From: Paul
Date: Thu, 31 Aug 2000 18:59:08 +0100
Subject: [TSSP] Mystery of the missing loss
Terry has provided a lumped equivalent circuit http://63.225.104.218/test/TeslaCoils/Misc/PaulNich/LumpedSecModel.gif which gives a very good description of the observed characteristics of the coil we've been looking at. With a measured value for Rsec, the other two equivalent resistances can be chosen to reproduce the observed Q factors, attributing a lower loss to the external toroid capacitance. Terry wrote: > ...and the added resistors accounted for > the currents traveling through various objects like the > ground, wall, floor, etc. In other words, Cself > and Rct or far from loss less capacitors. I'll just say a bit about how the model handles these losses. Cself represents capacitance from one part of the coil to another and the significant loss associated with this (air dielectric loss being negligible) is due to I^2R loss in the winding resulting from the displacement currents charging up Cself. The lumped equivalent model has to represent this as a separate current path, with its own resistance, since by definition it cannot get at the internal currents in L1. The computer model represents the internal capacitance currents explicitly and the loss represented by Rcself appears instead in Rsec and there is no need for a separate Rcself. As Terry says, Rct accounts for conduction losses in the return path of the external capacitance current loop. The computer model represents this as a loss factor Dp applied to the external capacitance. This is nice because the loss is distributed in proportion to the external capacitance which presumably reflects the distribution of ground currents arising from external flux. Up until now, Dp has been set very low, equivalent to less than 5 ohms Rct, ie negligible. The justification for this is a desire to focus on winding losses and, by restricting measurements to systems equiped with a good ground plane, the assumption is that the return path losses are of the same order as the bulk resistance of the ground plane, ie a few ohms. Terry's posting reminds me that I've no good evidence to justify neglecting Rct. I still think that the foil would be contributing only a few ohms to Rct, but the loss from the wider surroundings may be adding a lot more. Apart from these I^2R losses in the external E field, and possible eddy current losses from the B field, I think the list of significant sources of loss external to the coil is exhausted. I've tried a Dp value equivalent to Rct of around 300 ohms which brings the Q's down to the 60/80 region, but the predicted Q is higher without the toroid - opposite to what we measure. Tentative estimates of eddy current loss suggests that it goes up with f cubed and can add a hundred or so ohms into Rsec. Therefore I'd expect higher Q at the lower toroided f1, which is what we see. So theoreticaly I'm still inclined towards the eddy current theory. The major discrepancy between Q factors modelled largely on the basis of winding loss only, and the measured values, must be due to one or both of these two sources, and no significant other. I think we should devise some definitive tests to establish how the missing loss is apportioned between the external E field current return I^2R loss, and external B field eddy current losses. Some possible experiments: 1/ Split the ground plane. Already tried. Q went down, score: E one, B nill. 2/ Replace the toroid with a 25pF capacitor wired back to the central ground point. This will have a much lower Rct than 130 ohms. The toroided f1 should be reproduced, but if E return loss is significant, a higher Q factor should be obtained. 3/ Extend the foil ground plane to catch more of the external flux. See if the Q goes up. 4/ Tightly couple a shorted turn near the base of the coil to artificialy add extra eddy current loss, and see if the two Q factors diverge further. I'm sure there must be some cunningexperimental tricks to decouple these two potential sources of loss, and if we can do so unabmiguously then that would be a great step forward. Regards All, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.