TIME JITTER IN ROTARY-GAP TESLA COILS

 Submission for Jim Sheppard; (c) 1991 Robert M. Jamison 

 

                     TIME JITTER IN ROTARY-GAP TESLA COILS 

                     ------------------------------------- 

 

                               ABSTRACT 

 

The source of time jitter in rotary gap Tesla Coils is examined both 

experimentally and mathematically.  Calculations demonstrate that jitter 

appears even if the rotary gap is machined to high precision.  The 

principal source of jitter is shown to be the ringing of the capacitance 

and transformer inductance in relationship to the rotary electrodes.  A 

computer model of jitter was made and supplements the text. 

 

                                  -*- 

 

The tone of a rotary gap is the simplest and most immediate indicator of 

the presence of jitter.  A gap with little jitter has a musical tone and 

illuminates with a steady glow much like a natural gas pilot light.  As 

the jitter increases, the tone takes on a nervous quality and the gap 

illumination flutters in intensity. 

 

The jitter level of several embodied Tesla coil systems was higher than 

desired.  These systems, all large ones, were powered with inductively 

limited transformers.  The switching element was a rotary gap.  The 

following analysis identifies the sources and computes relative 

magnitudes of jitter in this type of system. 

 

As long as the peak firing voltage is kept under control, the effects of 

jitter are not catastrophic.  But the presence of jitter always 

degenerates the purity of the design.  The firing containing the 

greatest energy causes the highest secondary voltage so extra secondary 

insulation must be added.  Conversely, missing firings will increase 

losses because useful energy stored in the capacitor is not immediately 

utilized, but must wait for a while.  For small laboratory type Tesla 

coils this unproductive idle time and its attendant inefficiency is 

inconsequential.  But for high power systems such as those used for the 

wireless transmission of power it is worthwhile to explore various 

configurations of rotary gaps in advance of construction.  This 

exploration led to some revealing facts about jitter in Tesla coils. 

 

An oscilloscope was used to observe jitter.  After obtaining some 

experience with rotary gap Tesla coils of this type, the audible tone 

was found to be a more convenient alternate indicator of jitter.  In 

practice both methods were awkward to quantify the jitter magnitude.  So 

experiments and computations were used to localize and mathematically 

represent it. 

 

Jitter can be observed on the output electrode of the Tesla coil.  The 

origin of jitter was localized to the primary circuit by the following 

method.  The secondary was experimentally removed and jitter was 

observed to remain.  Admittedly, the secondary also can contribute to 

the amount of jitter.  But the scope of this analysis is limited to the 

iron core transformer, the rotary gap, and the Tesla primary.  The 

capacitor and air core primary also resonates at a low RF frequency. 

This frequency is several orders of magnitude above the frequencies 

discussed in this analysis. 

 

The simplicity and economy of an unenclosed rotary gap accounts for its 

popularity over more exotic switching means.  On the other hand, its 

operation is not as predictable as triggered gaps.  Instead of the 

forced firing immediately upon appearance of the trigger signal, the 

firing appears at an unspecified time during the gradually increasing 

voltage gradient.  Although the rate of increase of this gradient is an 

order-of-magnitude improved from fixed gap designs, there is still a 

measure of time uncertainty.  Of course, the amount of jitter can be 

decreased by increasing the rotational speed of the rotary gap.  Since 

jitter is inversely proportional to rate of closure of the electrodes, 

the uncertainty would be reduced proportionally.  From a practical 

standpoint, it is not worthwhile to exceed the speed of standard 

ungeared motors (3500 to 3600 rpm).  If the electrodes are mounted on a 

diameter of 9.4 inches, they will be moving at 100 miles per hour (147 

feet per second).  The diameter may be increased from this value 

somewhat, but large increases will invoke power, noise, safety, and 

speed-of-sound problems.  Strength must be a consideration if non- 

metallic wheels are used because the points on the circumference of this 

example sustain an acceleration of 1700 g's. 

 

Reasonable values may be applied to examine jitter levels in a typical 

rotary gap system.  Other than the claim of reasonableness, no 

particular level of precision is attached to the numbers that follow. 

But this approach allows computation of values so that they might may be 

put into proper perspective.  At one extreme, assume that if a voltage 

gradient of 175 KV per inch appears across the electrodes then breakdown 

will occur instantly.  Also assume the traditional value of below 76.2 

KV per inch where the electrodes will not break down at all.  In the 

band between these two values the electrodes will not break down 

immediately, but after some unspecified period of time.  It is the 

irregularity of the breakdown time that accounts for a portion of the 

total jitter.  For example, consider a 10 KV drop across the electrodes. 

Using the above figures, the breakdown may occur between 0.0013 inch and 

0.0006 inch.  The distance at which the gap may fire has an uncertainty 

of .0007 inches.  With a reasonable rate of electrode closure, such as 

100 mph in the above example, this peak to peak component of jitter is 

0.4 microsecond.  This magnitude is far smaller than the amount of 

jitter that was observed so the source of the firing irregularity must 

lie elsewhere. 

 

The consistency of the angular spacing of the electrodes is another 

contributory factor.  Assume an 1800 rpm system with one particular 

electrode displaced one degree of arc ahead of the ideal position.  This 

electrode will cause an interfiring interval 1 microsecond shorter than 

standard.  The subsequent interval until the next firing will be 1 

microsecond longer than standard.  The sum of this peak to peak jitter 

totals 2 microseconds.  Again, this magnitude could not account for the 

magnitude of jitter observed in the embodiments. 

 

Spherical shapes are generally used for the rotating electrodes. 

Although the sizes of these electrodes are well controlled, it is 

interesting to examine the effect of uneven sizes for their effect on 

firing irregularity.  Consider a closely set gap, a 100 mph closure rate 

and the diameter of one of the electrodes 0.005 inch larger than the 

other electrodes.  The firing would occur 3 microseconds earlier as this 

electrode approaches the gap and, since the remaining firings are 

unaffected, the peak to peak jitter would also be 3 microseconds. 

Once again, this irregularity is not a significant source of jitter. 

 

Normal erosion of the electrode surface finish will effect the above 

cited voltage gradient values somewhat.  In light of the small 3 

microsecond jitter shown, it is not cost effective to finish the 

electrodes finer than the pitted finish that will naturally occur after 

use.  It is rarely worthwhile to use any separate finishing operation on 

the electrodes. 

 

Another source of jitter can originate from an induction motor;  the 

type normally used to drive the rotary gap.  These motors have a slip 

frequency in the order of one hertz.  The rotational frequency and the 

number of electrodes can form a beat frequency with the line frequency 

which generates firings at irregular positions of the sine wave.  It 

could simplistically be calculated that a 1750 rpm motor driving a 12 

electrode rotary gap will form a 350 hertz tone.  Indeed, some firings 

will be spaced by 1/350 of a second.  But, even in an ideal system, the 

actual number of firings in one full second will fall short of this 

value.  Because of the slip frequency, there ideally would be six, but 

occasionally five, firings per half-sine.  Further, if a certain 

electrode moves into and out of firing position when the sine wave 

crosses zero there may be no firing at all.  This non-firing 

underutilizes the design because the embodied components stand idle for 

a time. 

 

To eliminate the slip frequency as a source of jitter, the motor in the 

above example was replaced with a 1800 rpm synchronous motor.  By 

physically positioning the electrodes at a desired relation to the phase 

of the motor shaft, firings were permitted only at consistently phased 

points on each half sine wave.  Even the small sources of irregularity 

such as electrode angular positioning and dimensional tolerances were 

eliminated by extraordinary machining techniques.  With all these 

precautions, there was still an untenable amount of jitter. 

 

The unsatisfactory results of these hardware experiments led to computer 

modelling and analysis.  The computer program simulates the electrical 

operation of the transformer with its Q and inductance, the capacitor, 

and the gap.  The parameters displayed and analyzed are:  instantaneous 

gap spacing, capacitor voltage, transformer current, incoming line 

phase, and energy during firing.  The program also emits an audible 

simulation of the firing. 

 

The computer program is available for downloading as ROTJIT.ZIP from: 

     Colorado Mountain College, Timberline Campus BBS System 

     Data:   (719) 486-2775 

     Voice:  (719) 486-0133 

     24 Hours 8/1/N 300/1200/2400 

The program is PC compatible and requires an EGA (or better) monitor. 

 

The high voltage iron core transformer combined with its low-Q 

inductive limiting properties is critical to the modelling. 

Conventional transformers have too low an output impedance to use 

directly, so some electrical compliance needs to be inserted in series 

with it.  A rheostat is sometimes chosen, but for large size Tesla 

coils, inductive limiting becomes a more practical choice because it is 

ideally lossless.  To obtain this inductance, an external iron-core 

inductor may be placed in series with with a conventional transformer. 

Since transformers already contain iron, the inductor can be combined 

with them.  Such transformers are commercially available for igniting 

domestic oil burners and for illuminating gas tubes.  In the program the 

actual location of the inductance is unimportant since the two 

configurations are equivalent.  This text will consider that the 

transformer itself contains inductive limiting. 

 

This transformer inductance will resonate with the Tesla primary 

capacitance at one frequency defined by LC.  If this resonant frequency 

is 60 hertz then the secondary of the transformer will make a resonant 

rise at that frequency to a voltage limited only by the transformer Q or 

the firing of a rotary gap.  This voltage may be high and, if 

uncontrolled, the transformer secondary can destroy itself. 

Unfortunately, the lower the transformer losses, the higher the resonant 

rise will be.  So the likelihood of destructive secondary voltage will 

increase with better quality transformers.  In the computer program, the 

Q is set to about 3 which is representative of one particular 

transformer.  Q is generally a parameter that is not controlled by the 

transformer manufacturer and can be a higher value, such as 10, 

depending upon the transformer design. 

 

In the computer program, the value of the primary capacitor and 

transformer inductance resonates higher than 60 hertz.  This resonant 

frequency can be observed by setting the gap to a very wide spacing.  At 

this large gap spacing, no firing occurs and there are no transients due 

to the rotary gap.  But at the turn-on point (at the left-hand side of 

the screen) the circuit at rest is stimulated with the non- 

differentiable turn-on transient of the sine wave.  A sine wave around 

zero angle is essentially a ramp input.  Although a ramp is a very 

gentle stimulus, the capacitor and transformer inductance visibly 

resonate.  This resonance can be observed adding to the initial cycles 

of the 60 hertz waveform.  Since the gap is not firing, the 60 hertz 

energy cannot supplement this LCR circuit with energy at the resonant 

frequency and the resonance dies because of the finite Q of the circuit. 

Demo C in the computer program shows this ringing and its damping.  It 

is more apparent in the capacitor current rather than the voltage 

because of the differentiating property of the capacitor. 

 

When an electrode fires in proper phase with the frequency of this LC 

circuit the stored energy in the tank circuit can be increased.  Under 

this condition the transformer and capacitor voltages can rise to very 

high values.  If the Q of the circuit is very high, this voltage can 

rise and break down the component most susceptible to overvoltage:  most 

likely the transformer. 

 

The mechanical phasing of the rotary gap with the line frequency is not 

important if there are many firings per cycle of line frequency.  But if 

only a few electrodes are used and they are oriented so that the few 

firings are near the 60 hertz zero-voltage crossing, some half-cycles 

may pass without a firing and jitter will be substantial.  Demo D in the 

program graphically demonstrates this undesirable feature. 

 

Another undesirable condition appears if the gap is set too small. 

Consider the instant where the capacitor is charged to a large value and 

the electrodes are far apart.  As the electrodes rotate closer to each 

other, the gap will eventually strike and the high energy in the 

capacitor will be transferred to the primary coil.  The electrodes will 

continue to become even closer and remain closer for a long period of 

time.  During this time interval the transformer charges the capacitor 

to a small voltage limited by the close electrode spacing.  This cycle 

repeats and many firings occur during a short time period.  But no large 

packets of energy are delivered to the primary.  The transformer no 

longer is supplying current to a capacitor with, on the average, a 

moderate charge, but rather to a capacitor with a very low voltage.  The 

current builds but is limited to the short circuit current of the 

transformer.  The effects of rapid firing and short circuit current 

combine and the electrodes dissipate much more heat.  As the gap rotates 

the electrodes eventually will move an adequate distance apart and 

normal operation will resume until the next electrode makes the gap too 

small once again.  Demo E in the computer program graphically 

demonstrates this undesirable feature. 

 

When all elements are properly selected, the firing rate is consistent 

from half-cycle to half-cycle.  Demo A in the computer program 

graphically illustrates the elimination of jitter.  Note the like energy 

bursts from one half-cycle to the next.  The capacitor voltage attains a 

smaller peak voltage than in a flawed system.  The computer speaker 

sounds at each energy burst and its rhythmic and monotonous sound 

indicates that the system is properly adjusted. 

 

                                  -*- 

 

ABOUT THE AUTHOR 

 

Mr.  Jamison is an independent engineering consultant.  To optimize his 

industrial Tesla coils, he developed the interactive Tesla coil Computer 

Aided Design program TSCAD.  A demonstration of this program is 

downloadable from CMC BBS as TSCADDEM.  Using mathematical Tesla coil 

modelling he has aided NASA in their extraterrestrial life research 

relating to the creation of amino acids by electrical discharges. 

 

                                  -*-