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Submission for Jim Sheppard; (c) 1991 Robert M. Jamison
TIME JITTER IN ROTARY-GAP TESLA COILS
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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.
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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.
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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.
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