From: Paul
Date: Sat, 26 May 2001 13:48:43 +0100
Subject: [TSSP] Topics on non-linear effects
These topics listed below all share a common theme of exploring the resonator load in the non-linear regime. There seems to be plenty of qualitative understanding of what's going on, but I'd like to find out what can be established quantitatively for certain situations, particularly with a view to performance optimisation of traditional Tesla coils. This kind of stuff is well outside my particular field of expertise, so I'll post these notes as a kind of wish-list. Personally, I'm fairly confident that the technical matters of modeling the distributed currents and voltages of a coupled resonator are manageable now, which shifts the emphasis over towards quantifying the load dynamics in a way sufficient to close the loop on the modeling and optimisation process. Time averaged load reactance ---------------------------- We need to decide whether, in the CW/brush discharge regime, the load resistance can be taken as a time averaged value, or whether in fact it changes value significantly during an RF half-cycle. What sort of error do we get if we assume a time averaged value? If it's too much, we have to recompute things a number of times during each cycle, which introduces its own source of (numerical) error over a number of cycles, so we'd prefer to use a time averaged value, recomputed say, just once per cycle. This boils down, I think, to measuring how close the topload voltage and/or current waveform is to a sine wave. Do we get a noticeably flattened top to the voltage waveform? I think the way to do this would be to capture scope waveforms, extract a cycle or two at a time and FT these. A similar question applies also to the load capacitance, which we expect to increase as the coil voltage rises above a certain level. Can this capacitance be time averaged over an RF cycle? Toroid breakout voltage ----------------------- Assuming the resonator is well designed and correctly tuned, we can assume that breakout will occur from the toroid before anywhere else, and then ask the question - what toroid voltage must be reached for the onset of streamer formation? Restricting to smooth toroids, we can take it that this occurs when a surface gradient of 26kV/cm is reached. Can we calculate this breakout voltage by E-Tesla field modeling - compute surface field, find the hottest spot, scale up/down to 26kV and report the scaled top voltage? How does this calculated figure compare with actual measurements? How is the 26kV/cm threshold above affected by a less-than-smooth topload surface? Can correction factors be determined by experiment for things like dryer duct, tape, etc? Topvolts measurements --------------------- Much of what we're talking about involves measuring the topload voltage - specifically the peak voltage. Can a 'standardised' way to measure this be devised - something that anyone can rig up, and require at most say DVM, scope and sig gen for calibration? This so that results from different experimenters can be reliably compared. Can we achieve 5% by some means? What techniques are available? Streamer length --------------- When it comes to optimisation, we must come up with a merit function for the system, which to many coilers will involve streamer length. Can we find a way to estimate the expected streamer length for a given topload and voltage? Perhaps this can be approached both numerically, by seeking an equilibrium between stored topload charge and a simple model of streamer charge using some uniform estimate of C/length for the streamer, and also by experiment - measuring streamer length for lots of toploads at different voltages. Surely a pattern will emerge from a careful collation of results. Primary gap voltage ------------------- The general understanding seems to be that gap loss is a significant factor in determining performance - to the extent that it may even be a major influence on the choice of Lp and thus Ls. The question of whether the gap can be represented by a time averaged resistance arises - can we represent the gap by a resistance in this way? As with the topvolts, I feel that a close look at scope traces of a primary ringdown will indicate whether this is possible. Once again, this could become a case of many measurements on many gaps in order to build up a quantitative picture and allow some sort of satisfactory representation to be derived. On the whole, I feel that with a concerted effort we might be able to make some progress towards addressing those simple questions - What size should I make my coil? How many turns? What shape primary?, and so on. Most appropriate that, after all the math, computing and modeling, things come back full circle to ultimately depend on the efforts made by individual coilers to measure and experiment with their systems. Regards All, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.