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. -*-