coil, it turns out, is very closely related to another high voltage machine, the Van de Graaf generator. Perhaps it would be more appropriate to state that relationship the other way around, since the Tesla coil predates the Van de Graaf by at least half a century. Excluding the rotary spark gap, if any, a Tesla coil is a Van de Graaf generator with no moving parts. The rotating insulated belt which carries the unidirectional charging current in the Van de Graaf is replaced, in the case of the Tesla coil, by the rotating vector of the sinusoidal oscillation which carries the bidirectional charging current. The essential physics of the charging of isolated electrodes is the same for both. The dielectric breakdown of air is but little different, a relatively minor modification being required on going from dc to low frequency ac, to high frequency ac. The Van de Graaf generator is simply a dc version of the Tesla coil. Whereas it has been found progressively more difficult to increase the charging current of Van de Graaf machines to much above a few milliamps, the charging currents associated with Tesla coils are measured in amps. This is because the charge q on the top electrode makes the journey from earth and back again in microseconds, and current is simply the rate of charging, dq/dt. As the frequency is reduced, the current for a given charge falls, and this helps to explain why Tesla coils tend to get more efficient as the frequency drops, as the resistive in-phase i2R losses for the circulating, wattless power in the secondary system (and primary) are generally smaller. Since the current falls with frequency, it also explains why the charging current for a Van de Graaf of the same top electrode capacitance is so much less at dc than for a Tesla coil at ac. Actually, this is not the whole story and in fact there is something unexpected about the role of resistance during the exchange of energy between the primary and secondary. Whilst resistance certainly is important in causing losses in circulating, wattless power in a tuned circuit, in the electromagnetic transfer of that power between circuits, we have a different situation. The losses in connecting a charged capacitor to an uncharged capacitor via a resistor are independent of the resistor value, and depend only on the relative capacitor sizes and the magnitude of the charge. The efficiency of the transfer of energy between primary and secondary therefore depends very little upon the efficiency Q, provided it is enough to ensure magnetic coupling which will be the case if QL is at least five. It is very unfortunate that the symbol Q can have two meanings, either a measure of the efficiency of a capacitor, coil or tuned circuit, or alternatively a quantity of charge in coulombs. In what now follows, Q and q are both amounts of charge. The following derivation is due to the late Professor Cotton of Nottingham University.

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So what exactly is a Tesla Coil?

If C1 is charged to a voltage V1 and a charge Q is stored on its plates, and C2 is uncharged, i.e. V2 = 0, after a time, a charge q will have been transferred to C2. The potential differences across the capacitors will be:

and hence

Therefore

or

Integrating

Therefore

Now q=0 when t=0; therefore http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (3 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

Thus

as

Rate of change of energy = i2R

Hence for the total energy lost in the resistance R we have

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So what exactly is a Tesla Coil?

from which it can be seen that the amount of energy lost in the transfer is independent of the value of the resistance R, the product i2R remaining constant as R is varied. It is the relative sizes of the two capacitors and the charge on C1 (or in other words the voltage to which C1 is charged) which determines the efficiency of the transfer. (The late Professor Cotton's contribution ends here and Q reverts to being a measure of efficiency.) This obviously has application to the Tesla transformer:

If the two circuits are linked by an ideal transformer, with coupling constant k=1, transformation ratio T and no leakage inductance, nor reactance, nor resistance, the transformer and C2 can be replaced by another capacitor, C2'.

The value of C2' is now given by the equivalent of C2 as seen in the primary circuit by C1 and R. This is simply C2 multiplied by the square of the transformation ratio, T2. In other words, the amount of energy lost in each cycle of oscillatory power transfer depends only on the magnitude of the charge being transferred and the relative sizes of the capacitors. Evidently then, the most efficient transfer overall will occur in one half cycle, i.e. the most efficient transfer of energy corresponds to critical damping. This will occur if in one half cycle the top load on the secondary has sufficient charge deposited on it to cause dielectric breakdown of the air. Frequently, however, this is not the case, and a number of cycles elapses with the charge on the topload increasing at each successive (positive or negative) peak of the oscillation http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (5 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

before dielectric breakdown can occur; in other words, the secondary system acts as an integrator for ac, rather like the inverse of logarithmic decrement. We might thus call it logarithmic increment. However, whilst coil resistance has little if any effect on the efficiency of energy transfer between primary and secondary capacitors, it should be clearly remembered that the losses in the coils do most certainly effect the amount of energy stored in the tuned circuits as circulating, wattless power. Now this does not matter much with spark transmitter-driven coils because that energy doesn't circulate for more than say half a dozen cycles prior to spark breakout, but with valve transmitter-driven coils it's a different story, of which more later. Thanks to the fact that in the spark transmitter-driven coil, the primary capacitor does the job of wattless energy storage when it is charged by the power supply, energy accumulation by the Tesla secondary is not required, and the most effective spark-driven coils are generally those which have a large energy storage in the primary and good quenching at the gap. A large secondary topload is vitally important in these systems, as we shall see. Van de Graaf generators usually don't give the spectacular spark display of a Tesla coil simply because the charging rate is too low and as the charge on the top electrode raises the potential to breakdown it simply begins seeping away by corona discharge and an equilibrium is rapidly reached with the charging rate, no spectacular breakouts ever occurring. The charging rate with a Tesla coil - particularly a spark transmitter-driven one - is so high that no chance is given for equilibrium to be attained prior to spark breakout. On occasion you may see film footage of the insulating pressure vessel being lifted off a small Van de Graaf when it is still running. Under an inert atmosphere, e.g. sulphur hexafluoride, the charge on the top electrode of a Van de Graaf can reach similar proportions to a Tesla coil, and then as the pressure vessel is lifted and the gas drifts away, very briefly, you get a short-lived explosion of sparks, just as with a Tesla coil. The physical similarities do not end there. Whilst it appears at first sight that the Tesla top load is not insulated from ground, the turns of the secondary coil do in fact perform the same function as the stack of equipotential rings often used in Van de Graaf generators, i.e. they provide a graded potential difference along the length of the support. In fact, as the number of turns increases, so each turn approximates more nearly to an equipotential ring. If we consider the top electrode to be instantaneously charged, then it can be seen that the self-inductance of the coil will act as a perfect insulator on an instantaneous timescale because it resists changes in current flow, and the turns are indeed equipotential rings under these conditions.

A Wee Diversion It has been noticed that whilst sinusoidally-driven Tesla coils (e.g. powered by valve power oscillators) show as expected no signs of net polarisation, spark-driven coils do on occasion show a net dc offset which registers on an electrostatic voltmeter placed in the neighbourhood of the working coil. Whilst it is possible that there is some polarisation effect at the sparking top load this is unlikely, due to the extreme voltages and if indeed this were the case it might be expected not only to occur with more coils, http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (6 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

including sinusoidally-driven ones, but to be of the same polarity each time, neither of which is true. A far more likely explanation lies in the nature of the ground contact to which the base of the secondary is connected. ●

●

●

The Frenchman, Professor Edouard Branly invented his 'coherer' over a century ago, and it depends for its operation on as-yet-unexplained conductivity mechanisms between conducting particles under damped wave excitation. This effect is entirely absent with sinusoidal stimulation. It is well known that if it is desired to measure the resistance of a ground connection, that ac must be used and not dc, else electrolytic polarisation takes place and the ground resistance measurements are totally false. Moreover, they vary with polarity. It is also known, thanks to the work of Fessenden, that a thin contact point of wollaston wire barely dipping into an electrolyte (nitric acid) solution has the ability to rectify radio frequency oscillations.

It seems likely that a combination of these effects is responsible for partial rectification of the excitation applied to spark discharge driven Tesla coils, and that the difference in ground connection from one coil to another is responsible for the variable reports of net dc polarisation of Tesla coils. The exact nature of the ground connection, where the metal meets the soil, will vary tremendously with geology and moisture content and will be very different from one location to another. If this is the true explanation, then it would be expected that the coils showing this effect would also show a significant second harmonic component, since this is to be predicted by Fourier transform theory if rectification is occurring. Interestingly, whilst these polarisation effects have been reported with "quarter wave" coils, they are apparently absent from "half wave" coils. Whether or not this be the case, it may also prove possible to introduce and control a deliberate net dc offset by installing e.g. a thyratron in the earth lead, by means of which proportional control of the resulting unidirectional pulsed charging current could be effected by the usual means applied to dimmer switches and the like.

To return to the charging of isolated electrodes. Classical physics tells us that there is a voltage gradient produced at the surface of a charged conductor, and that ionisation of the air will occur when this gradient has a value of between 2 and 3 megavolts per metre (20-30kV/cm). The variables are pressure, temperature and particularly humidity, and frequency of the voltage if it is alternating. The gradient at the surface may also be influenced by the total charge, fairly obviously, and also by the geometry of the surface, a sharp radius enabling ionisation at a much lower potential than a gently rounded surface. For dc, there is a simple relationship between the breakdown potential and the radius of the conductor. If we assume that we need three megavolts per metre to bring about ionisation, then we can calculate: http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (7 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

(note - the capacitances of the spheres are shown for convenience and of course do not depend on the breakdown voltage) Breakdown Voltage, kV

Sphere Diameter, cm

Capacitance, pF

50

3,3

1,8

150

10,0

5,7

200

13,3

7,4

250

16,7

9,3

300

20,0

11,1

350

23,0

12,8

400

26,7

14,8

450

30,0

16,7

500

33,3

18,5

600

40,0

22,2

750

50,0

27,8

1000

66,7

37,0

Whilst the capacitances of toroids will vary considerably according to major and minor diameters, the breakdown voltage of a toroid of a particular minor diameter will be very similar to a sphere of equal diameter, the curvature of the sphere or toroid determining the surface potential gradient. The above table may thus be used to estimate the breakdown voltage (noting that it will vary according to temperature, pressure, humidity, frequency) of a given toroid. Example: a toroid has a minor diameter of six inches. This is about 15cm. From the table, a sphere of 13,3cm has a breakdown voltage of 200kV and a sphere of 16,7cm a breakdown voltage of 250kV. The toroid thus will have a breakdown voltage of the order of 225kV dc. We now need to ask how much energy is needed to produce this voltage, and if we are dealing with a spark transmitter-driven coil then according to the accepted formula it will be ½CV2 referred to the secondary capacitor (losses are responsible for making this approximate when referred to the primary capacitor). However, we may wish to ask a slightly more intelligent question: how many electrons do we have in the bottle, and is there a better way of getting them there? http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (8 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

From this it can be seen that the charge q increases with capacitance. If C increases (from the middle equality) then q2 must increase for the same amount of energy. The potential required to stick the electrons in the bottle will decrease, i.e. the work required to put the electrons in the bottle will be less (bigger bottle = more room for the electrons = less mutual repulsion). For spontaneous breakout of a spark, the top load must then be given a smaller minor radius if it is a toroid, or a sharp spike or elevated small sphere should be attached. With a large secondary capacitor, there will be more electrons in the bottle for a given energy. This is the best reason for large top capacitances on Tesla coils. It has little to do with coupling or matching, and nothing whatever to do with the theory propagated for years (around eighty years) that the spark length produced by the secondary has something to do with the Q of the secondary. That theory is wrongly applied to spark transmitter-driven Tesla coils, it applies to double tuned intermediate frequency transformers (IFTs) which, though related closely to Tesla coils, are in subtlety very different, largely because of the fact that IFTs are fed by continuous waves, and it predicts the largest sparks for the smallest secondary capacitances. A couple of IFTs are shown below. The coils and capacitors can be clearly seen.

The theory given above is in agreement with experiment, that it is the total charge on the top electrode which determines the spark length and this increases with secondary capacitance for spark transmitterdriven coils. The only useful function performed by Q in spark transmitter-driven Tesla coils is to provide for an efficient transfer of energy from primary to secondary under conditions where an iron core cannot be used for obvious reasons. Here it is sufficient for the unloaded Q of the secondary to be http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (9 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

say at least ten, since all it needs to do is couple the wattless power accumulated by the primary capacitor. Hence my old 500VA coil secondary, battle scarred by direct strikes and with a measured unloaded Q of just 35 gave just as good results as when it was new. However, valve-driven coils need a high secondary Q. This is because the secondary system of a valvedriven coil has to perform the wattless power accumulation which in a spark transmitter-driven coil is performed by the energy storage on the primary capacitor prior to spark discharge across the primary gap. In the case of valve-driven coils, a small top load will prove beneficial because the Q - important in a valve-driven circuit - decreases with increasing capacitance, just as with an IFT. Here, spherical top loads are likely to be better than toroids, since a high breakdown voltage will allow a large charge prior to dielectric breakdown of the air, and the small capacitance will keep the Q high. Evidently there is a compromise to be made between the maximum charge for a given energy and the large Q which is needed to allow the necessary charging current to be built up over a large number of cycles. This is one of the reasons why the theory developed for IFTs cannot be applied in the same way to spark transmitter-driven Tesla coils - the IFT is a "continuous wave" system whilst the spark transmitterdriven Tesla coil is in essence a "one-shot" system. The other reason why the theory which was developed for intermediate frequency transformers cannot be applied to Tesla coils generally, in exactly the same way as it is to IFTs, is simply due to the difference in the form of the secondary capacitors. In the IFT the secondary capacitor is of the conventional multi-plate type, and any net charge on the "live" plates induces a corresponding opposite charge on the "earthed" plates, which are physically very close to them. The electrostatic fields from these charges are equal and opposite throughout all space, except in the very close vicinity of the plates, and it is only between the plates and in the dielectric where a significant field exists. (This is analogous to the cancellation of fields found in parallel conductor transmission line systems.) Even this is minimised by the presence of the dielectric, since a dielectric works by reducing electric fields by polarisation. There is thus no net field external to the capacitor of any consequence, and the only voltage which is measured is the potential difference between the plates, which increases as the capacitance is reduced. In the Tesla coil, the secondary capacitor is an isolated electrode, effectively in "free space". The electrostatic field developed by any charge on this electrode does indeed induce opposing charges on surrounding objects in the vicinity, but these are removed by some considerable distance and the local field is not counteracted by them. The local field generated by the charge q is given by:

where q is the charge in coulombs, r is the radius in metres, 4πε0 = 1,11265 x 10-10 and E is the electrostatic field in volts per metre. Thus we have the apparent paradox that the biggest sparks are http://home.freeuk.net/dunckx/wireless/scotty/scotty.html (10 of 11)6/20/2011 2:53:38 PM

So what exactly is a Tesla Coil?

produced in the spark transmitter-driven Tesla coil when the potential across the Tesla secondary is low and the top capacitance large. It is the charge q in the bottle which "does the damage", exactly as for the Van de Graaf generator. The spark length is dependent on the charge. If we have two Tesla coils, one of which has double the charge on its topload than the other, the greater charge will produce a spark 1,4 times (square root of the charge ratio) as long, to a good approximation. The potential in volts at any distance from this charge is:

I am still puzzled over the exact mechanism which determines spark length for a given q, undoubtedly it revolves around an equilibrium of forces, but am reasonably assured that this will follow given that (after eighty years of misunderstanding) the mechanism of operation of the Tesla coil is now plain. I am enormously relieved that it can be explained in terms of known theory. "Great are the deeds of the Lord! They are studied by all who delight in them." Psalm 111 v 2 Back Homepage

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Maximising Power 1

The Spark Transmitter. 2. Maximising Power, part 1.

"I think a famous French mathematician and physicist was guilty of only slight exaggeration when he said that no discovery was really important or properly understood by its author unless and until he could explain it to the first man he met on the street." Sir J.J. Thomson

By means of a suitable condenser, inductance, spark gap and high voltage source it is possible to generate power at r.f. (radio frequency). Having generated power at r.f. it is necessary to ensure that it is transferred efficiently to the load, be that an aerial or Tesla coil, where it can do something useful. The question of "how?" is now one to be considered in greater detail. Maximising Output.

Consider a generator connected to two resistors in series. Call the resistors R1 and R2. If the generator produces an emf E volts, then the voltage across R2, call it E2, is equal to:

and the power P2 dissipated in R2 is equal to:

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Maximising Power 1

This value is a maximum when R2 = R1 and the power dissipated in R2 then becomes:

Now imagine that R1 is inside the generator itself. The above expression for the power P2 in R2 is the maximum which can be obtained by connecting a generator having internal resistance R1 to the resistance load R2. This is a very important result and is generally called the maximum power theorem. It demonstrates that the maximum power transfer can only occur when the two resistances are equal, and the generator and load are then said to be matched. Resistances, Reactances, Impedances and Resonance. What has been stated above is not only true for circuits containing pure resistance. In a circuit containing a coil and/or a capacitor, there will not only be the resistance of the coil to consider, but the reactances of coil and capacitor too. The reactance of a coil or capacitor can be thought of as the resistance of that component to alternating current (ac) and because the frequency of ac can obviously vary, the reactance of a coil or capacitor is frequency-dependent, or in other words, the resistance of a coil or capacitor to the passage of ac depends on the frequency. The reactance is given the symbol X and is measured in ohms as is a resistance. The formulae for capacitive and inductive reactance are:

This begs the question, what is the real difference between a resistance and a reactance if both are measured in ohms? It is necessary in ac circuits to take account of the relative phases of voltage and current, and the difference between a pure resistance and capacitive and inductive reactances is one of phase. In a purely inductive circuit, the voltage leads the current (this is called a positive phase difference and is shown by +j) and in a capacitive circuit, the current leads the voltage (a negative phase difference shown by -j, j being the square root of -1). In a purely resistive circuit, there is no phase difference. In other words, the difference between resistive and reactive ohms is not real but imaginary (sorry about that.) Only resistances consume power, because for power to be consumed, the current and voltage within the component must be in phase. Reactances do not consume power (aside from any resistance they may have) but take it from the supply over part of a cycle and give it back over the rest. We might then amend our formulae to take account of this, and, whilst doing that, we can rename the http://home.freeuk.net/dunckx/wireless/maxpower1/maxpower1.html (2 of 6)6/20/2011 2:48:45 PM

Maximising Power 1

2πf bit, which appears with monotonous regularity, as the Greek letter ω.

Inevitably in a circuit containing reactance there will always be resistance too. The combination of reactance and resistance is called "impedance". This too is measured in ohms and is given the symbol Z. If the coil or capacitor is efficient, the resistance can often be neglected (this is particularly true of capacitors) and the impedance is then numerically equal to the reactance. In other cases we must calculate the effect of the resistance, and in a circuit where there is a combination of significant resistance, capacitive reactance and inductive reactance, we must calculate the net result thus:

If there is more capacitive reactance than inductive reactance, the value of Z will be something multiplied by negative j; if there is more inductive reactance, Z will be something multiplied by positive j. Whenever the squares of the inductive and capacitive reactances do not come to zero under that square root sign, there is net reactance (shown as +j or -j) present in the impedance Z, and Z is said to be a reactive load. Now, as we said above, only if the generator is suitably matched to the load will the maximum power be transferred. In the case of reactive loads, it is not enough for the generator to have the same impedance the impedance Z of the generator must be the "conjugate" of that of the load - conjugate effectively means "equal and opposite" - and if the impedance of the load contains positive (inductive) reactance then the impedance of the generator must contain negative (capacitive) reactance of equal magnitude. [Psssst - this of course means that the load and generator together are resonant!] Happily, this complexity is greatly reduced in the case of resonant tuned circuits as loads, because the reactances at resonance of capacitor and coil have equal and opposite phase differences and the load appears to the generator to be a simple resistance - the impedance Z of the tuned circuit as a whole is a pure resistance because the squares of the capacitive and inductive reactances under that square root sign sum to zero. I have to confess a marked objection to the various statements sometimes seen that the reactances "cancel out". The reactances are not sentient beings! Coils and capacitors do not sit and conspire together to reduce their reactances to zero as the resonant frequency is approached! The reactances within each of the components are still very much present at resonance as is the relative phase difference due to them (if you were to take the components out of the circuit and measure their individual

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Maximising Power 1

reactances at that same frequency you would see it) but the net phase difference across the input terminals becomes zero because phase differences, unlike reactances, do cancel and all the generator sees is a pure resistance. Hence the conjugate impedance required of the generator to get the most power into the load is also a pure resistance. As we saw in the paragraph above, a reactive load must be driven by a reactive generator having a conjugate impedance, and a vital consequence of the maximum power theorem is therefore demonstrated by tuned circuits themselves. The Maximum Power Theorem inside Tuned Circuits. Any tuned circuit at resonance obeys the requirements of the maximum power theorem. This is because, at resonance:

The impedances are "conjugate"; in terms of the reactances we know that XL = -XC. This equation corresponds to two physical realities:

1. The capacitor is fully charged and there is no current passing through the coil. This situation is unstable and the capacitor spontaneously discharges via the coil, creating a current in it which is linked with a magnetic field. The energy stored in the capacitor (potential energy) is exchanged for the energy associated with the magnetic field and flowing current (kinetic energy) in the coil. In other words,

The capacitor is the generator, and the coil is the load. 2. The current flowing in the coil is at a maximum and so is the associated magnetic field. The capacitor is fully discharged. Unfortunately, because of this, at this very moment the power supply fails. The situation is unstable. The current flow ceases momentarily, the magnetic field gradually collapses, and a current is induced in the coil, passes out of the coil and charges up the capacitor. Kinetic energy is exchanged for potential energy, the above formula is effectively written the other way around, the coil has become the generator and the capacitor has become the load.

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Maximising Power 1

Since the impedances of coil and capacitor are conjugate, the maximum power is transferred from (transferred from, not consumed by!) one to the other at the condition of resonance. If there was no resistance in the circuit, this exchange or oscillation would continue indefinitely because the current and voltage are out of phase in each branch of the circuit and no power is consumed; the damping and decrement would be zero and the Q infinite. Moreover, if the exchange of energy is attempted at any other frequency than the resonant frequency, the impedances are not conjugate and less than the maximum power will be transferred from one to the other. Power is not consumed by the tuned circuit, except in any resistance which may be present, but is transferred from one component to the other and back again. This enables the tuned circuit to act as a sort of "accumulator" for radio frequency power and in a transmitter which is sending say 500W to the aerial and taking say 750W from the power supply, there may be over 7kW circulating in the tank circuit. The phase difference between voltage and current at resonance is equal and opposite in the coil and the capacitor and so at the terminals of the circuit there appears to be no phase difference at all. It's still there for each component - you just can't see it - the reactances don't "cancel", but the phase differences do. The tuned circuit at resonance appears to be a pure resistance because of the cancellation of the phase differences at the terminals, but it obviously is not exactly the same thing as a pure resistance because a resistive load by definition consumes power and converts it to heat, light, radio waves, mechanical energy etc. This is particularly evident in a parallel tuned circuit as shown, since at resonance the apparent resistance is very high (theoretically infinite). This in fact tells us a lot about loads which are not at resonance but contain net reactance - a reactive load receives power from a generator for part of the alternating cycle, and gives it back over another part. Since the voltage and current are not in phase, power is not actually consumed except by the resistive component of the load. Such unconsumed, circulating power is called "wattless power" because it doesn't do any work. Electricity meters still measure it however, and you still pay the bill for it, so it is an excellent idea to minimise the wattless power taken by any electrical appliance, which of course we can do by cancelling the phase difference present at its input terminals. This is called "power factor correction", is generally achieved by connecting appropriately rated capacitors across the mains input to the appliance, and a purely resistive load on the mains supply has a power factor of one, meaning there is no wattless power for which you are being charged. Not only is this advantageous to the consumer, but it would be a disaster for the power company if the distribution system was feeding a huge reactive load with massive out of phase components (remember the maximum power theorem!) and power companies require that all large loads are power factor corrected. All appliances which you buy and which have a significant reactive component to their load characteristics are power factor corrected by the manufacturer, so please don't try "tweaking" them! The next installment will examine the meaning of Q and how to achieve an impedance match by inductive coupling. Back

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Maximising Power 1

Homepage

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Maximising Power 2

The Spark Transmitter. 3. Maximising Power, part 2.

"What may seem to the uninitiated a simple explanation, may appear to the expert as a most round-a-bout way of stating the ideas; the technical words are the short cuts." C.R. Gibson, F.R.S.E.

Unloaded Q and Loaded Q. The parameter Q has been mentioned several times and it is now appropriate to consider what is meant by Q. The definition of this quantity is simply the ratio between reactance and resistance, or in other words, wattless power divided by in-phase losses. It can also be expressed as the amount of power circulating in a resonant circuit divided by the amount of power which must be added per cycle to keep the oscillations at constant amplitude. There is a variety of definitions therefore, but all with the same underlying meaning; Q is a measure of efficiency and is frequency-dependent. Unloaded Q refers to the Q of the coil, capacitor or tuned circuit itself with no other factors considered. This might reasonably be the Q value measured on a Q meter, or the Q of a Tesla secondary operated without ionisation of the air or spark breakout. Loaded Q might refer to the same component or circuit, but now under operating conditions such that it is expected to be coupled in some way to a resistive load in which power is being dissipated. Thus it could be the Q value of a valve transmitter output tank circuit when that transmitter has been properly adjusted to feed an aerial, or, what is effectively the same thing, the Q of a Tesla coil primary circuit when the coil is in operation and sparks are being drawn from the secondary. The difference comes about very simply because coupling a tuned circuit to a load reflects the resistance of that load into the tuned circuit (how much depends on the coupling). If Q is the reactance divided by the resistance, then if the resistance goes up, Q comes down. In fact, operating a spark transmitter or Tesla coil in the unloaded condition is asking for serious trouble: if the primary circuit has nowhere to dump its power which might come about through serious mistuning, all of that "output" will remain in the primary circuit, causing severe overheating at the gap with damage to the sparking surfaces and probable breakdown of the capacitor insulation. The same is true of valve transmitters, where the circulating output power results in a badly overheated anode, and in modern semiconductor circuits where it results in dead transistors if the protection circuitry isn't quick enough. The efficiency of an output tank circuit is simply:

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Maximising Power 2

and the relationship between the voltage, power and QL of a tank circuit under pure sinusoidal conditions is given by:

where P is the power, ω is 2π times the frequency, L the tank circuit inductance and QL the loaded Q.

Thus high unloaded Q, QU , is necessary to ensure low losses in the components themselves, and low loaded Q, QL , to ensure that there is not a build-up of power circulating in the tuned circuit, but is transferred to the load and thereby to ensure reasonable overall efficiency. Simply adjusting the coupling between the primary and secondary will vary QL within reasonable limits. (More about coupling and the coupling constant k later.) Tight coupling gives low QL, loose coupling gives high QL. In a transmitter, this value of QL matters for another reason, namely that it gives added harmonic suppression and transmitters generally compromise with a QL value of between say 5 and 15. Lower than 5 and the harmonic suppression suffers. Higher than 15, and the components in the tank circuit begin to get hot.

The reason for this is not hard to see. If Q is defined as wattless power divided by losses, then the losses are not restricted to heating losses - a tank circuit feeding an aerial has a power loss to the aerial, and the wattless power is that being transferred between the coil and capacitor (remember the maximum power theorem inside tuned circuits). If QL is 15, what this means is that there is fifteen times as much circulating, wattless power as there is being delivered to the aerial. There will, of course, be fifteen times as much heating loss as for operation with Q = 1 because whatever the circulating current, it will also pass through whatever resistance is present in the tuned circuit and being in-phase in the resistance, will produce i2R losses. A 500W transmitter at full output may take 750W from the supply if it is efficient; if the loaded Q of the tank circuit is 15, then there will be 15 x 500 = 7,5kW circulating as wattless power in the tank circuit. Likewise, in a Tesla secondary there may be a very large wattless power circulating, built up over a number of cycles, which is periodically dumped into a large spark as in-phase power as soon as the wattless power accumulated is sufficient to bring about ionisation of the air.

In a spark transmitter or Tesla coil, increasing the loaded Q up to this point restricts the power transfer to a narrower range of frequencies and if the balance is right, the maximum current in the aerial (or Tesla secondary) will increase, yielding better results, always assuming the primary voltage developed is within

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Maximising Power 2

the primary capacitor rating! But it isn't quite as simple as that, because the value of QL also sets the level of circulating current in the coil and hence the magnetic field and hence the efficiency of power transfer; QL values less than about 4 are quite difficult to extract sufficient power from without an excessively high coupling constant and close proximity of the coils. The really big (read megawatt) transmitters obviously cannot afford to use a high loaded Q in the tank circuit and operate with QL of 3 or 4 at most; in such cases, special techniques are employed to obtain efficient coupling and good harmonic suppression. Let's look at an example of valve technology (modern transistor technology tends to do things differently for a variety of reasons) in which a valve output circuit is delivering power to a transmission line of 50 ohms impedance. Let us assume it transmits on 200kc/s and that we want to design for a loaded Q of eight.

Firstly we decide on the reactance of the tuned circuit components. This is simply QL times the transmission line or load impedance, so it's 8 x 50 = 400 ohms. Now using the standard formulae backwards we calculate the values of L and C at 200kc/s which will give 400 ohms reactance:

These values of L and C will not only resonate at 200kc/s, but when coupled to a load of fifty ohms via a link coil will allow a loaded Q of eight to be readily achieved without the output link being so close that there is a danger of high tension flashover. This evidently has serious application to Tesla magnifiers, as we shall see later.

Measuring Q. Use a Q meter! These occasionally turn up at ham radio rallies. If you have an oscilloscope and a signal generator (couple both very loosely to the tuned circuit) you can find the resonant frequency and the two frequencies, one either side of resonance, which give 0.707 times the voltage maximum at resonance, call them f0 for resonance, f1 and f2 for the lower and the higher frequency respectively (the other coil primary or secondary - must not be in the vicinity when this measurement is made, i.e. the measurement is to be made on the uncoupled system). The unloaded Q is then equal to the resonant frequency divided by the bandwidth:

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Maximising Power 2

Accounting for resistance. In the real world, we must modify the equation we had for a tuned circuit which described the energy stored in the capacitor as being equal to that in the coil, so as to include the losses due to resistance. We now have:

or, rearranging:

It is now possible to see the importance of high unloaded Q in the primary inductance of the spark transmitter. (This of course applies also to the secondary.) The potential energy stored on the capacitor is divided between the kinetic energy of current and magnetic field in and around the coil on the one hand (wattless power) and the heat energy dissipated in the resistance (in-phase power) on the other. But there's more to it than that. Remembering that the resistance is proportional to the number of turns on the coil (number of turns multiplied by π by diameter equals length of conductor) and the inductance is proportional to the square of the number of turns, as we add turns to the coil, the inductance increases more rapidly than the resistance. In other words, coils of high inductance tend to be more efficient than coils of low inductance because the ratio of inductance to resistance is higher (at a given frequency this means that QU is higher) and hence the division of energy between inductance and resistance favours the inductive kinetic energy rather than resistive heating losses. This inductance helps overall efficiency when you consider that there is also the resistive loss associated with the primary spark gap to be taken into account. It was often noticed by radio amateurs after around 1912 (when, following the loss of the "Titanic" they were banished to wavelengths shorter than 200 metres / frequencies higher than 1.5Mc/s) that at these higher frequencies it was difficult to get a spark transmitter to operate efficiently because of the need to use small coils, and lead lengths had to be kept very short to ensure that most of the inductance was in the coil (which being coupled to the aerial, would do some good) and not in the interconnections where it would be wasted. Spark transmitters and Tesla coils alike benefit from plenty of inductance in the primary circuit to help offset the resistive losses in the spark gap. However, there is indeed a limit to the usefulness of more turns. As the inductance goes up, the current goes down, and the resistance of the gap is inversely proportional to the current. As a coil acquires more turns, so the radio frequency resistance of the coil is increased over and above that due to the additional length of wire by the "proximity effect" between all those turns, which tends to reduce the cross-sectional area of the wire over which the current can flow. Then there is the "skin effect"

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which constrains high frequency currents to flow on the outside of the conductor. This is more noticeable with thick wires than thin wires, and the ratio between the rf resistance of a thick wire and its dc resistance is likely to be large, resulting in the curious fact that there is an optimum wire size for a given size of coil and a given resonant frequency. So in practice there is always an upper limit to which inductance of a coil can be increased, for a given frequency of operation, size of wire, spacing, and overall length and diameter, before the efficiency starts to fall off. Happily, in the case of primary windings, this limit is seldom approached. With Tesla secondaries, 600 - 2000 turns may prove useful before anything untoward is noticed, and this will vary widely according to the variables stated above.

The photo above shows a low loss transmitting inductance at the Rugby station in the early 1920s. The scale of things can be gauged by the two workmen. The proximity effect is very hard to predict, but the skin effect is much simpler. In copper wire at 20°C, the skin depth in centimetres is given by: http://home.freeuk.net/dunckx/wireless/maxpower2/maxpower2.html (5 of 8)6/20/2011 2:49:19 PM

Maximising Power 2

If you imagine a circular wire, the skin depth is represented by a thin ring around the circumference and all the current may be thought of as flowing in it. This is not the physical reality; the current actually decreases exponentially with depth and there are major phase changes too, but the skin depth is the thickness of a ring in which all the current could flow and give the same observed resistance, assuming no proximity effect (which sadly is only true if there are about ten wire diameters between turns!) The skin depth is proportional to the square root of the resistivity of the wire and resistance wire accordingly suffers less from the skin effect than copper, since a resistance wire must be much thicker than a copper wire at a given frequency before the effect becomes noticeable. Accordingly, where wires are thick enough to exhibit skin effect, there is less difference between the rf resistance of copper and resistance wire than the dc resistance difference between the two might lead you to expect, since the lower thickness of the copper skin in which the current is flowing tends to be compensated for by the greater thickness in which the current flows in the resistance wire. The resistance of copper wire at 20°C of diameter d centimetres in ohms per centimetre at radio frequency is:

The solutions to the problems of proximity and skin effect were worked out by a number of early wireless technology researchers, and originally it was German wireless engineers who, around the time of the First World War, came up with the solution called "litzendraht". Litzendraht, or litz, consists of a number (anything from three wires to several thousand) of individually insulated wires braided together, the individual wire diameter chosen such that the skin effect is negligible in each wire, and braided together in such a way that each wire has a reasonably equal share of the inside and outside of the composite wire so formed. For the sort of frequencies commonly encountered in Tesla coils, 0.08mm (44swg) is a fair compromise and coils having an extremely high Q can be wound with litz made up from 44swg wire. It is astonishingly expensive to buy (currently around £12 for one ounce) and for anything except the small coils used in wireless work, it is best to "roll your own" even if that means that the optimum braiding is unlikely to be achieved. Whilst it is now extremely expensive, using litz has become very much easier since wires ceased to be enamelled with real enamel. In my Father's day, litz of 50swg was in common use for frequencies around 1-2Mc/s, and the enamel had to be carefully scraped with a sharp razor blade from each 0,025mm strand before it could be soldered, resulting in a certain amount of "litz rage" when large numbers of wires had to be treated - and broke. Small diameter litz of more than 27 strand was accordingly none too popular. These days, with plastic insulation, you just solder it using a hot iron which burns clean through the covering.

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Maximising Power 2

However, Q in the secondary can be made sufficiently high for practical purposes without the complexity of litz simply by using wire of the optimum thickness; though a coil can always be made more efficient at frequencies under 1Mc/s by using litz, it can become critical on the efficiency of the braiding of the strands and the insulation which spaces each strand. Calculations of optimum thickness of a single strand were yet again done around the time of the First World War and books on wireless technology of preWW2 vintage often give ideas and references should you be keen to try. A particularly valuable paper on this whole topic was written by Professor C.L. Fortescue and published in the Journal of the Institute of Electrical Engineers, pp 933-943, 1923. This, and the references in it, and more particularly the criticisms in the discussion at the end of the paper itself, are a good guide to the design of coils - and also a guide to the pitfalls. Whilst the skin effect is essentially conquered by these techniques, proximity effect can only be overcome by trial and error spacing of the turns. It often transpires that the losses associated with the proximity effect are more acceptable than the extra length of wire and extra resistance if the turns are to be spaced, and this is particularly the case with large diameter single wires. With wires of optimum diameter or litz, spacing is usually effective, but litz is in a sense automatically spaced because of the insulation around each strand and the overall covering, usually silk (real or artificial). Another invention from this same era was the ferrite core. Ferrite cores concentrate the magnetic field produced by a coil into a small volume, and a greatly increased inductance can be obtained from a small coil by using a ferrite core. Since the inductance has been increased without significantly increasing the resistance (you must be careful to provide a small amount of clearance between the ferrite and the coil or the ferrite will increase resistive losses) the Q of the coil improves dramatically, values in the high hundreds being common. Unfortunately, ferrite cores in Tesla coils are generally not a good idea, and this for several reasons: 1. The coil response now extends down to dc and is no longer confined to the resonant frequency alone! Basically, the ferrite core reduces leakage inductance and increases the coupling constant k to something a lot closer to one. This makes for an exceptionally vicious pulse transformer which responds to all oscillating magnetic fields regardless of frequency, rather like an iron cored audio transformer and with similar characteristics of broad frequency response with a high frequency hump due to resonance at the top end. Not only do you get the benefits of the decaying oscillatory sinewave rf discharge, but you get the massive wallop from the initial dc pulse out of the capacitor. Whereas with a small air cored Tesla coil of say ten watts it is perfectly safe to take the spark discharge into a piece of bare metal held in the hand, if it is ferrite cored the result will be extreme pain if not risk to life. I found this out the hard way, fortunately through the handle of a wellinsulated screwdriver. Though separated from the metalwork by one inch of clear plastic, I could feel every single spark like a stinging slap on the palm of my hand. Mercifully, I was expecting trouble and took the precaution of using the screwdriver; I dread to think of how it would have felt if I had been using a bare piece of metal instead. The conventional, air cored coil I usually used with the same power source gave a spark which I could take to a key or metal rod with nothing felt. 2. The ferrite core has a saturation limit, or in other words, for a particular frequency there is a limit

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Maximising Power 2

to how much power you can couple through each cubic inch of ferrite. The more powerful the coil, the more ferrite is needed and this, like litz, is not cheap. 3. Ferrite is not a perfect insulator. Some grades are actually of quite low resistance, only a few hundred ohm-centimetres. In my experiments I simply potted the ferrite (which was a high resistivity grade, being one inch diameter interference suppression beads intended for slipping over half inch diameter cable) in beeswax and wound the coil on a thin former over that, and there was no trouble with insulation breakdown. That's all well and good for a low-powered baby coil of ten watts input, but I wouldn't expect it to hold for a kilowatt! Coils using ferrite cores are not a good idea for these reasons. If you simply must try it, make a baby coil with not over ten watts input, and under no circumstances try to take the discharge into a bare piece of metal in your hand, or I promise you will regret it. This caution is of less importance if the source is a sinusoidal generator rather than a spark transmitter. The next section looks at the vexed question of the ideal conductor for radio frequencies. Back Homepage

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Inductive Coupling of Tuned Circuits

The Spark Transmitter. 4. Inductive Coupling of Tuned Circuits.

"All is riddle, and the key to a riddle is another riddle." R.W. Emerson

Will we ever get to the load? Well, it's getting closer . . . trust me, I'm a doctor. Inductive Coupling. Having generated power at rf, it is necessary to transfer it from the primary circuit where it originated to the secondary circuit where it will do something useful. Remembering the requirements of the maximum power theorem, it is clear that the conditions required are those of an impedance match. In the diagram, the primary and secondary coils are coupled inductively by means of a mutual inductance M. This has a reactance at the operating frequency Xm. For perfect matching, the resistance coupled into the primary circuit must be equal to the resistive load which the generator expects to see. If the load is itself reactive, then to get a perfect match two out of the three reactances Xp, Xs, and Xm must be variable. Fortunately, if primary and secondary are tuned circuits at resonance, things become greatly simplified and we have the possibility of obtaining a perfect match purely by varying the mutual inductance coupling. This we do according to the equation:

where Rp and Rs are the resistances associated with both circuits. (The value of the mutual inductance M can then be calculated if we know the frequency of operation.) Well, what exactly are these resistances? For the primary circuit, Rp is the resistance associated with the generator (remember the maximum power theorem!) But what is Rs? That is a harder question to answer. It also seems likely, for a Tesla coil secondary, that it will vary according to whether a spark is being produced from the top electrode or not. At least with an aerial it will be constant. With a resonant aerial in fact it's fairly easy, being equal to the sum of the http://home.freeuk.net/dunckx/wireless/inductive/inductive.html (1 of 6)6/20/2011 2:51:04 PM

Inductive Coupling of Tuned Circuits

resistive losses in the aerial, the ground and the radiation resistance. The radiation resistance is a fictitious resistance, which if it was included in the aerial would cause as much power loss through heating as the loss of power due to radiation from the aerial. So in the case of a Tesla secondary, what we need here is a "spark resistance" which would cause the same amount of power loss as is caused by spark discharge from the top electrode. It is by no means easy to see what value this should be. We can, however, state with certainty that it is unlikely to be very useful trying to reduce the rf resistance of the secondary to a value much below that of the ground connection, as the two act in series. Fortunately, we can be ignorant of the exact requirements here and adjust the mutual inductance coupling by the physical separation of the primary and secondary coils and, according to time honoured wireless practice, "tune for maximum smoke"! [You can usually tell when you've damaged an electronic component because the smoke they put in it at the factory leaks out. I don't know who it was who invented smoke as a means for indicating faulty components but all I can say is, it's a jolly clever idea and I wish I had the patents on it.] One of the reasons (by no means the only one, nor, as it happens, anything like the best one) why Tesla secondaries give bigger sparks with larger top capacitances is because there is often insufficient mutual inductance coupling for perfect impedance matching (this may be because decreasing the separation between the coils causes sparking into the primary) and when the top capacitance of the secondary increases, the resonant frequency drops, more turns are needed on the primary (which may be too small in relation to the primary capacitance) and the effective size of the primary is increased, thereby increasing the proportion of input power converted to rf, and increasing the mutual inductance and improving the match. It may also happen that reducing the secondary reactance (corresponding to the drop in frequency) improves the impedance match and we get a better power transfer from that cause too. (We'll come to the best reason for big secondary capacitances later.) But there's more. The mutual inductance coupling between primary and secondary can be related to their self-inductance by means of the coupling constant k:

Notice that since k is defining the relationship between magnetic flux linkages in the circuit, it can never be greater than 1. A value of 1 means that all the flux produced by the primary is linked with the secondary and vice versa. A value of k greater than 1 would mean that more than all of the flux produced by the primary is linked with the secondary and thus values of k greater than 1 (and I have seen people claim it!) means you have a problem! In fact, k = 1 is never achievable! The closest you are likely to get is in the output transformers of high quality valve amplifiers where primary and secondary are split into interleaved windings, and in specialist types of instrument transformers where the construction is similar. Power transformers used for supply distribution are also quite good, fortunately for the supply companies and the end user. Neon sign transformers and welding transformers are examples of designs where the value of k varies considerably with the load and is sometimes a lot less http://home.freeuk.net/dunckx/wireless/inductive/inductive.html (2 of 6)6/20/2011 2:51:04 PM

Inductive Coupling of Tuned Circuits

than 1. Transformers of this latter type are called "magnetic leakage transformers" because the design is such that a large proportion of the flux generated by each coil can escape from the magnetic circuit associated with the other coil. Under load, the proportion which "leaks" increases. This gives intentionally poor power regulation and ensures that when a short circuit is placed across the secondary (the striking of the welder's arc, the conductive breakdown of the neon gas, or the flashing over of the primary spark gap) the output voltage is suddenly reduced until the "fault condition" is removed. Mr. Melville ClappEastham in the USA can be credited with the introduction of this type of transformer for spark transmitters, and his Model E transformer has a prominent place in wireless history. Similar results can be obtained from a power transformer of the closely coupled type if there is an external inductance (choke) in series with the primary and this external choke provides the necessary "leakage inductance". The coupling constant is independent of the number of turns in a coil. The number of turns in a coil determines the magnetic field which will be produced for a given current. The coupling constant is concerned with how the lines of magnetic force produced by one coil interact with another coil, and hence the coupling constant between two air spaced coils depends only on their physical size and disposition in space. Hence to obtain the best coupling between primary and secondary in an air-cored transformer we can only change the size and spatial relationships of the coils. With a tapped coil it may be noticed that changing the tap position changes not only the self-inductance but also the coupling constant. This is of course because when the tap is moved to a different position, the effective size and spatial relationship of that coil are changed as well as its self-inductance. When we have the critical coupling, which exists when the voltage output is optimised, then we have an additional relationship between kc the critical coupling constant and the Q values of primary and secondary:

The value of coupling constant is important in a spark transmitter because the tightness of coupling determines the rate at which the primary loses power to the secondary, and hence determines decrement, damping, sharpness of tuning (loaded Q) and intensity of current at resonance (and hence secondary voltage in a Tesla coil.) Remember those nice graphs showing the logarithmic decrement and loaded Q? The graph of decrement δ = 0.09 and loaded Q = 34.6 corresponds to the critical coupling constant having a value of kc = 0.17, which, from the records left by the old-time spark wireless operators, is around the maximum which can be used with a quenched spark gap of multi-plate construction. Hence for a critical coupling constant of kc = 0.17, the product QpQs must be 34.6. We can of course split that product between a wide range of possible Qp and Qs values! If both are equal to Q = 5.88 (the square root of 34.6) the decrement of each circuit individually is given by the graph of δ = 0.53. http://home.freeuk.net/dunckx/wireless/inductive/inductive.html (3 of 6)6/20/2011 2:51:04 PM

Inductive Coupling of Tuned Circuits

The diagram shows the effect of varying the coupling on the frequency distribution (read 'logarithmic decrement') of a spark transmitter. As the coupling is increased much beyond 20%, k = 0.2, the frequency spread increases dramatically, indicating that the logarithmic decrement has increased and that loaded Q has decreased. The square of the current, plotted on the y axis, also plummets drastically.

The next diagram shows that, in order to get the highest possible secondary current, the primary and secondary circuits have to be slightly detuned. In each case the primary circuit remains tuned to a wavelength of 650m, whilst the aerial circuit (secondary) is varied from 500 - 650m. The best result is for 585m. This was obtained in an experimental test circuit chosen to demonstrate the effect clearly, and the best detuning is here about 11%. For the average aerial and coupling k=0.17, the detuning was normally about 3%.

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Inductive Coupling of Tuned Circuits

Curves like these are recorded by coupling an rf ammeter into the circuit. I have seen circuit diagrams in which the meter is placed directly in the primary circuit, but evidently these were low voltage circuits (possible with the quenched gap which will operate on just a few hundred volts) and it is more usual to couple the meter to the aerial circuit and then indirectly by means of a coupling loop. A thermocouple ammeter would be the instrument of choice, but these curves were recorded most likely with a hot wire meter, whose deflection is proportional to the square of the current - hence the plot of I2 on the y axis. The mutual inductance coupling ensures that everything critical to the operation of the spark transmitter (or Tesla coil) is dependent on just about everything else, and that is why trying to find the global optimisation for a Tesla coil to give the biggest spark for a given input power is so very difficult. It isn't that we have such an enormous number of variables - it's the interdependence of all of them simultaneously on each other! All of which goes to show how very complicated the inductively coupled spark transmitter (or Tesla coil) really is. It's a nice demonstration of the fact that there is not necessarily a direct correlation between the number of components in a circuit and its complexity of operation. The spark transmitter circuit is one of the simplest - just seven components (power transformer, primary capacitor, primary inductance, primary spark gap, secondary inductance, secondary capacitance and mutual inductance) and yet a detailed description of its operation would require a lot more space than this and cartloads of higher mathematics. Any electrical circuit can be broken down into just four fundamental 'units' inductance, capacitance, resistance and mutual inductance - and with just seven components, this circuit has the lot. As a mere radio ham tinkering outside my sphere of professional competence I can only scratch the surface. I am left gasping with admiration at the achievements of the old timers who built and operated spark transmitters and Tesla coils often without a clue as to the frequency of operation or technical knowledge much above Ohm's law. They did it, of course, by a combination of knowing inside out what there was to know, by meticulous method and by sheer patience and dogged determination. Oh, by the way. We have now arrived at the load.

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Inductive Coupling of Tuned Circuits

We're not through yet though. The next section looks at transmission lines and magnifier circuits. Back Homepage

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The Induction Coil

The Induction Coil "Now does my project gather to a head My charms crack not, my spirits obey, and time Goes upright with his carriage. How's the day?" Prospero, "The Tempest"

At last! It lives! My novel sidetone generator is complete! (Cue thunder & lightning, maniacal laughter, clanking chains, baying hounds etc.)

I've wanted one of these things since I was a lad, it has only taken thirty years but I've finally gone http://home.freeuk.net/dunckx/wireless/inductioncoil/inductioncoil.html (1 of 8)6/20/2011 2:56:14 PM

The Induction Coil

and done it. The details of what to do and how to do it were obtained mainly out of reprints of relevant constructional articles from Lindsay Books (http://www.lindsaybks.com) One or two tweaks I had to discover for myself.

The induction coil primary was wound with a couple of layers of 1,7mm wire. This can be seen protruding from the centre of the coil to the left in the photo below. Around 200 turns were used in total. The coil covering is heavy photo card from a stationers, later on I sprayed it with aerosol wax polish and it attained a deep shine, just like the ebonite sheet which was once used for this job. The primary core is packed with about 11 ounces of 1mm iron fence wire, which was annealed in a barbecue charcoal fire.

The primary former is a length of cardboard tube, and both end cheeks on the primary former are also short lengths of cardboard tube which were a good slip fit, stuck on with PVA wood glue. This slides inside a length of Tufnol tube, 1,5 inches outside diameter and approximately an eighth of an inch wall thickness obtained from RS Components (http://rswww.com) which also provided Tufnol sheet for the base and main coil end cheeks, and more half inch Tufnol tube for the EHT standoffs also seen in this picture. The phosphor bronze balls used as discharge electrodes are half inch diameter, sadly no longer available, but brass will do as well and small doorknobs (really intended for chests of drawers) can be obtained from several chains of DIY warehouses, in fact I used a one inch doorknob as the discharge ball on the Tesla coil. All other metal supplies and many hand tools (e.g. taps and dies) used for projects on these pages, I obtained from Macc Model Engineers, 45a Saville Street, Macclesfield, Cheshire, SK11 7LF, tel. 01625 433938 - their service is first rate, and they are now on the internet!

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The Induction Coil

You can find MACC here.

The silver contacts I used for the interruptor, around a quarter of an inch diameter, were from a piece of silver I've hoarded for years. This I melted, cast into an ingot, er - lump, and then machined to size. Silver has the curious property that, when molten it absorbs oxygen from the air, which is expelled again when the metal solidifies. The silver castings are riddled with minute blow-holes from this cause, irritating but harmless.

The picture above shows the ever-versatile Unimat 3 being used to wind the "pies" of the secondary, and a variac was used to regulate the speed. The winding gear is a simple thing made from a couple of thin Tufnol sheets with a brass spacer, and it runs on a rod which passes through the Unimat headstock as the pies are too big to swing over the lathe bed. The wire was guided by hand, moistening my fingers with linseed oil. The secondary is constructed from around 2lbs of 42swg enamelled and double silk covered wire. I was lucky to find this as a production over-run at the Scientific Wire Co. (http://www.wires.co.uk) otherwise it would either have been unobtainable or have cost a fortune. It's worth making a telephone or email enquiry as not all they have is on the website. The coil gives (unloaded) a spark of an inch and a bit between half inch phosphor bronze balls. It is very hot and will ignite paper and card rapidly. The completed pies are shown below. A ruler gives an idea of scale.

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The Induction Coil

Two of these were lost in the initial test when the insulation (here paper disks) blew through. The insulation was replaced with three layers of card soaked in melted beeswax per pie, and molten wax mixture was painted on around the seal between the Tufnol tube and the card washers. The pies were insulated with a molten mixture of beeswax and rosin (from a musical instrument shop) just as the originals. This was brushed on with a fine paintbrush whilst winding the coils; the motor was slowed to a crawl whilst doing this. The unevenly-insulated pies were then cooked gently in an oven at around 50C just to soften the wax mixture until the insulation became homogenous. The pies, part-assembled on the Tufnol tube (with the initial paper insulation) are shown below.

To mount the coil I chose a piece of West African mahogany from South London Hardwoods (http://www.slhardwoods.co.uk) and I also bought a couple of sticks of ebony. The latter were used to make handles for the coil discharge electrodes, for the core of the Ruhmkorff commutator switch, and for the pillar on which the Tesla secondary stands. Hard rubber, called ebonite, was used for this, but dry wood seems OK at these voltage and power levels. To my knowledge, there is

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The Induction Coil

just one compounder of ebonite left in the UK, in Manchester, and it's fine if you want a few tons!

The design of the radio frequency part of this project called for months of experimentation with the part-made induction coil, at that time screwed to a piece of very tatty plywood whilst many design changes were made. It was decided to use a primary of two layers of eighth inch brass boiler band from Macc, supported on wooden dowels which were soaked in melted beeswax. It is essential that the holes for these are drilled exactly vertically in the baseboard, otherwise the primary will look very uneven and will not contact all of the octagonally-spaced supports. Here the Unimat is being used to sink these holes.

More woodwork was needed when it came to hiding the Fizeau condenser across the contact breaker points. The condenser used was an old WW2 vintage Dubilier nitrogol 2uF 400V unit. It had already been established that 1uF was not enough, and the voltage rating is essential to cope with the back emf. Here's the inletting nearing completion. I placed a ruler across the bottom of this shot to give an idea of scale, but the divisions aren't very visible, unfortunately.

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The Induction Coil

The wood looks quite pale prior to French polishing with Liberon button lac dissolved in methylated spirits. It was rubbed down with sandpaper between coats until all the wood pores were filled, and thereafter rubbing down with Liberon 0000 steel wool and linseed oil. It's the first time I've ever tried doing it and it's neither easy nor perfect to look at - but not a bad job for a novice. The near-finished baseboard, together with a few components, is shown below. The octagonally-spaced dowels for the boiler band primary can clearly be seen, and the condenser is well fitted in its hole. Aerosol wax polish should not be used on shellac finishes, as the solvents in it will dissolve the French polish which took you so long (and so many attempts!) to get looking good. Use the solid stuff in tins instead.

Bottom left in the above photo is part of the Ruhmkorff commutator switch. This was a most infuriating thing to make, requiring some of the most dubious soldering I have ever done (with a 50-year old 230W thermostatic iron!) but we got there eventually . . . final polishing was with some amazing Japanese Tamiya abrasive paper, down to 2000 grit, which I got from Brouckx model shop in the Koning Albertstraat, Hasselt, Belgium. The components of the switch appear here.

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The Induction Coil

The Tesla secondary was around 700-800 turns of spare wire left over from the induction coil, around an inch and a quarter diameter and seven and three quarters long. It's very unevenly wound, the turns even cross over at a few places! The coupling coil is an unknown number of turns (try until it works!) of 36swg tinned double silk covered copper, also from Scientific Wire, wound on a cardboard pot which once held Fair Trade cocoa powder. The condenser is a cheat. I was going to use an ex-Admiralty WW2 vintage 28kV 0,0011uF mica condenser, but its losses hampered spark production (the input to the induction coil is only 30-70 watts or so - my QRP radio friends will cringe - but that's not much to make sparks with, especially given the inefficiency of induction coils) so I used ten 0,01uF 1kV polypropylene units from RS Components in series, hidden inside the wooden box. The odd value of the ex-Admiralty mica is due to its being exactly one standard Admiralty "jar" of capacitance in old units! The output from the Tesla coil is shown below.

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The Induction Coil

The sparks are maybe 1,5-2 inches long. I have changed the colour balance of the photo, as the original is too blue. This is still not right, but it's closer to the purple which your eye actually sees. There's an evident difference in the spectral sensitivity between eye and film, especially at low light levels. In operation, the most important thing is to ensure that both the interruptor contacts and the sparking balls are kept clean. Every ten minutes or so of operation necessitates a break for cleaning with abrasive paper. The setting of the spark gap is also very critical to success, and the sparks from the Tesla coil make a strange squeaking noise when all is tuned correctly. A good ground connection is important, and a large metal object (I have used a big metal case maybe five feet by two by two) is better than the ground rod I use for my amateur radio transmitter.

The only problem with this thing is the copious quantities of ozone emitted (honestly, you can't have it switched on for more than a minute without needing to leave the room, it's that bad!) With the fundamental around 2Mc/s, plus the emissions of the interruptor, it does cover all amateur bands though . . . simultaneously! Back Homepage

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The Quenched Spark Gap

The Quenched Spark Gap

"...and here's the practice o' it." Unknown

The quenched gap, as popularised by Telefunken, was a great success owing to the very high rate of switching which lent increased efficiency to their transmitters. It was said that a 500 watt Telefunken set with its quenched gap could outperform a Marconi set of 2.5kW with its rotary gap, and this was mostly down to the efficiency of the Telefunken gap, an early and poor quality illustration of which was included in "Alternator, Arc and Spark." I decided at the outset of my attempt to replicate a spark transmitter that I wanted to use a multi-plate quenched gap and hence had to set about making one. At the time, I could not obtain copper sheet in the sizes I wanted, nor copper rod at all, so the whole thing was made from brass. The electrical and thermal conductivities of a metal are related through the Wiedemann-Franz law which states that the ratio of these conductivities is a constant, independent of the metal and varying only with temperature. Regarding electrical conductivity, the difference is not enough to cause concern as the skin effect gives some degree of compensation (as will be shown later) and the periphery of each gap is large, but regarding the thermal conductivity of brass I was a little concerned that the inferior thermal properties might be the ruin of my plans. I need not have feared. For the relatively short time that I fire the thing up, the gap never gets more than tepid at the most; however, had I the choice and was starting over again I would use copper, although it is much less pleasant to machine. Aluminium would also be a good choice for the cooling flanges, though probably not for the gaps.

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The Quenched Spark Gap

The cooling flanges are about 15cm/6 inches in diameter and are made from 1,6mm thick brass sheet. The eight flanges had to be cut by hand using a 52 tooth-per-inch piercing saw with occasional lubrication with cutting fluid. This took a long time as may be imagined, each flange having a circumference of 47cm/18¾ inches, all eight amounting to sawing a line 3¾ metres/12ft 6 inches long, and consumed several weeks' worth of evenings and weekends, with considerable wear-and-tear on elbow and wrist joints and many tired fingers! The blades are fortunately not expensive, which is just as well as each blade lasted little over one flange.

The next stage was to mount all eight flanges together, drill a 1/8 hole through the centre of all eight on a friend's drill press (thanks Dennis, G7OGN) pin them to prevent their moving relative to one another and attack the edges with a file until they were all about even; an electric drill with carbide roughing disk speeded this process considerably, but flying burrs necessitated good eye protection with polycarbonate safety goggles. Following the smoothing of the edges and removal of many sharp burrs with suitable care to avoid impaled fingers, not always successfully, the eight flanges were mounted together on the trusty Unimat 3 and three holes drilled at 120°, each hole starting out one eighth in diameter, and by progressive stages being enlarged to half an inch, pinning these holes in turn to prevent rotation of the flanges between or during drilling operations. Drilling these three holes necessitated keeping one hand on the Unimat motor (for those who are not aware, the Unimat 3 motor is not continuously rated) and switching off when it became too hot to hold, which was often. This was a long, slow, laborious business, even with plenty of cutting fluid. That brass sheet is tough old stuff, and there's 8 x 1,6mm = 12,8mm (a bit over half an inch) of it in total to be got through.

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The Quenched Spark Gap

The next job was by way of light relief. The brass cooling flanges were now supported by nailing them very loosely to a piece of scrap wood through their centre holes and having masked their centres (where the electrical contact with the gaps would be made) spray painting them with black matt barbecue paint. There are chemical methods for blacking brass, which I would use if I had access to the chemicals (my PhD is in chemistry!) but sadly I didn't at this time so had to make do with paint. If the authenticity bug bites very deeply, I may just strip all the paint off and do the job properly, but I doubt even I could tell much difference. Other tasks performed, but not photographed, were: ●

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the cutting and drilling of end plates from Tufnol paper/phenolic composite (takes the edge off a plane in minutes, giving the blade the appearance of having been attacked by a file) this composite being chosen as it looks very like Bakelite; turning, cutting with a die, hardening and tempering the pressure screws and their mounting nuts, which are used to compress the gaps tightly together;

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The Quenched Spark Gap

●

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turning thick fancy brass washers to place under the nuts of the tension studding; cutting and trimming Tufnol tubing to act as insulators over the studding, the studding and insulator passing through the three half inch holes in each cooling flange; ●

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sawing with an eighty-teeth-per-inch piercing saw blade mica washers out of two inch mica disks 1/16 thick. These had to be smoothed down to a flat, parallel profile and this was very tedious indeed, being accomplished by a combination of rubbing the washer against a piece of sandpaper stapled to a board (and losing half the fingerprints from the tips of my fingers in the process ouch! - and the blood on the mica doesn't help its insulating properties either) and holding the washer in the three jaw chuck of the lathe, which was free to rotate, and bringing up upon it a small grindstone spinning at 4000rpm in the drill chuck (shown above) - unfortunately the soft mica rapidly plugs the grain structure of the grindstone. I started with forty disks and ended up with about fifteen washers between 1-1,1mm thick from which to select the best ones for the gaps - obtaining complete uniformity was impossible; ●

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The Quenched Spark Gap

●

turning twenty brass disks, one and a half inches diameter and around a quarter of an inch thick to act as the electrodes for the ten gaps. Ten gaps was the number selected on the basis of 1kV per gap. This operation was photographed but unhappily the flash unit mistimed and the fault was not noticed until the job had been done and the film then developed. A sketch of an electrode disk is appended. The recessed groove was cut later as a result of experience and it very effectively prevents the spark from "walking" its way through the insulating washers. The height of the protruding sparking surface was matched to the washer giving an overall gap length of around 8mm for 10kV, or 0,8mm/ 1/32 inch per gap. The rim was progressively reduced in thickness in order to increase the pressure applied to the washers (pressure = force / area) and improve the sealing, but obviously the strength of the brass limits the extent of this thinning process. These gap electrodes were silver plated by a local firm on the basis that a chapter on spark transmitters in an old book I have says the electrodes were silvered - the silvering lasted mere minutes under normal conditions of use, so the electroplated layer of ten microns was obviously far too thin. The finished gaps do look nice though.

The photograph above shows one completed rack of five gaps at the top, comprising four cooling flanges and ten silvered brass electrodes, each pair of electrodes separated by a mica washer, barely visible as five thin black vertical lines between gap electrodes. The end two gap electrodes have no cooling flange and are accordingly made much thicker; contact to these is made by 4mm radial holes http://home.freeuk.net/dunckx/wireless/quenched/quenched_gap.html (5 of 7)6/20/2011 2:48:08 PM

The Quenched Spark Gap

into which a plug can be inserted. Below the completed rack lie the components for its partner. The blue thing at the top centre is a tube of silicone high vacuum grease with which to help seal the gaps to the washers (not entirely successful.) Immediately below the tube of grease are four mica washers and to the left and right of them the two Tufnol end plates. The Tufnol plate to the left has the pressure screw resting horizontally just above the captive nut through which it normally passes, whilst the right hand plate simply has a hardened bearing for the stack of gaps to rest on. The four cooling flanges are on the outside to left and right. Below each Tufnol plate are four gap electrodes. Below the four mica washers is an assembled gap consisting of two electrodes (one invisible underneath) and a mica separating washer, the rim of which can be seen. The mica washers are translucent and in operation, dim light from the discharge can be seen to cover the whole area of the discharge surface. A small hole is visible on the back of the upper electrode. These were machined in pairs, one of each pair having a hole, the other having a pin, and these pins are pushed through similar holes in the centre of the cooling flanges and the partner electrode then mounted on the other side of the flange. The centre holes in the flanges do not really show up in this photo, but they do on the picture showing the flanges mounted for spraying as there is a nail through the black masking circle on each one. The spacing of the three half inch holes on the cooling flanges is such that when the three Tufnol insulating tubes are passed, with their tension studding, through the flanges, the tubing just clears the two inch diameter mica washers. Below the mounted gap are the three horizontal insulating Tufnol tubes, to the right and left of which are the six (total) fancy brass washers. Below the three tubes are the three lengths of studding and below them, six nuts and six plain washers. The studding, plain washers and nuts were purchased. Everything else was made. In all, this project occupied around four months of spare time. Around a kilo of scrap brass was produced, a small mountain of scrap mica, and large numbers of piercing saw blades and Unimat drive belts were broken.

These gaps are NOT for sale!

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The Quenched Spark Gap

The next section looks at some questions of efficiency. Back Homepage

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The Synchronous Rotary Mechanical Bridge Rectifier

The Synchronous Rotary Mechanical Bridge Rectifier.

Synchronous spark gaps are deservedly popular with many people who like to build Tesla coils. So is dc operation of Tesla coils. However, modern semiconductor rectifiers are not altogether happy with high levels of rf and have limits to their current capability and peak inverse voltage tolerance. The old fashioned synchronous rotary mechanical bridge rectifier (SRMBR, the original bridge rectifier) offers a solution to this problem.

Here is a 250kV SRMBR built by Siemens Brothers and Halske for hospital therapeutic x-ray service around the time of the First World War. With suitable tubes it produced x-rays of 0.05 Angstrom for treating tumours. The transformer is composed of two 125kV units in series on a common iron core and the secondaries are oil filled. At the front are two chokes (horizontal circular 'pies' on insulated stands) to help protect the transformer against rf from the sparking at the rectifier. The synchronous motor is mounted in the centre and above the transformer. An insulated shaft extends either side of the motor. Mounted on both sides of the motor are two heavy wires at 90 degress to one another, but one of the total of four wires is invisible owing to the angle and a support which obscures it. The wires in the 10 o'clock - 4 o'clock direction are most easily seen, but one wire at 7 o'clock can be seen just clear of the end support at the left front. The stationary electrodes of the bridge can be most clearly seen at the front of the array, where on the left hand side of the motor, two stationary electrodes are commoned at the top and connected to one of the chokes by a downcoming vertical wire. The action of the bridge should need no further explanation - it's a pretty simple piece of technology, and a semiconductor bridge simply replaces the rotating mechanical switches by solid state ones, so if puzzled you ought to be able to figure it out from there. The sketch below shows the general arrangement.

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The Synchronous Rotary Mechanical Bridge Rectifier

Back Homepage

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Transmission Lines and Magnifiers

Transmission Lines and Magnifiers

"Rigour is a much misused term, and not only in expository writing but in original scientific investigations it is too frequently another name for lack of a sense of proportion." Sir Arthur Eddington

Having arrived at the load, we can cast a rearwards glance as it were and see if it were possible to get here some other, better, way. One of the things which struck me when I began using Tesla coils as dummy loads for my spark transmitters was that the process of simply sticking the secondary into the primary was a bit hit-and-miss when it came to both the coupling and the impedance matching. Nothing I have ever seen in valve transmitter circuitry gets anywhere near this level of crudity. I never fail to be impressed by how well such an incredibly simplistic and inflexible approach actually works in practice. Then I considered the Tesla magnifier. A curious-looking beast, I thought. I wonder why it is put together like that? The answer was not long in coming. The characteristic base-feed impedance of a Tesla secondary is of the order of a thousand ohms, at least when a spark is being drawn. It might, under various conditions, be five thousand or ten thousand. The point is, it is of the order of a thousand. Now, this is highly inconvenient, as we shall see, but it did present Tesla with an alternative method of coupling and matching to the hit-and-miss "stick-the-secondary-in-the-primary-and-see" method, which at that time was quite probably the best that anyone could do.

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Transmission Lines and Magnifiers

Here we have the original magnifier, with a minor amendment or so in the primary circuit. N1 simply allows the regulation of resonant charging and helps the quenching, particularly if a power transformer, as opposed to a magnetic leakage transformer, is being used. The important parts are the coil marked Lx and the wire marked TL. The power from the spark transmitter must be conveyed by means of a mechanism which is a good impedance match between primary and secondary (maximum power theorem!). The coil Lx plus transmission line TL (for that is what it is) approximate to this. A single wire a metre or two above ground has a characteristic impedance of the order of a couple of hundred ohms, give or take. The coil Lx with its self-capacitance, and the loading of the Tesla secondary, constitutes an impedance of thousands of ohms or so, give or take. We thus have a reasonable match between the base feed impedance of the Tesla secondary (when sparking, that is; it is much, much lower when not sparking) and the coupling and matching system. We also have, alas, several problems. 1. This is a high impedance matching system. This means that, for any given power level, the voltages will be higher than if it was a low impedance matching system. For example, under pure sinusoidal conditions, and with a power of 1kW, in a 1kΩ system we would have 1000V. Under damped wave conditions, the initial peak intensity will be several times this, say 5kV. In a 50 ohm system, that same kilowatt will produce just 220V, maybe 1kV under damped wave conditions. The voltage is equal to the square root of {the impedance times the power}. 2. The second problem is that there is a factor of maybe five or so between the characteristic impedance of the transmission line and the base feed impedance of the Tesla coil, and between the transmission line and LX. This gives rise to standing waves on the transmission line and these give rise to an increased voltage on the line and top of the magnifier coupling coil. If our pure, sinusoidal kilowatt was flowing through a 1kΩ system it would produce just 1kV, but a mismatch into 5kΩ will lift this to approximately 2kV thanks to the standing waves. Under damped wave conditions this is more likely to be 10kV peak. So the voltage problem gets worse with the mismatch on the line. Unfortunately, the design provides no simple way to make any adjustment, the only possible adjustment being to add or remove turns from the coupling coil, which is hardly convenient in use. 3. The next difficulty is that it is very hard to couple power effectively into a high impedance system from a low impedance primary when the system is air cored, which is what we have. It gets harder still when there is an impedance mismatch on the transmission line. To do it needs a high value of the coupling constant k; we need tight coupling to get efficient transformer step-up action and hence we need to reduce leakage inductance. This gives rise to the third of the problems associated with magnifier systems, that the primary and coupling coil Lx need to be physically very close to each other. This aggravates the difficulties associated with the high voltages inherent in any high impedance matching system, especially where there is additional voltage rise due to mismatch and standing waves, namely the often-encountered problems with insulation and one coil sending sparks into the other. http://home.freeuk.net/dunckx/wireless/magnifier/magnifier.html (2 of 6)6/20/2011 2:52:19 PM

Transmission Lines and Magnifiers

4. The fourth problem derives from the third. Owing to the fact that a high value of k is needed in a low-to-high impedance coupling and matching system, there are severe problems with quenching at the gap. Hence the addition of the choke coil N2 of a few tens of millihenries. Spark wireless operators, who must on occasion have had an awkward, high impedance aerial to deal with, suffered exactly the same problem and evolved this solution. Normally, there are sufficient gaps such that the spark refuses to jump all the gaps in the multi-plate arrangement shown. Even on maximum voltage from the transformer in the power supply, those last two gaps will not conduct. However, if they are bridged by a choke coil, the potential of the end gap is communicated to the end-but-two gap. Now the main spark can jump, but when it hits the end-but-two gap the current cannot pass through the choke coil. However, there is now no problem in jumping two gaps. So the choke coil provides a means of stretching the spark over an extra number of gaps and hence when there are quenching problems, this little dodge saves the day. I have tried this and it certainly works, but under conditions where there are no quenching problems, the extra gaps actually make things worse instead of better, due to the extra resistance in the primary circuit. I have no doubts that if my primary circuit was experiencing quenching difficulties, this old 'wrinkle' would do the job. So we now have a question: is there a better way? Answer: yes. Enter the low impedance magnifier. This, as will be screamingly obvious to old thermionic valve radio fans, is nothing more than good ol' 50 ohm tuned link coupling, 1930s vintage.

I have shown the primary circuit in the "balanced" configuration as it might be if you used a centretapped secondary on the power transformer. It isn't essential to use such a primary circuit with e.g. neon sign transformers, but it offers the possibility of earthing the mid-point of the coil Lp, though this is by no means obligatory. Placing the link coil at the centre of a balanced primary reduces stray capacitive http://home.freeuk.net/dunckx/wireless/magnifier/magnifier.html (3 of 6)6/20/2011 2:52:19 PM

Transmission Lines and Magnifiers

coupling to the link LL because there is then little in the way of voltage difference between them. Using a "single-ended" primary, a similar reduction in stray capacitive coupling may simply be achieved by placing the coupling coil LL at the earthy end of the primary. If things get problematic regarding stray coupling, you simply interpose a Faraday screen between the two coils. I do not, however, expect any serious problems caused by stray coupling in this application as the operating frequencies are quite low, typically low hundreds of kc/s. The coil LL is brought to resonance by the capacitor CL and the other end of the low impedance transmission line is attached to the secondary at two places, the base and by means of a tapping point. The reactances of the primary Lp and Cp, LL and CL need to be calculated on the basis shown before in a previous installment. The primary circuit needs a reactance of around 400 ohms for each component as does the link circuit, and this will give a loaded Q value of 8 for both circuits, which from decades of valve transmitter development has been shown to be very forgiving and non-critical. The base tapping points on the Tesla secondary are obtained in the time-honoured manner of radio amateurs: guesswork. Actually, the tapping points aren't quite as crudely anticipated as that. In a parallel tuned circuit with impedance Z, the impedance ratio of a tapping point between that point (say Z0) and Z is equal to the square of the ratio of the turns of the two coils. Let's say we have a coil of 1500 turns which, together with top hat capacitance at the self-resonant frequency has an impedance of 50kΩ. If we wish to tap it at the 50ohm point, then the impedance ratio is 1000 and therefore the turns ratio is 31,6 i.e. we tap at the 47th turn. This calculation is seldom exactly matched by reality, and it is usual to supply a number of tapping points either side of the calculated position to allow for adjustment. Not knowing if this idea was going to work at all with a Tesla secondary, I made just one tap at the calculated position for my "technology demonstrator". It was good enough to show that the idea worked, and also good enough to show that more adjustment is necessary - the same coil in the usual plain inductively coupled non-magnifier configuration gives around 30-35cm sparks whereas in low-Z magnifier configuration it would not break out and to a grounded wire gave only 13cm sparks. There was plenty of clearance between the primary and link coils; indeed the best results were obtained with the two barely overlapping, indicative of the benefits of a loaded Q of around 8. In subsequent experiments I have been able to show that the tuning on this configuration is extremely sharp (having reduced some 2250V mica capacitors used to tune the link coil to a smoking mess!) which may even indicate an excessively high loaded Q greater than 8, although my feeling is this was simply due to mistuning, as mobile whip aerials for "Top Band" 1,82Mc/s are renowned for their very narrow bandwidth and critical tuning, and Tesla coils are of course far worse viewed from this perspective. My experiments with this low impedance matching system are continuing. This experimental configuration is shown below. The Tesla coil proper is to the left, the primary and link coils to the right, both the latter using skeleton former construction. The primary is the short, wide coil and the link coil sits inside it, being rather taller. The top ten turns of the link coil are widely spaced to allow connection of a crocodile clip without shorting to adjacent turns. The tapping http://home.freeuk.net/dunckx/wireless/magnifier/magnifier.html (4 of 6)6/20/2011 2:52:19 PM

Transmission Lines and Magnifiers

point on the Tesla coil can be seen at the very base of the Tesla coil to the right, just above where the wire changes colour.

I believe this is the first time that 50 ohm tuned link coupling has been used with a Tesla coil, and though I claim no originality for low impedance tuned link coupling, it does surprise me that it has taken until now for someone to apply it to Tesla coils. I have used similar systems with valve transmitters and like thousands before me found this to be an excellent way of doing the job. Although the first tests with a Tesla coil were not impressive, the fact is it works, and when correctly tuned there are none of the problems of high voltages, high coupling constants, sparking between coils or poor quenching, which are inevitably associated with the original magnifier configuration. There is also the possibility of having a far wider range of adjustment for coupling and matching purposes than there ever could be either with the plain inductively-coupled Tesla coil or the original magnifier. Of course, the reason why Tesla didn't do it this way is because in his day, commercially-available low impedance transmission line did not exist, and did not come into being until the end of his life when his experimental days with high frequencies and high voltages were long over. Though I have no information on the topic, it would not at all surprise me to be told that Tesla had something to do with the inception of low impedance feeder systems, because he certainly would have appreciated the benefits of them.

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Transmission Lines and Magnifiers

Next up: So what exactly is a Tesla coil? Back Homepage

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Alternator, Arc and Spark - The First Wireless Transmitters

Alternator, Arc and Spark. The first Wireless Transmitters.

"Anyone who has had actual contact with the making of the inventions that built the radio art knows that these inventions have been the product of experiment and work based on physical reasoning, rather than on the mathematicians' calculations and formulae. Precisely the opposite impression is obtained from many of our present day text books and publications." Edwin H. Armstrong

The origins of wireless, as it was then known, are to this day the subject of occasional dispute. Suffice to say that many independent scientists and engineers contributed something of significance as will be shown below, but it was the youthful Marconi who in the 1890s drew the threads together and, via his family's substantial business contacts and not inconsiderable wealth, plus his own indisputable talent for scientific investigation and improvisation, made a commercial success of it. It is also worthy of note that the company Marconi established one hundred years ago and which bears his name is still doing business today. However, it is beyond doubt that had Marconi not commercialised wireless when he did, then somebody else would have done so very quickly. The evidence for that is in the great rapidity with which Marconi found himself to have competitors in the new technology, many of them commercially successful, some of them embarrassingly so. For example, Germany's first antenna installation was erected by Professor Slaby and Count Arco on the tower of the "Heiland" Church in Sacrow in August 1897, their first successful transmitting experiments having covered half a kilometre in June of that year, only three months after Slaby had witnessed a series of demonstrations by Marconi on Salisbury Plain. This should be compared with Marconi's demonstrations on Salisbury Plain only one year previously, in September 1896, which covered 2.8km. The efforts of Slaby and Arco were later joined with those of Professor Ferdinand Braun and the firm of Siemens Brothers and Halske, from which union the giants AEG and Telefunken were born - two more commercial names still very much with us today. The essential elements of wireless were thus well known to many people and the technology for developing alternating current at radio frequencies (r.f.) widespread and generally well understood. Many a nation could boast its own expert, from the great Indian scientist Sir Jagadis Chandra Bose FRS who in the 1890s developed practical microwave and semiconductor technology, to the Canadian Fessenden, the Dane Poulsen, the Englishman Professor David Hughes who in 1879 failed to impress his learned friends in the Royal Society with his discovery and a multitude of others, including of course the Balkan genius of Tesla and the American dentist Mahlon Loomis whom many acknowledge to have carried out the first successful experiments many years before anyone else in the 1860s but without http://home.freeuk.net/dunckx/wireless/sparksnarcs/sparksnarcs.html (1 of 9)6/20/2011 2:44:06 PM

Alternator, Arc and Spark - The First Wireless Transmitters

obtaining any publicity or financial backing. There were three methods of producing r.f. power prior to the work of Fleming and De Forest, which latter of course issued in true continuous wave generation of high purity, at high efficiency and modest expense through the thermionic valve. These "pre-electronic" methods were: High frequency alternators. The main exponents of this, Ernst Alexanderson and Professor Goldschmidt, produced high speed rotating machinery to generate the desired power directly, exactly as Tesla had done for George Westinghouse's household low frequency a.c. distribution system in the USA years before. Indeed, the first successful r.f. alternator was made by Tesla himself in 1899 and operated at 30kc/s. Alexanderson was Swedish by birth but spent most of his life in America and produced his alternator for the Canadian Reginald Fessenden, who was once chief chemist and engineer for Thomas Edison. Fessenden himself was the inventor of many significant devices, one of which, the "roller coaster" variable inductor, is still in use today. It was with one of Alexanderson's alternators, suitably tweaked by Fessenden, that the first voice broadcast took place on Christmas Eve 1906. The technique was expensive to apply because of the high rotational speeds and high electrical losses at high frequencies, but nevertheless enjoyed considerable commercial success and gave rise to the first true continuous wave (sine wave) wireless transmissions of high spectral purity, though it had the great mechanical limitation of being restricted to comparitively low frequencies, up to 100kc/s. This could not compare with spark, which was used at over 1.5Mc/s, but the trend at the time was to longer and longer wavelengths and lower frequencies, where the alternator could compete exceptionally well. Indeed, one notable Marconi spark station in the USA was replaced by an alternator of Alexanderson's design. Efficiency was not impressive in the smaller versions, over 10 horsepower (7.5kW) input being required for 2kW output, there being great heating losses in the copper windings and iron armature and frictional losses in the gear trains used to achieve high rotational speeds of 20000rpm.

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Alternator, Arc and Spark - The First Wireless Transmitters

In Germany a somewhat different strategy was developed based on frequency multiplication. This was sometimes referred to as "the Arco system" and such an alternator, built by AEG, is shown in the photo (apologies for the quality - the original is of very poor contrast). Telefunken made some large machines, one water cooled of 400kW was installed at Nauen and opened for business with great festivities in 1920; it escaped the penalties associated with high rotational speeds, and high frequency copper and iron losses by using the frequency multiplication technique, which was based on saturable transformers having a dc winding, to produce a range of possible output frequencies based on the relatively low 6kc/s output from the generator. The rotor measured 1.65m in diameter and weighed seven tons, the output was 450 amps at 1200V. The output could be on-off keyed by spoiling the frequency multiplying action of the first of the chain of multiplying transformers by a resistance keyed in and out of one of its windings, which was a great advantage over the rival arc transmitters. The antenna current was typically 400 amps with a feedpoint voltage of 80kV or more and the transmitter was keyed mechanically at 80 words per minute (wpm); others of this period in the USA at New Brunswick and Annapolis could be keyed at 100wpm, and all without sparking at the contacts! A lot of development work was done on the frequency-multiplying transformers, since these extended the utility of the alternators, which could only generate the higher frequencies by using very high rotation rates and losing much power in iron and copper losses. These transformers were generally 90% efficient, but because of the high powers normally used were cooled in an oil bath, which also aided insulation at high frequencies, oil insulation being even more effective at high frequency than at low as Tesla had shown years before. Latour developed a frequency-multiplying transformer which could be used for producing the third or fifth harmonic at will, and without needing a dc winding on the core. He used a special nickel steel alloy, which saturated at low magnetic field and which had low hysteresis probably a forerunner of the more modern permalloys and the like. A transformer of his, for 12-15kW, used just 500 grams of nickel steel and lost only one kilowatt in heat. It was used for tripling 33kc/s to 100kc/s. The Nauen station building still exists and is still used for radio transmission, which must make it one of the oldest monuments to wireless which has been in continuous use for the purpose for which it was built, though the alternators it once housed have long gone. One large working example of these magnificent machines, built according to the Alexanderson method, remains at Grimeton in Sweden, and is run up ceremonially each year. Alexanderson has left us with another legacy in the form of the magnetic amplifier, a saturable reactor which is controlled by a dc winding. It was with this that Fessenden modulated the alternator output for his 1906 broadcast and magnetic amplifiers of many forms are still used for a wide variety of purposes today. The electric arc. In 1898 a Dr. Simon from Frankfurt had noticed that the electric arc could be made to sing by means of a modulating voltage on the arc supply. After a number of experiments he showed that the electric arc made a reasonable loudspeaker which he demonstrated in public auditoria. Also, the modulated arc produced not only sound but a modulated light beam by means of which the German Navy managed to make intership telephone calls using a modulated arc searchlight and a photosensitive

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Alternator, Arc and Spark - The First Wireless Transmitters

selenium cell. In England, William Duddell, an electrical engineer responsible for inventing the moving coil oscillograph (an early device for the photographic recording and observation of oscillating audio frequency waveforms which was still in use in the 1940s) and the thermo-galvanometer (later used for measuring antenna currents and still used in slightly modified form today) discovered that by placing a series tuned circuit across the arc, audio frequencies could be produced by spontaneous oscillation without the need for a separate modulating supply, but that the efficiency plummeted as the frequency was increased. In 1899 Duddell demonstrated a musical instrument which was based on this discovery. The Danish inventor, Valdemar Poulsen, who had demonstrated the 'Telegraphone' (the world's first magnetic recording device) at the Paris exhibition of 1900, turned his inventive genius to the problem and by means of a water cooled copper anode and by making the discharge occur in an atmosphere of hydrogen or illuminating gas, succeeded in raising the efficiency and frequency to the desired level; Poulsen's arc could generate frequencies of up to 200kc/s or so and he patented it in 1903. The Poulsen system and its variants were enormously successful, much to Marconi's chagrin; the American Navy in particular seemed very keen on them. The use of a reducing atmosphere meant that glowing particles of metal oxides could not be formed, and it was these particles of incandescent metallic oxides, which at high temperature emitted thermionic electrons into the arc - a phenomenon explained in 1904 by Wehnelt and later exploited in the "dull emitter" cathodes of indirectly heated valves - which had extended the quenching time of the arc in air and limited the experiments of Duddell. Even hot metal particles could prove troublesome and to eliminate as far as possible the effect of electron-emitting particles, the arc of larger transmitters was placed in a strong magnetic field in order to sweep these out of the system and improve the quenching. Arc transmitters were widely used and scored some notable successes, the Belgian experimenter Robert Goldschmidt using one for voice broadcasts at Laeken and only closing down his station shortly before the invading troops of Kaiser Wilhelm arrived at the onset of war. The technology to build large arcs had already been created for the chemical industry in 1902 (the "Atmospheric Production Co." based at Niagara Falls) and subsequently brought to a high state of efficiency by two Norwegians, the physicist Prof. Kristian Birkeland and the engineer Dr. Samuel Eyde, in order to fix nitrogen as nitrogen oxides, which could then be dissolved in water to make nitric acid, nitrate fertilisers and explosives. Calculation indicates that around 8kWh was needed to produce one kilo of concentrated nitric acid, and thus these massive arcs could only be sited where there was an abundance of "white coal" - water power. It is no coincidence that Dr. Samuel Eyde went on to become the first president of the famous Norsk Hydro company, remembered by most in connection with the 'Heroes of Telemark' who sabotaged heavy water production in the Second World War. A diagram of a Birkeland and Eyde http://home.freeuk.net/dunckx/wireless/sparksnarcs/sparksnarcs.html (4 of 9)6/20/2011 2:44:06 PM

Alternator, Arc and Spark - The First Wireless Transmitters

arc is shown to the left.

The magnet poles (diagonally shaded) are horizontal to the left and right of the central arc chamber, and on each pole can be seen three separate magnet windings. The copper arc electrodes, which are hollow and drilled with many holes through which air (shown by the arrows) circulates, are above and below the magnet poles. Many arc transmitters were commissioned, few of which needed the prodigious power plants associated with the Birkeland and Eyde process. Most were of a few tens of kilowatts or less, but there were stations of 100kW or above at Lyons, Nantes, Paris (Eiffel Tower), Rome, Saloniki (the Thessalonica of the New Testament), San Francisco, Hawaii and at least eight more in the USA, Cairo, Horsea Island and Portsmouth, these last two in England where their presence must have made Marconi wince. A few truly gigantic arc stations were built, of Birkeland and Eyde proportions, and were the most powerful of all early radio transmitters. Having scanned an admittedly ancient copy of the World Radio and Television Handbook I cannot actually find anything from our own time which compares with the biggest of the old arc stations. The Dutch East Indies, as they then were, boasted a monster of 3.6 megawatts (input power). The copper windings for the electromagnet which helped quench the arc weighed twenty tons. This transmitter was situated at Malabar, was designed by a very appropriately named Dr. de Groot ("Groot" in Dutch means "big") was still active in the early 1920s and transmitted on 6100m (49.2kc/s) using the callsign PMM. The power generation, at 25kV, was by an American General Electric hydroelectric plant at Pengalengan. As if de Groot's giant was not enough, there were three more Poulsen arcs at Malabar, plus a "whistling spark" transmitter as well - the Dutch authorities were evidently taking no chances. Another giant was the French station at Bordeaux, known as Lafayette or Croix d'Hins, which had eight masts 250m (820ft) high, covered an area 1.2km by 400m, had an earthing system of one hundred square metres of copper plate connected by one hundred copper tubes, buried 20m deep in the ground (which is probably still there!) and ran one megawatt. The transmitter itself weighed eighty tons, the majority of that in the electromagnet. It transmitted on any one of seven wavelengths between 13850 - 23500m (12.8 - 21.7kc/s) but was doomed, as were all arc transmitters, by the fact that the arc had to burn continuously and thus morse transmissions were by frequency shift keying (fsk) in which the transmitter was switched between two slightly different radio frequencies separated by a few kc/s. Whilst some of the smaller arc transmitters were used for voice transmissions or, for morse purposes, could key on-off by dumping the output into a resistive load, megawatt-sized dummy loads were then as now in short supply and the frequency-shifted output from an fsk-operated arc was inevitably dumped into the 'æther'. (Perhaps they should have used a Tesla coil as a dummy load . . .) The odd megawatt of power shifting its none-too-clean frequency footprint up and down the waveband by a few kc/s generated more than a fair amount of interference as may be expected. Surprisingly, this only became objectionable when receiver technology improved (the price of progress!) as the receivers http://home.freeuk.net/dunckx/wireless/sparksnarcs/sparksnarcs.html (5 of 9)6/20/2011 2:44:06 PM

Alternator, Arc and Spark - The First Wireless Transmitters

originally used to detect spark transmissions were very sensitive to the jagged damped wave trains generated by spark, but were relatively deaf to the more nearly undamped sinusoidal emissions of the quenched arc. If you wanted to receive arc transmissions, you had to use a special receiver, such as Professor Pedersen's "tikker" or Fessenden's heterodyne receiver, and thus other spectrum users with sets sensitive only to spark transmissions weren't offended by the harmonic-rich output of an fsk-operated arc - but that changed when after the First World War everyone went over to the new electronic technology, the thermionic triode, which could not distinguish between alternator, arc and spark and was sensitive to the lot. In England, radio amateurs had their apparatus confiscated during the First World War, purportedly to prevent espionage, but also because the Post Office wanted to clamp down on 'interfering radio amateurs'. This did not unduly impress the radio hams, who by and large caused little trouble (though one indignantly refused to surrender his equipment and was sentenced to six months in jail by the unsympathetic authorities) and when the Post Office opened a large arc transmitter at Leafield near Oxford in 1920 operating on 12200m the interference caused by this official source received a somewhat critical response. To add insult to injury, the British Post Office now insisted that amateur transmitting licences should carry a hefty price tag as a deterrent, and after a somewhat heated exchange of words, radio hams got their apparatus and transmitting licences back at a more reasonable price. Given the low frequency fundamental, the harmonics from an arc transmitter would be spaced, in the case of the Leafield station, every 25kc/s or so on up the spectrum for hundreds of kc/s like teeth on a comb, each 'tooth' jumping a handful of kc/s from side to side as the transmitter was keyed. This pretty well knocks the present day radio ham's complaint of television timebase interference into a cocked hat, and a Paris conference in 1920 had decided that all such transmissions should be prohibited, though Leafield and Dr. de Groot's mercifully distant masterpiece seem to have lingered on for a while. Happily, fsk is still with us and is used, in far more spectrum-friendly guise, in a variety of narrow-band data modes. The great arc transmitters have all gone, and little other than their means of modulation remains of their contribution to the art of wireless. A one megawatt arc, intended for the U.S. Navy, but cancelled at the end of the First World War, made its way by a circuitous route to the University of California at Berkeley where its large magnet formed the basis of Dr. Lawrence's cyclotron in the 1930s. This cyclotron has been preserved at the Lawrence Radiation Laboratory as a memorial. Curiously, Dr. Simon's singing arc which started the ball rolling, made a brief and unspectacular reappearance in the 1950s. A Parisian inventor, Sigmund Klein, patented a new type of loudspeaker called the "Ionophone". It consisted of a radio frequency corona discharge inside a quartz tube which opened into an exponential horn. The radio frequency discharge was amplitude modulated by the incoming audio signal and this, coupled to the horn, produced extremely high quality sound reproduction at high frequencies. It was briefly manufactured in England and also in France, but was not a commercial success. The Ionophone is shown below.

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Alternator, Arc and Spark - The First Wireless Transmitters

Spark, a.k.a. Damped Waves, alias 'Mode B'. The great spark stations, like the arc stations, have long closed down, but as in the case of arc and alternator stations have in a number of cases left behind buildings and antenna bases and guying blocks (see Peter Jensen's excellent 1994 book "In Marconi's Footsteps - Early Radio" ISBN 0 86417 607 4) although perhaps surprisingly they too have left vestiges of their technology behind them in strange places. The current high-tech amorphous alloys are made by a process which owes more than a passing debt of thanks to the first toothless rotary spark discharger used by Marconi at Poldhu in Cornwall in 1901, the high speed rotary cooling disk onto which the molten alloy is poured giving a cooling rate of more than a million degrees per second, so fast that the alloy doesn't have enough time to crystallise, and quite good enough for quenching a 300kW spark. The first commercial development of the Poldhu rotary discharger was a variant having teeth - the modification was so successful that the toothed from of rotary gap is now thought of as the norm, but the original had no protrusions from the disk. Unfortunately, the receivers of the day worked at long wavelengths and had to retrieve spark signals from amongst the crashing noises of natural static, the difference between them not being very great and the toothed discharger gave a characteristic rasping tone to the transmissions which aided the operator in picking out the signals from the emissions of mother nature. The toothless disk produced a more constant aerial current, but the sounds this created in the headphones were less easily distinguished from natural "interference". Marconi's first sales of the new discharger were to the British Royal Navy and in the photo the ten inch rotary disk, in the lower left, can dimly be seen, labelled D; at least three of the protruding studs are visible. The sound deadening cover is hinged open to allow the view.

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Alternator, Arc and Spark - The First Wireless Transmitters

In the right foreground, labelled K, are four of the eight condensers. The zinc plate and glass condensers were immersed in oil and each was kept in a metal tank - hence the origin of the name "tank circuit" to describe the power output tuned circuit of a transmitter. This illustration is of the Marconi 5kW "Battleship" set and was installed on large warships of the Royal Navy in the First World War. Amazingly, this photo was published during that conflict. Just how likely would it be today for a major power to allow the publication of a photo of one of its naval communications centres during wartime? Chronologically, the oscillating current produced by the spark discharge of a condenser through a coil was of course the first method used to generate electromagnetic radiation and it remained until long after arc and most of the alternators had gone. From the experiments of Hertz and Bose in the late 1800s, through the syntony of Lodge, the impedance matching of Slaby, and the beginnings of (tuned and deliberate!) spread spectrum technology during the First World War (the "commutator receiver") spark generation of r.f. power proved amazingly durable, surviving until well after the Second World War. According to the British General Post Office "Handbook for Wireless Operators" published by Her Majesty's Stationery Office in 1954, spark transmission was still permitted on 500kc/s as emergency signalling reserve for ships, lifeboats etc as fixed "by Article 33 of the Radio Regulations", this referring to the annexe to the International Telecommunication Convention of Atlantic City, 1947. In 1954 it was still a requirement of both the Post Master General's First and Second Class certificates that the holder (subparagraph d): "have a theoretical and practical knowledge of the operation, adjustment, and maintenance of Spark, C. W., I.C.W., R.T. and D.F. Installations, . . ."

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Alternator, Arc and Spark - The First Wireless Transmitters

The spark transmitters referred to were the peak of spark development and used the multi-plate discharger of Max Wien (though arguably invented by Nikola Tesla) which formed the basis of most of Telefunken's spark sets and was the source of the "whistling spark" used by many stations and commonly known as the "quenched" spark gap, and a Telefunken gap of this type is shown above. Spark transmitter theory still featured in the written examinations of the period, as evidenced by the appearance of the terms decrement and damping in this 1954 specimen question for the Second Class certificate, for which the theoretical knowledge was only expected to be "elementary": "Define the terms 'wavelength', 'amplitude', 'decrement', and 'damping'. Find the resonant frequency of a circuit consisting of a coil of 500 microhenries inductance in series with a capacitor of 2,000 picofarads." This examination question from barely fifty years ago seems a pretty good starting point for a discussion on how to optimise the output of a spark transmitter for the purpose of coupling it to a Tesla coil. Back Homepage

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Spark Transmitter Basics

The Spark Transmitter. 1. The Basics.

"Define the terms 'wavelength', 'amplitude', 'decrement', and 'damping'. Find the resonant frequency of a circuit consisting of a coil of 500 microhenries inductance in series with a capacitor of 2,000 picofarads." (Specimen exam question, Post Master General's Second Class Certificate, 1954. Eight such questions were to be answered in three hours.)

'Wavelength'. In accordance with the mathematical predictions of James Clerk Maxwell, the experiments of Heinrich Hertz, Sir Jagadis Chandra Bose and others demonstrated that electromagnetic radiation propagates through space as a wave motion, consisting of an electric wave and a magnetic wave whose planes of oscillation lie at right angles to one another. Propagation through free space occurs at a velocity of very nearly 300,000 kilometres per second. If we call the frequency of oscillation in cycles per second f and the velocity of propagation of electromagnetic radiation in metres per second c we have a simple equation to relate the two:

where the Greek letter λ (lambda) is the wavelength in metres. The wavelength is the shortest distance which separates any two points in the wave which are undergoing exactly the same motion at the same time (Einstein permitting). 'Amplitude'. Following on from the work of Fourier, Ohm, Helmholtz, Heisenberg and others, we know that a pure emission on a single frequency takes the form of a sinusoidal oscillation of infinite duration, where both the electric and magnetic vectors of the radiation are oscillating sinusoidally. If this energy should have its intensity represented by e.g. the voltage it induces in a wire, the peaks of the sinusoidal variation of voltage against time as observed on an oscilloscope may be said to represent the peak amplitude of the wave. Alternatively, the peak value of the wave divided by the square root of two gives what is called the root mean square (rms) value of the amplitude. The sinusoidal curve traced out on the oscilloscope screen is a representation of the instantaneous amplitude of the wave against time.

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Spark Transmitter Basics

A similar argument can be applied to any oscillation, even if it is not sinusoidal, but the determination of the rms value of a waveform which is not sinusoidal from the shape of the waveform requires a knowledge of its frequency components. Happily, it is possible to measure the rms value of the current produced by such a wave directly, as the rms value is equal to the direct current (dc) e.g. from a battery which will produce an equal heating effect. Instruments such as Duddell's thermo-galvanometer convert current into heat and use the heating effect to generate a dc output from a thermocouple (in a slightly modified form, these instruments as used today are referred to as thermocouple ammeters; three are shown here) which can be measured with a meter, and these instruments can, with some care, be used to determine the rms amplitude of any current, of any waveform, at any frequency. This even applies to waveforms which are of composite frequency and of very short duration, provided that they are repeated sufficiently often that their time average is non-zero on the timescale of the galvanometer response. Duddell's thermo-galvanometer is shown to the left. Q is a quartz fibre by means of which a small mirror M is suspended. This is joined by a glass fibre G to a silver loop L suspended between the poles N and S of a magnet. The end of the loop terminates in a bismuth-antimony thermocouple Bi Sb suspended above a heater. The current to be investigated is passed through the heater, usually a fine platinum wire for low resistances to say 40 ohms, or a platinised glass fibre for higher resistances and lower currents. The heater is only a few millimetres long and hence has very low inductance and capacitance. In modern thermocouple ammeters, the heater is a piece of resistance wire two or three centimetres long of a composition and diameter appropriate to the current to be measured, and a thermocouple, e.g. copper-constantan, is joined to it at approximately its midpoint. The leads from the thermocouple are then taken to a moving coil microammeter of conventional construction.

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Spark Transmitter Basics

The amplitude of a wave is hence its intensity variation with time, with or without a suitable weighting factor. 'Decrement'. Only a pure sinusoidal wave of infinite duration can be said to have one single spot frequency. As the duration is reduced, so the frequency spectrum of the wave is broadened according to the Heisenberg uncertainty principle. Normally, the difference this makes for communication purposes is relatively trivial (try telling that to a mobile phone company!) but in some applications, e.g. radar and Fourier transform nuclear magnetic resonance spectroscopy (the MRI scanners used in hospitals are an example with which many people will be familiar) which both employ pulses of very short duration, the effect is of great importance. It was also of vital significance during the years of spark. The emissions from the LC tuned circuits of a spark transmitter have the characteristic of short bursts of oscillation separated by gaps of inactivity. Each of these bursts, called "jigs" by Marconi, consists of a sinusoidal oscillation, the peak amplitude of which decreases with time according to an exponential law, the precise constants of which are determined by the resistive losses in the tuned circuit generating the oscillations and in the "radiation resistance" of the aerial through which these bursts of energy are "lost" as electromagnetic radiation. Decrement, often called logarithmic decrement, is a measure of how rapidly the peak amplitude of the wave decays, of how rapidly the oscillating circuit and/or aerial loses its energy, and hence how broad the frequency spectrum will be, and it is from this vital fact - that measuring the decrement (which is easy to do) gives a figure of merit for the broadness or narrowness of the frequency distribution (which in the early days was very difficult to observe) that the decrement of a wave became a useful quantity to know. Logarithmic decrement was the Victorian spectrum analyser. It is thus related to another two useful quantities, the loaded "Q" of the system and the "damping" as described later. From around 1910, laws were passed in all active transmitting nations limiting the decrement of the waves emitted by transmitters, and the commonly accepted upper limit was 0.2, being equivalent to 23 (or 24, depending on how you calculated it) complete oscillations from the start of the burst of oscillation to the point at which the peak amplitude was reduced to 1% of the initial peak amplitude.

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Spark Transmitter Basics

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Spark Transmitter Basics

The above graphs give a good idea of firstly a barely legal emission with the maximum permitted decrement of 0.2, a decidedly illegal emission with a decrement of 0.53 and an emission having a value of decrement which good operators were able to achieve in practice, 0.09. In fact, these examples have been chosen with a purpose as we shall see later. The value of logarithmic decrement, though great, was not without its shortcomings. A persistent wave of high harmonic content, e.g. a sawtooth or square wave, could have a low decrement, but be capable of causing severe interference, and this of course was the case with arc transmitters, which, though they produced continuous oscillations which did not die away in short bursts, nevertheless managed to generate not one sinusoidal oscillation, but a vast number at different frequencies all at once. Decrement therefore was a term which originated with spark transmissions and had its greatest significance in relation to the logarithmically-decaying sinusoidal oscillations associated with the intermittent charge/discharge cycles of the resonant circuits in them. There is a simple relationship between decrement and the value of loaded Q in a tuned circuit:

from which it can be seen that δ, the logarithmic decrement, is a measure of the energy lost in circuit resistance (or consumed by coupling into a load which has an effective resistance) in proportion to the energy stored in the circuit. This is also equal to

where the currents I1, I3, I5 and I7 (etc) are the currents of successive maxima (the even numbered currents correspond to the minima and could in fact be substituted just as well) and δ is the logarithmic decrement, defined as the natural logarithm (log to base ε, written ln) of the ratio of successive maxima. This can be expressed in exponential terms of the ratio of successive maxima (or minima) in an exponentially-decaying wavetrain:

The number of oscillations m in a wavetrain to the 1% of initial amplitude limit is given by the equation:

If the number of oscillations is large, δ is small, and this simplifies to: http://home.freeuk.net/dunckx/wireless/sparktx/sparktx.html (5 of 7)6/20/2011 2:45:36 PM

Spark Transmitter Basics

and hence two different answers may be obtained for the number of complete cycles in a wavetrain. This same thinking can be used to obtain Q if a decaying wavetrain can be recorded in some way. Let the number of complete cycles to the point of 50% decay equal m50. Then:

Since one complete cycle contains one maximum and one minimum, the problem of determining complete cycles is reduced to one of counting the number of maxima (or minima). 'Damping.' The equation which describes the damped oscillations shown in the above graphs is:

Here, E is the initial voltage, L the inductance, ω (omega) equal to 2πf and t the time. The factora is called the damping of the circuit and is given by:

where R is the resistance in the circuit. Note that it is not possible to decide by looking at the value of decrement δ, loaded Q or dampinga whether the resistance R brings about a thermal loss of energy and thus is the cause of inefficiency (i2R losses in the coils, connections, spark gap and to a lesser extent the capacitors) or is the reflected resistance into the circuit of e.g. an aerial (or Tesla coil) by which energy is lost as radiation (or sparks), which adds to the efficiency of the station in communicating. As far as these quantities are concerned, R is simply the means by which energy "escapes" from the system. 'Find the resonant frequency of a circuit consisting of a coil of 500 microhenries inductance in series with a capacitor of 2,000 picofarads.' If the resistance in a tuned circuit is negligible, then the resonant frequency is given by the well-known formula:

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Spark Transmitter Basics

where L is the circuit inductance and C the circuit capacitance. Therefore the resonant frequency of 500µH plus 2000pF is 159kc/s (post-moderns may prefer this in kHz: I am not a post-modern, the numbers are identical in both cases and anyway this is a 1954 exam paper, so kilocycles per second it is!) This concludes the basics of the spark transmitter, but as we shall see there is still a long way to go. I have also failed miserably to answer the question in twenty minutes, thus falling short of even Second Class Wireless Operator standards: however, I plead belligerent modern technology in the form of formula editor, spreadsheet and graph creation software, and an utterly fascist html creator which insists on automatically modifying things I type without either asking me or allowing me to turn it off (thanks Star Office). In the next section we shall look at how to build a quenched spark gap. Back Homepage

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Conductors at Radio Frequency

Conductors at Radio Frequency "Mathematics . . . a kind of lazy-tongs by means of which conclusions may be reached without straining the intellect." Alfred M. Still

I have a problem. What is the better form of conductor to use at radio frequency? Is it a tube or is it a flat strip? The problem is not made any easier by the fact that one contender expresses his views nonmathematically in a way which is at once easy to grasp, appeals to the reason and exercises one's appreciation of some fundamental physical realities, whilst his opponents state theirs in terms of partial derivatives and Bessel functions. But let me introduce the contenders. In the red corner, the late, the great, Frederick Emmons Terman, ScD, Professor of Electrical Engineering and Dean of the School of Engineering, Stanford University; Past President of the Institute of Radio Engineers, author of "Radio Engineering", "Radio Engineers' Handbook" etc etc. In the blue corner, the almost-unheard-of Mr. A.G. Warren, late of the Armament Research Department, Ministry of Supply, ably aided and abetted by the late Professor Alexander Russell, Fellow of the Royal Society, the late Professors C.L. Fortescue and G.W.O. Howe, the internationally renowned Mr. S. Butterworth designer of filters extraordinaire and that Victorian bastion of the scientific community, His Lordship the late Lord Rayleigh, whose collective achievements and honours would fill (and do fill) several books. It should be noted that Messrs. Russell, Fortescue, Howe, Butterworth and Rayleigh each contributed a significant portion to our knowledge of the flow of alternating current in metallic conductors at high frequencies. Also sticking their oar in for the blue corner (a rowing blue no doubt; somewhat unsportingly in my view) we have apparently the assistance of the Bureau of Standards, Washington. Right now it doesn't look too good for Professor Terman, but it has been known for more hopeless cases to rise triumphant. Let me state the cause of the dispute. Professor Terman says (p. 20, "Radio Engineering") that a flat strip conductor is not a good choice for radio frequencies since the interaction of the current with the magnetic flux it produces will, by virtue of producing the skin effect, force the current to flow down the two opposite edges of the strip and hence the majority of the surface is unused as a conductor. The suitability of a conductor for radio frequencies is not a simple matter of its surface area, but the disposition of the conductor in space is a vital factor. He implies that a tubular conductor of circumference equal to the width of the flat strip is always to be http://home.freeuk.net/dunckx/wireless/terman/terman.html (1 of 9)6/20/2011 2:50:15 PM

Conductors at Radio Frequency

preferred. Dr. Cadd (that's me) adds by way of comment that it is easy to see Professor Terman's point by considering a crosssectional view through a circular wire carrying radio frequency current. By the skin effect, the radial current distribution decreases exponentially from the outside, tending thus to be concentrated in an annulus around the circumference of the wire. A flat strip is simply a thin slice taken across the diameter of the wire, in which the current flows down the two edges, exactly as Professor Terman states.

So far, so good. Now it's Mr. Warren's turn. Mr. Warren says . . . actually, Mr. Warren doesn't say much at all, leastways not in English, and therein lies half my problem. Mr. Warren mutters various obscure incantations, inscribes mystical symbols and makes peculiar signs with his learned pen which only the truly wise and enlightened may comprehend the significance of. However, I do not hold that against him, nor do I see any great reason to curtail his views simply because they are expressed in a language other than my own. Unfortunately, he does go on a bit; succinctness is not a strong point of his. Mr. Warren, the webpage (and half of cyberspace) is yours .....

The wide parallel strip is represented as in the diagram where it is shown in cross-section. Its width is b , its thickness 2a ; b >>2a. The current flows in a direction represented by the normal to the paper (or screen - Ed.). At a distance x from the mid plane OO' the current density is g , the intensity of the magnetic field is H (directed along BC, or CB), the flux per unit length within the conductor, and to the right of BC, is φ; the external flux to the right of the conductor is φ'; the current within the section OBCO' is Ix ; the potential difference per unit length of the conductor is e . Proceeding round the path ABCD the current enclosed is 2Ix and therefore the magnetomotive force is 8πIx . This is equal to H x 2b .

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Conductors at Radio Frequency

(In what follows, µ is the magnetic permeability of the conductor, ω is 2πf, ρ is the resistivity of the conductor and j is the square root of -1. Ed.) Hence

or

From equation 1

From equations 4 and 5

Differentiating this with respect to x gives

Assuming that g varies sinusoidally and interpreting equation 6 as a vector equation one obtains

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Conductors at Radio Frequency

the solution to which is

Since g is the same for ±x , A1 = A2 and the solution may be written

or

The current per centimetre width of the conductor is

or

If

then at the surface

and therefore the impedance per centimetre of 1cm width of the conductor is

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Conductors at Radio Frequency

(This impedance does not include the "external" reactance; this does not matter since Z1 is being determined to find R1, the resistance of 1cm width of the strip.) Writing

and

Writing

we obtain

giving

Putting 2a = t , the thickness of the strip, gives

where R1 is the resistance of a strip 1cm wide.

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Conductors at Radio Frequency

At low frequencies (mains power frequencies) equation 15 may be used to determine the increase in resistance due to eddy currents. To the first order, when α is small,

For copper, k = 0.215f½ and therefore α = 0.152f½. At f = 50, α = 1.075. For a strip 1cm thick αt = 1.075; sinh 1.075 = 1.2943; sin 1.075 = 0.8796; cosh 1.075 = 1.6356; cos 1.075 = 0.4757; and so

an increase of resistance of 0.74%. An approximate expression for λ when αt is small, is

At high frequencies, when αt becomes big, sinh αt and cosh αt become equally very great, while sin αt and cos αt remain finite so that the resistance of unit width of strip approximates asymptotically to ρα/2. Thus at f = 106, α = 152 and a strip of considerable thickness would have a resistance of 76ρ, independently of the actual value of the thickness. It is clear, however, from equation 15, that at a constant frequency, as the thickness is increased, the resistance passes through a number of maxima and minima. A strip of finite thickness may have a lower resistance than one which is indefinitely thick. Using the same nomenclature as for equation 14, then if

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Conductors at Radio Frequency

Maximum and minimum values occur when

or Since both S and s being zero corresponds to a conductor of no thickness this case cannot be considered. S 0, therefore s = 0 for a maximum or minimum value. At maximum or minimum values αt = π, 2π, 3π, 4π, etc. When αt = 2nπ, cos αt = +1 and

When αt = (2n + 1)π, cos αt = -1

Successive maximum values of R1 are

Successive minimum values of R1 are

The particular value of interest is tanh(π/2) = 0.917; all subsequent values differ from unity by only a

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Conductors at Radio Frequency

negligible amount. For this case, when αt = π, i.e. t = π/152 = 0.0206 cm, the resistance is 8.3% less than the resistance of a thick strip.

Thank you Mr. Warren. It appears then from your work that a copper strip just a shade over 0.2mm in thickness has a resistance at 1Mc/s (α = 0.152 x the square root of frequency) which is over 8% lower than any other thickness. Unfortunately, Mr. Warren does not see fit to extending the argument to tubular conductors, which presumably follow a similar pattern. The difficulty I have with this is that effectively this is saying that flat strip conductors are good at radio frequency, which disagrees with Prof. Terman. The specific argument I will pick with Mr. Warren's argument is that he has chosen from the beginning the way in which the current distributes itself over the conductor cross-section. Is there any good reason for not doing the calculations with the geometry as shown here, and then working out how the balance of factors distributes the current over the strip?

I would also suggest reaching the desired answer by considering a gradual perturbation of the system, by drawing the circular wire shown beside Professor Terman's argument through progressively more oval dies of equal circumference and noting the redistribution of current at each stage, until the last die is rectangular and of thin section. Presumably, depending on frequency, resistivity, dimensions and current, an equilibrium will be reached between the penetration of the current and flux into the strip, and the forces tending to move the electron flow to the surfaces and to the edges of the strip. That is the computation which needs to be done in order to decide the current distribution and hence the strip resistance. So is Professor Terman right or wrong when he says that a flat strip is not a good choice at radio frequencies? Evidently the basis for the calculations is here. But how to actually do it?! I have no idea, the mathematics are quite beyond me. Perhaps someone has measured the radio frequency resistance of a strip and a tube of the same thickness on a bridge and factored the resistances according to the width of the strip and the circumference of the tube. I just wish I could find the answer somewhere. The next section concludes the journey from the generator to the load with a look at inductive coupling. http://home.freeuk.net/dunckx/wireless/terman/terman.html (8 of 9)6/20/2011 2:50:15 PM

Conductors at Radio Frequency

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http://home.freeuk.net/dunckx/wireless/qdvttc/qdvttc.html

The Quick & Dirty VTTC

Via the internet, I discovered that to my surprise and delight, the "Ionophone" referred to elsewhere on these pages is very far removed from defunct. Several versions have been produced around the world by different manufacturers. One man, Ulrich Haumann, even went so far as to build his own. He in turn inspired others to follow suit. It was from Ulrich's plans that I swiftly (and I mean in 2-3 hours and very leisurely at that) threw together the coil which appears here. First, the circuit diagram, which is a little changed since I have at present no modulation capability for the plasma:

Ulrich reported minor problems with the rf choke RFC in the above. With a little experimentation I found that the inductance of this component is not important, but that if a second Tesla coil TC is wound, this serves perfectly as the choke. This Tesla coil/choke should be say 25-40 turns of thick (0,9mm - 2,2mm) wire wound to a diameter of 25 - 35mm, the thing is completely non-critical, so long as both are the same. Apparently the self-resonance of this choke at the operating frequency performs admirably to keep the oscillations from escaping into the power supply (and no, the HT side isn't earthed to anything, I simply threw it all together breadboard fashion!) The first choke I used was 164uH and physically rather large. It can be seen lying horizontally behind the Tesla coil and valve (EL37) which http://home.freeuk.net/dunckx/wireless/qdvttc/qdvttc.html (1 of 5)6/20/2011 3:07:16 PM

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are at the front of the layout. It was not resonant at the operating frequency, and though it is made of 1,6mm wire and carries only 160mA, it got warm in use! The second Tesla coil I wound, which I used in place of this choke, remains stone cold. A later photo shows this component. At the rear left is the HT transformer, on top of which is perched the 10H choke, which is essential when using a mercury rectifier. This valve, type 83, is to the right of the HT transformer, centre rear. At the right rear with its LT centre tap sticking straight up is a homebrew filament transformer for the 83. Despite only putting out 5V at 3A, this secondary needs high voltage insulation because it forms the positive HT terminal and can be at up to 400V. In front of that, right midfield, is the LT heater transformer (6,3V) for the EL37. Left midfield is the 4uF smoothing capacitor on top of which is a very large 30k resistor. The front row shows the Tesla coil on the left, atop which is the plasma, barely visible against a steel band of the HT transformer (bad siting on my part for the photo.) Near the valve base of the EL37 to the left is a parallel pair of 4,5nF 4kV ceramic capacitors. The value isn't very important, but a high voltage rating is, as the "hot" side is connected to the loop L, seen at the top and outside of the Tesla coil as a thick brown wire. In front of the valve base is the 15k grid resistor (read it right to left - brown, green, orange) and to the right of the valve base the 0,5uF screen bypass capacitor. The white blob apparently hovering in mid air at the left shoulder of the EL37 is the screen resistor of 4,3k (actually a 3,3k resistor in series with a 1k which is out of sight). One important feature of the circuit is that the heater/filament volts can be switched on independently of the HT volts. With a semiconductor rectifier this doesn't matter, but with a mercury rectifier it is vital, as mercury rectifiers are easily damaged electrically, something rare amongst valves. The filaments must heat for long enough to evaporate any mercury droplets from within the electrode structure before the HT volts go on, or there will be a flashover with damage to the valve. "The book" says thirty seconds. Mercury rectifiers are getting hard to find, and I give mine two minutes. Even so, I have had the occasional blue flash at switch-on, fortunately with no damage to date. So why use them? They're expensive, delicate mechanically, delicate electrically, generate waste heat, generate interference, take up space, demand a separate and very well insulated filament transformer http://home.freeuk.net/dunckx/wireless/qdvttc/qdvttc.html (2 of 5)6/20/2011 3:07:16 PM

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with a centre tap (this centre tap actually matters if you want them to last long) demand a choke coil to restrict the peak amperage drawn, require you to wait a while for the filament to heat before you can switch the main power on and when they finally give up, disposal is a real problem (which so far I have not had to face) as you obviously can't throw them in the household rubbish (though I bet that's exactly where most of them went years ago.) So why? Well, they're a lot more interesting to look at than a 1N4007. Even an exploding 1N4007 isn't half as pretty as a mercury rectifier. The blue glow from the mercury vapour inside the two anodes of the 83 contrasts nicely with the bright orange filaments, though the filaments haven't really shown up too well in this photo. The unaided eye sees them much better.

The plasma has to be "ignited" by allowing a well-insulated screwdriver to brush the tip of the Tesla coil, the stray capacitance of the metal being enough to incite the arc to strike. On no account should a bare piece of metal be used, as not only the radio frequency power but also the dc HT positive will short to earth through the object (and you if you are holding it). On the other hand, a well-insulated object can be inserted into the plasma. Here, a glass tube (supported on a rubber tube, supported on the wellinsulated screwdriver tip) is being heated to white heat by the plasma. The glass becomes electrically conductive, and a yellow rf arc is drawn to the glass, though the yellow doesn't show up too well against the brilliant white-hot glass:

Out of focus, behind the Tesla coil and at an angle is the second Tesla coil which is used as the rf choke, now replacing the very large horizontal choke shown in the previous shot. Whilst a slight glow of the EL37 heater is barely visible, these things are much better seen in the dark: The plasma is now clearly http://home.freeuk.net/dunckx/wireless/qdvttc/qdvttc.html (3 of 5)6/20/2011 3:07:16 PM

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visible as a bright white "flame" to the left. To the eye it appears blue with a green tip from the copper wire. Far right is the orange glow of the EL37 heater, and to its left a blue light from the 83, plus an orangered blur above from the 83 filament. The blue fluorescence of the EL37 glass (due to very high vacuum in the valve) is also seen, thanks to another photo-shoot with faster film (Jessop's 200ASA). Midway up the coil is the bright light of a neon bulb held nearby, the gas is ionised by the rf field of the coil. In this photo, a small filament lamp connected across a few turns of wire is being held at the top of the Tesla coil. Rf energy from the Tesla coil is then induced in the coil across the lamp and lights it, demonstrating the presence of inductivelycoupled energy. The lamp used to perform another trick, until I got it too close and cooked it . . . the gas in the lamp would light up blue and it was possible, once the filament had lit (electron emission produced thermionically helps ionise the gas filling) and the gas had ignited, to raise the lamp with its coil just above the plasma flame, rotate the plane of the coil on the lamp through 90 degrees to reduce inductive coupling to near zero, and the blue glow from the gas would remain due to capacitive coupling of rf from the Tesla coil. Unfortunately, as I said, I got a bit carried away with this neat trick and it wouldn't do it for the camera! Another shot on Jessop's 200ASA. Here's a closeup of the plasma flame, on Jessop's ASA200, the blue glow from the 83 is visible in the right background. This has been an interesting illustration of the differing http://home.freeuk.net/dunckx/wireless/qdvttc/qdvttc.html (4 of 5)6/20/2011 3:07:16 PM

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sensitivities of the eye and film to different wavelengths at low levels of illumination. The plasma flame is distinctly blue to the eye, but less so to the film, also the tip of the flame is greenish, whereas the film sees it as yellow! I've also noted that weak Tesla streamers from the induction coil setup elsewhere on these pages are very blue to the film, but purple to the eye! This coil has now been dismantled and the bits recycled for other experiments. Most of my projects tend to go that way, only a very few things end up as keepers. It's interesting to note that, despite the resonant frequency of this coil being around 29Mc/s the amount of radio interference was low - nice one for the law of conservation of energy - you can either radiate it as radio waves, or use it to ionise the air and make it hot, but not both at once. All photos Olympus OM1 plus Kodak Gold ASA100 unless otherwise stated. Back Homepage

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Weblinks

Some Links MACC Model Engineers A great little Model Engineering supply company.

Other handy suppliers Rapid Electronics. Ask Jan First for all manner of high voltage capacitors, valves and other fantastic vintage stuff. Manufacturers of superb quality transformers. Quartz crystals to order. Excellent source of high end audio tubes and guitar amp parts. Manufacturer of Weber Loudspeakers, high quality recreations of vintage AlNiCo designs and more. Used test gear and all manner of interesting bits. Lovely bits of timber.

Strange Stuff Yes, gas turbines. Big, scary, noisy ones. Mike Harrison's electric thingies.

Astronomy http://home.freeuk.net/dunckx/weblinks.html (1 of 4)6/20/2011 3:08:16 PM

Weblinks

Bob May's pages. BBC Sky at Night. ATM archive resource. Cloudy Nights scope reviews.

General Wireless Resources Early Wireless History German Wireless developments

An Alternator Resource The Swedish Telecommunications Museum, with links to the Grimeton site

Poulsen Arc Resources The San Francisco Museum An interview with Dr. Fuller, who designed many Poulsen Arcs A Danish Poulsen site A Dutch Poulsen site Build your own Poulsen Arc Some photos of the French Croix d'Hins (Lafayette) radio station masts during construction by the US Navy, from Al Heiden

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Weblinks

Aerial Resources One of the most informative sites on radio aerials Numerical Electromagnetics Code information

Shooting Resources Perfidious Albion: The Banana Republic of Great Britain and Northern Ireland strikes again The Dunblane massacre resource page.

Wire Resources Percy Hawkins Wire

Tesla Coil Resources Alan Sharp's Theology and Tesla Coils page Tesla Coil Builders of the UK

A Reading Resource Lindsay Books

An Academic Resource The US National Academies

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Weblinks

Another Academic Resource The University of Bums on Seats (formerly Peckham Polytechnic)

A Search Engine Hotbot

Return To: Alternator, Arc and Spark Homepage

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