From: Paul
Date: Thu, 28 Dec 2000 00:49:31 +0000
Subject: Re: [TSSP] pn2511 is baloney
Bert Hickman wrote: > The EMF defined in 3.1 should have a dI(y)/dt term instead of I(y). > Minor typo. Yes, fixed. > In section 4, would the general equations describing the resonator be > capable of handling a horizontal resonator (as in a single horizontal > bipolar coil) via changes to the boundary conditions? (To my knowledge, > this is a resonator configuration that has not been completely solved > before). Yes, I've kept all options open in this respect - the equs 4.9 and 4.11 are valid I think for any configuration. Up to section 5 the analysis is quite general. The simulator software would need a slight alteration to solve the free space case of the bipolar, and I would need to prepare a different capacitance matrix solver for the horizontal bipolar above ground plane, but without too much difficulty the bipolars can be handled. (The alteration to tsim is just to move the feed point from end to middle and to insert one extra boundary condition). > In section 5 (resonances) you mention that the equations used to > generate the resonance charts were extended to include the effect of > losses. It would be nice to explicitly state which losses were included > and which ones were not (and why not). Also, showing the modified > equations would also be valuable and would lend more credibility to the > charts. Yes, there is a section on the lossy equations still to come. I'm content to introduce it just as a Q factor for the purposes of section 9, and the mention of loss in 5 is to prevent the alert reader complaining that the peaks should go to infinity. Fortunately everything up to sect 9 can be established without introducing loss, so deferring discussion of loss till later helps clarity I think. > In section 6, the Current and Voltage Amplitudes chart shown on page 12 > is an eye-opener - especially the current profile! Yes, it was a surprise to me when it fell out of the model. I'm glad it's fairly easy to explain by inspection of equ 6.4. > Although the > longitudinal coupling terms in the equations are can be seen as > significantly different than the common transmission line equations, > this chart really drives the point home versus the previous distributed > TL model of a resonator. A question: I know that Terry has done a number > of voltage profile measurements which are consistent with the predicted > voltage profiles. Have there been any current measurements that > empirically confirm the predicted maximum at around 1/3 of the way above > the grounded base? I apologize if this is old ground, since I'm only a > recent participant on the TSSP list. To my knowledge, no. I'm inferring the validity of the current peak from the successful voltage profile comparisons. With the reasonably good match on dV/dx it seems there's little else the current can do. I do realise this is weak though, but an unequivocal current profile would be hard to obtain. I can think of indirect ways - I could predict the emf induced across a sliding search coil as a function of position, say, but then thats more or less what dV/dx is! > Section 7 was especially interesting to me, as it defines shunt and > "energy equivalent" capacitances and inductances for the resonator, and > shows how they relate to lumped inductance and capacitance measurements > and base-current and topload voltage measurements that coilers can make. > This approach more rigorously defines these very useful "lumped" > parameters via a more rigorous understanding and framework of > distributed behavior within the resonator. And it shows "why" lumped > analysis appears to be a valid approximation of gross resonator > behavior. And, unlike certain helical resonator and coherence theories, > the theory presented in your paper appears to be fully consistent with > Conservation of Energy and reproducible experimental measurements... :^) There are a number of measureable ratios which are predicted from the equivalent reactances. I've put them all on the things to do list http://www.abelian.demon.co.uk/tssp/todo.html Remains to be seen just how well they can be confirmed. The resonators have to be modeled at some precision to obtain the equivalent reactances, but we have the software tools to do so, and to a sufficient precision I think to clearly isolate the values of Cee and Ces, which can be quite close at small h/d. I hope pn2511 succeeds in establishing some well defined 'Cselfs', the lack of which spells demise for most discussions on 'self capacitance'. > Sections 8 and 9 looks good thus far. It looks as though extending the > model to integrate topload remains as a future task. No, we can handle lossy toploads. The point made in sect 8 is that it's not exactly right to just add x pF of top cap to a Ces or a Cee, ie despite calling them 'equivalents' it still remains an approximation to put them into an equivalent circuit involving other reactances connected to the top. The approximation is valid for small pertubations such as a probe cap, but if you add 50pF of topload to a coil with Ces of 20pF, the Fres is not going to change by the naive amount. But if we compute the reactances so that they include the topload (ie use the VI profiles appropriate to the toploaded resonator to weight the physical caps) then we end up with a Ces and a Cee which 'contain' the topload, ie equs 8.8 to 8.10 which simply redefine the reactances apply to the whole resonator. I don't see a way to define any equivalents that will disguise the fact that they are only valid in an equivalent circuit at one single frequency. > - Equation 9.3 should have energy "lost" per cycle instead of "lossed" > per cycle. Yes, fixed. > Also, has a list of references been generated for this paper? I'm assembling a list. Thanks for your valuable comments Bert. I've uploaded a corrected v0.1e, http://www.abelian.demon.co.uk/tssp/pn2511.ps I'll try and get some more typed up, but I've been using the holiday period to finish some major changes to the modeling software - a boundary element method for the caps, and primary coupling. I'm afraid the todo list is going to get a bit longer shortly. Cheers, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.