265 lines
16 KiB
Plaintext
265 lines
16 KiB
Plaintext
Submission for Jim Sheppard; (c) 1991 Robert M. Jamison
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TIME JITTER IN ROTARY-GAP TESLA COILS
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ABSTRACT
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The source of time jitter in rotary gap Tesla Coils is examined both
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experimentally and mathematically. Calculations demonstrate that jitter
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appears even if the rotary gap is machined to high precision. The
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principal source of jitter is shown to be the ringing of the capacitance
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and transformer inductance in relationship to the rotary electrodes. A
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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
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the presence of jitter. A gap with little jitter has a musical tone and
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illuminates with a steady glow much like a natural gas pilot light. As
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the jitter increases, the tone takes on a nervous quality and the gap
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illumination flutters in intensity.
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The jitter level of several embodied Tesla coil systems was higher than
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desired. These systems, all large ones, were powered with inductively
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limited transformers. The switching element was a rotary gap. The
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following analysis identifies the sources and computes relative
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magnitudes of jitter in this type of system.
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As long as the peak firing voltage is kept under control, the effects of
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jitter are not catastrophic. But the presence of jitter always
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degenerates the purity of the design. The firing containing the
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greatest energy causes the highest secondary voltage so extra secondary
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insulation must be added. Conversely, missing firings will increase
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losses because useful energy stored in the capacitor is not immediately
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utilized, but must wait for a while. For small laboratory type Tesla
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coils this unproductive idle time and its attendant inefficiency is
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inconsequential. But for high power systems such as those used for the
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wireless transmission of power it is worthwhile to explore various
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configurations of rotary gaps in advance of construction. This
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exploration led to some revealing facts about jitter in Tesla coils.
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An oscilloscope was used to observe jitter. After obtaining some
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experience with rotary gap Tesla coils of this type, the audible tone
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was found to be a more convenient alternate indicator of jitter. In
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practice both methods were awkward to quantify the jitter magnitude. So
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experiments and computations were used to localize and mathematically
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represent it.
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Jitter can be observed on the output electrode of the Tesla coil. The
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origin of jitter was localized to the primary circuit by the following
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method. The secondary was experimentally removed and jitter was
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observed to remain. Admittedly, the secondary also can contribute to
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the amount of jitter. But the scope of this analysis is limited to the
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iron core transformer, the rotary gap, and the Tesla primary. The
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capacitor and air core primary also resonates at a low RF frequency.
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This frequency is several orders of magnitude above the frequencies
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discussed in this analysis.
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The simplicity and economy of an unenclosed rotary gap accounts for its
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popularity over more exotic switching means. On the other hand, its
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operation is not as predictable as triggered gaps. Instead of the
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forced firing immediately upon appearance of the trigger signal, the
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firing appears at an unspecified time during the gradually increasing
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voltage gradient. Although the rate of increase of this gradient is an
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order-of-magnitude improved from fixed gap designs, there is still a
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measure of time uncertainty. Of course, the amount of jitter can be
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decreased by increasing the rotational speed of the rotary gap. Since
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jitter is inversely proportional to rate of closure of the electrodes,
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the uncertainty would be reduced proportionally. From a practical
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standpoint, it is not worthwhile to exceed the speed of standard
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ungeared motors (3500 to 3600 rpm). If the electrodes are mounted on a
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diameter of 9.4 inches, they will be moving at 100 miles per hour (147
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feet per second). The diameter may be increased from this value
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somewhat, but large increases will invoke power, noise, safety, and
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speed-of-sound problems. Strength must be a consideration if non-
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metallic wheels are used because the points on the circumference of this
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example sustain an acceleration of 1700 g's.
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Reasonable values may be applied to examine jitter levels in a typical
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rotary gap system. Other than the claim of reasonableness, no
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particular level of precision is attached to the numbers that follow.
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But this approach allows computation of values so that they might may be
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put into proper perspective. At one extreme, assume that if a voltage
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gradient of 175 KV per inch appears across the electrodes then breakdown
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will occur instantly. Also assume the traditional value of below 76.2
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KV per inch where the electrodes will not break down at all. In the
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band between these two values the electrodes will not break down
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immediately, but after some unspecified period of time. It is the
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irregularity of the breakdown time that accounts for a portion of the
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total jitter. For example, consider a 10 KV drop across the electrodes.
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Using the above figures, the breakdown may occur between 0.0013 inch and
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0.0006 inch. The distance at which the gap may fire has an uncertainty
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of .0007 inches. With a reasonable rate of electrode closure, such as
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100 mph in the above example, this peak to peak component of jitter is
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0.4 microsecond. This magnitude is far smaller than the amount of
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jitter that was observed so the source of the firing irregularity must
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lie elsewhere.
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The consistency of the angular spacing of the electrodes is another
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contributory factor. Assume an 1800 rpm system with one particular
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electrode displaced one degree of arc ahead of the ideal position. This
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electrode will cause an interfiring interval 1 microsecond shorter than
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standard. The subsequent interval until the next firing will be 1
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microsecond longer than standard. The sum of this peak to peak jitter
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totals 2 microseconds. Again, this magnitude could not account for the
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magnitude of jitter observed in the embodiments.
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Spherical shapes are generally used for the rotating electrodes.
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Although the sizes of these electrodes are well controlled, it is
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interesting to examine the effect of uneven sizes for their effect on
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firing irregularity. Consider a closely set gap, a 100 mph closure rate
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and the diameter of one of the electrodes 0.005 inch larger than the
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other electrodes. The firing would occur 3 microseconds earlier as this
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electrode approaches the gap and, since the remaining firings are
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unaffected, the peak to peak jitter would also be 3 microseconds.
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Once again, this irregularity is not a significant source of jitter.
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Normal erosion of the electrode surface finish will effect the above
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cited voltage gradient values somewhat. In light of the small 3
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microsecond jitter shown, it is not cost effective to finish the
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electrodes finer than the pitted finish that will naturally occur after
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use. It is rarely worthwhile to use any separate finishing operation on
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the electrodes.
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Another source of jitter can originate from an induction motor; the
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type normally used to drive the rotary gap. These motors have a slip
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frequency in the order of one hertz. The rotational frequency and the
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number of electrodes can form a beat frequency with the line frequency
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which generates firings at irregular positions of the sine wave. It
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could simplistically be calculated that a 1750 rpm motor driving a 12
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electrode rotary gap will form a 350 hertz tone. Indeed, some firings
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will be spaced by 1/350 of a second. But, even in an ideal system, the
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actual number of firings in one full second will fall short of this
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value. Because of the slip frequency, there ideally would be six, but
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occasionally five, firings per half-sine. Further, if a certain
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electrode moves into and out of firing position when the sine wave
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crosses zero there may be no firing at all. This non-firing
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underutilizes the design because the embodied components stand idle for
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a time.
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To eliminate the slip frequency as a source of jitter, the motor in the
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above example was replaced with a 1800 rpm synchronous motor. By
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physically positioning the electrodes at a desired relation to the phase
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of the motor shaft, firings were permitted only at consistently phased
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points on each half sine wave. Even the small sources of irregularity
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such as electrode angular positioning and dimensional tolerances were
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eliminated by extraordinary machining techniques. With all these
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precautions, there was still an untenable amount of jitter.
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The unsatisfactory results of these hardware experiments led to computer
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modelling and analysis. The computer program simulates the electrical
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operation of the transformer with its Q and inductance, the capacitor,
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and the gap. The parameters displayed and analyzed are: instantaneous
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gap spacing, capacitor voltage, transformer current, incoming line
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phase, and energy during firing. The program also emits an audible
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simulation of the firing.
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The computer program is available for downloading as ROTJIT.ZIP from:
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Colorado Mountain College, Timberline Campus BBS System
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Data: (719) 486-2775
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Voice: (719) 486-0133
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24 Hours 8/1/N 300/1200/2400
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The program is PC compatible and requires an EGA (or better) monitor.
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The high voltage iron core transformer combined with its low-Q
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inductive limiting properties is critical to the modelling.
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Conventional transformers have too low an output impedance to use
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directly, so some electrical compliance needs to be inserted in series
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with it. A rheostat is sometimes chosen, but for large size Tesla
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coils, inductive limiting becomes a more practical choice because it is
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ideally lossless. To obtain this inductance, an external iron-core
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inductor may be placed in series with with a conventional transformer.
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Since transformers already contain iron, the inductor can be combined
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with them. Such transformers are commercially available for igniting
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domestic oil burners and for illuminating gas tubes. In the program the
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actual location of the inductance is unimportant since the two
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configurations are equivalent. This text will consider that the
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transformer itself contains inductive limiting.
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This transformer inductance will resonate with the Tesla primary
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capacitance at one frequency defined by LC. If this resonant frequency
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is 60 hertz then the secondary of the transformer will make a resonant
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rise at that frequency to a voltage limited only by the transformer Q or
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the firing of a rotary gap. This voltage may be high and, if
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uncontrolled, the transformer secondary can destroy itself.
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Unfortunately, the lower the transformer losses, the higher the resonant
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rise will be. So the likelihood of destructive secondary voltage will
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increase with better quality transformers. In the computer program, the
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Q is set to about 3 which is representative of one particular
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transformer. Q is generally a parameter that is not controlled by the
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transformer manufacturer and can be a higher value, such as 10,
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depending upon the transformer design.
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In the computer program, the value of the primary capacitor and
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transformer inductance resonates higher than 60 hertz. This resonant
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frequency can be observed by setting the gap to a very wide spacing. At
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this large gap spacing, no firing occurs and there are no transients due
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to the rotary gap. But at the turn-on point (at the left-hand side of
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the screen) the circuit at rest is stimulated with the non-
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differentiable turn-on transient of the sine wave. A sine wave around
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zero angle is essentially a ramp input. Although a ramp is a very
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gentle stimulus, the capacitor and transformer inductance visibly
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resonate. This resonance can be observed adding to the initial cycles
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of the 60 hertz waveform. Since the gap is not firing, the 60 hertz
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energy cannot supplement this LCR circuit with energy at the resonant
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frequency and the resonance dies because of the finite Q of the circuit.
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Demo C in the computer program shows this ringing and its damping. It
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is more apparent in the capacitor current rather than the voltage
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because of the differentiating property of the capacitor.
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When an electrode fires in proper phase with the frequency of this LC
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circuit the stored energy in the tank circuit can be increased. Under
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this condition the transformer and capacitor voltages can rise to very
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high values. If the Q of the circuit is very high, this voltage can
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rise and break down the component most susceptible to overvoltage: most
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likely the transformer.
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The mechanical phasing of the rotary gap with the line frequency is not
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important if there are many firings per cycle of line frequency. But if
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only a few electrodes are used and they are oriented so that the few
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firings are near the 60 hertz zero-voltage crossing, some half-cycles
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may pass without a firing and jitter will be substantial. Demo D in the
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program graphically demonstrates this undesirable feature.
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Another undesirable condition appears if the gap is set too small.
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Consider the instant where the capacitor is charged to a large value and
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the electrodes are far apart. As the electrodes rotate closer to each
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other, the gap will eventually strike and the high energy in the
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capacitor will be transferred to the primary coil. The electrodes will
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continue to become even closer and remain closer for a long period of
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time. During this time interval the transformer charges the capacitor
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to a small voltage limited by the close electrode spacing. This cycle
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repeats and many firings occur during a short time period. But no large
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packets of energy are delivered to the primary. The transformer no
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longer is supplying current to a capacitor with, on the average, a
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moderate charge, but rather to a capacitor with a very low voltage. The
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current builds but is limited to the short circuit current of the
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transformer. The effects of rapid firing and short circuit current
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combine and the electrodes dissipate much more heat. As the gap rotates
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the electrodes eventually will move an adequate distance apart and
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normal operation will resume until the next electrode makes the gap too
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small once again. Demo E in the computer program graphically
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demonstrates this undesirable feature.
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When all elements are properly selected, the firing rate is consistent
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from half-cycle to half-cycle. Demo A in the computer program
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graphically illustrates the elimination of jitter. Note the like energy
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bursts from one half-cycle to the next. The capacitor voltage attains a
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smaller peak voltage than in a flawed system. The computer speaker
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sounds at each energy burst and its rhythmic and monotonous sound
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indicates that the system is properly adjusted.
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ABOUT THE AUTHOR
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Mr. Jamison is an independent engineering consultant. To optimize his
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industrial Tesla coils, he developed the interactive Tesla coil Computer
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Aided Design program TSCAD. A demonstration of this program is
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downloadable from CMC BBS as TSCADDEM. Using mathematical Tesla coil
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modelling he has aided NASA in their extraterrestrial life research
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relating to the creation of amino acids by electrical discharges.
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