23 October 2000
Revised 27 January 2001
GENERAL: The primary Circuit in this discussion includes T1, L1, L2, S.G, Cp and T2. T1 supplies the input AC power, L1 and L2 provide RF isolation between T1 and the main oscillating components, Cp and Lp, the primary of T2. The primary of T2 will be referred to as the Primary Circuit inductor Lp. The Spark Gap S.G. should be considered an open circuit when C is charging, and as a short circuit when Cp and Lp are exchanging energy (oscillating).
PRIMARY CIRCUIT CAPACITOR
The Primary Circuit capacitor is the heart of the Tesla Coil. The amount of electrical energy it contains is determined by its capacitance and magnitude of voltage charge.
For example, a 0.037uF capacitor charged to 13kV will contain 3.1 Joules of energy.
PRIMARY CIRCUIT INDUCTOR
In the Tesla Coil arrangement the Primary Circuit inductor Lp receives electrical energy from the primary circuit capacitor in the form of discharging current when S.G. is shorted. This discharging current goes from zero to maximum at a sinusoidal rate. At the peak value all energy is transferred and is in the form of a magnetic field. This energy is expressed as a function of inductance and current.
Peak current in Lp can be calculated since the energy it received from the capacitor (3.1 Joules) and its inductance (50uH) are known. My pocket scientific calculator tells me it is 352 Amperes. During energy transfer some is lost due to circuit resistances, capacitor dielectric losses, radiation, etc. so the actual peak current will be less than that value.
The transfer of energy from the capacitor Cp to the inductor Lp just described is the beginning of oscillation. The first 90 degrees of a complete cycle occurred at a sinusoidal rate. At this point the voltage in the capacitor is zero. With no capacitor voltage left the circuit current is at a maximum. The current continues to flow back into Cp charging it up in the opposite direction at a sinusoidal rate. The self induced voltage in Lp due to its collapsing magnetic field keeps the current flowing back into Cp. This is the energy transferring back to the capacitor. The current correspondingly decreases at a sinusoidal rate until it again reaches zero. When it does, Cp will have charged up to a peak voltage of the opposite polarity and 180 degrees of oscillation will have been completed.
The above process continues for the next 180 degrees at opposite voltage polarities and current directions to complete one cycle of oscillation. If no energy is dissipated in the form of heat due to circuit resistances and radiation, the oscillation would continue indefinitely. However, There are always resistance and radiation losses in the circuit, so the energy will decrease exponentially which is normally regarded as damped oscillations. (This is regarded as "Ring-down" in some circles)
The circuit oscillating frequency is determined as follows:
For example, the resonant frequency of a 0.037uF capacitor and a 50uH inductor is 117kHz Such oscillations would continue indefinitely if it were not for resistances in the circuit which dissipate the energy in the form of heat. Energy will also be lost in the form of electromagnetic radiation which is not desireable in terms of intereference (EMI). In other words, a damped oscillation takes place.
The values mentioned so far are for Tesla Coil operation. Note that the capacitor must withstand voltages in excess of 10kV and be capable of handling charging and discharging peak currents in excess of 300 Amperes through its terminals. Furthermore, the dielectric must have very low loss at the RF frequencies involved The inductor must withstand the same high currents. As such, these components are not normally available from electronic and radio parts distributors. That means they must be designed and constructed to Tesla Coil specifications.
LOSSES AND Q
Losses in the primary circuit are mostly due to its resistive components. The circuit Q is a measure of these resistive components. Q = XL/R where XL is the inductive reactance of Lp and R is the effective resistance in series with Lp. Q's in excess of 50 should be strived for. Well constructed Primary circuits will have Q's of between 50 and 100. Copper tubing coils and low density polyethylene capacitor dielectric material give good results. Low density polyethylene sheet material has excellent RF characteristics.
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