Q. I have noticed that TCBA NEWS is somewhat thin on the mathematics end of Tesla coils. It would appear to me that this is an important phase and should be given more coverage?

A. I agree that there should be greater coverage of the mathematical aspects of Tesla coil operation. In past issues, we have allotted space to the basic math principles such as equations for finding inductance, frequency, wavelength, capacitance, impedance, and so on. However, the math involved in coil operation can be a bit hairy. That is, it would include such phenomena as interrelationships between electrostatic and electromagnetic field, frequency beating, harmonics, reactive and impedance shifting, ohmic and radiation losses, phase shifting and a number of other theoretical parameters. As you can see, the simple tuned spark oscillator is subject to many complex factors not taken into account by the usual math. Still, TCBA would welcome any papers directed to the math of TC circuits.

Q. Can you give some idea of the relationships of spark length and voltage ratios?

A. Probably not. It is best if we rate our coils by ratios of spark length to input power and forget the output voltage. Dick Aurandt looked into this subject and found that a study by Kotter* showed a greatly reduced spark length-to-voltage ratio with higher frequencies. For example, it was commonly taken for granted that a spark one meter in length represented over 1/2-million volts. Kotter's result has shown that at 28.5 KHz, the actual voltage is only 150 KV. He also found that electrode geometry greatly affected the results. So much for the 30 KV per inch of spark theory. I suggest that you review D.C. Cox's article in Volume 2, #1 of TCBA NEWS. Cox advocated rectifying the transformer output and measuring the intermittent spark. This could then be interpolated with DC spark length-to-voltage tables.

Q. What is meant by resonant rise?

A. In radio circles, it usually refers to an effect in resonant frequency when a capacitance is placed in series with the antenna. Other than that, I am not sure how you saw it in print so am not able to provide further explanation.

Q. Can I take a large capacitor and charge it with my little ignition transformer to obtain a large charge?

A. This is one of those questions that can best be answered by actually trying it. The actual charge upon a capacitor is determined by both the applied voltage and the capacitance rating of the unit.

Q. Doesn't the distributed capacitance of a coil have to be known in order to utilize the 1/4-wave principle?

A. A coil with a given length of wire will have a natural resonant frequency of its own. If distributed capacitance is significant, the coils have resonated at more than one frequency. This is why distributed capacitance is undesirable. It only becomes a problem when building very large coils.

Q. A recent TCBA News stated that there are free oscillations in the secondary after the primary is damped out. How long do these free oscillations continue in the secondary?

A. It depends upon the resonant frequency. Generally, we are talking about 100,000 ths of a second or shorter.

Q. A man named Nichelson says that he has built a Tesla coil based on patent 593,138 that is 800% more efficient than a regular transformer of comparable dimensions. He shows mathematically a secondary half-voltage damping time of 7.32 minutes. He claims that his transformer could make electric cars more practical.

A. A lot of theoretical math never made it into reality. I believe that his is one good example.

Q. You have made mention of the importance of employing a ground in Tesla coil circuits. I am not sure that I understand the purpose of a ground?

A. A good ground is essential in electrical circuits and especially so where high voltages are encountered. The purpose of a ground is to keep associated components at equal (ground) potential. Otherwise, a potential difference between them could develop and destroy the units. Also, a ground tends to establish a greater difference of potential between it and the output terminal thus providing a longer spark. Lastly, a good ground is essential for the safety of the operator. NEVER OPERATE HIGH VOLTAGE ELECTRIC CIRCUITS WITHOUT A SUITABLE GROUND!

Q. The “impulse mode” of operation was mentioned in a previous TCBA NEWS. What is meant by this?

A. Some interesting effects can be obtained by rectifying the output of a power transformer and using it to charge a large capacitor of the TC circuit. When the coil fires, and intermittent lightning-like spark comes forth from the coil. It has the characteristics of a spark from a Van de Graaff generator more than the hairy and wavy sparks of the Tesla coil. Pete Lefferts is planning on demonstrating this very principle at the forthcoming UNCONVENTION.

* IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, Vol. PAS-102, No 6, June 1983.