




An investigation of the solenoid inductance and impedance calculation
techniques described in this website and elsewhere was given
as an article by Paul Zwicky, HB9DFZ, in the German language
magazine Funkamateur
(Oktober 2013, p10801084, + picture on p1032): "Optimierung der Güte einlagiger zylindrischer Luftspulen" [ Optimising the Q of singlelayer solenoid air coils ]. Paul has very kindly made his work files available as pdfs, with comments translated into English, and has allowed them to be published here. They are as follows: Coil calculation with Medhurst and G3YNH . Checks to see whether the coil calculation method holds against measurement. Search for best Q while holding volume constant . Scans through the main parameters to find the optimum number of turns while keeping volume constant Algorithm for optimum coil and minimum volume . Procedure to calculate mechanical data from an electrical specification. Selfcapacitance corrections . The effect of C_{0} on Q factor. In email correspondence, Paul added the following: " I have also tried to use the method given in Arnold's paper ['The Resistance of RoundWire SingleLayer Inductance Coils'. A H M Arnold. Proc. IEE Part IV. Institution Monographs, Oct. 1951. Vol. 98, p94100]. In 2011 I converted all the necessary tables into approximations and was able to calculate Φ_{Arnold}. Then I did the same thing as in the file "searching for optimum". The result for η_{opt}(n) looked sensible. But α_{opt}(n) looked too flat especially at small numbers of n. It even tended to have a maximum at >2, and that couldn't be true. Simply minimizing the wire length gives an α_{opt} of 0.45. Looking into the Arnold paper we see that the verification is only by comparing with Medhurst. That means for n = 25 to 50. So I gave up. Then I worked with Glenn Smith ['The proximity effect in systems of parallel conductors and electrically small multiturn loop antennas'. Glenn Smith. Dec 1971. Tech. Report No. 624. Division of Engineering and Applied Physics. Harvard Univ. Cambridge, MA 02138], which looked like very serious work for n = 2 to 8. I tried to extrapolate his findings for n > 8. I did not succeed well. So I worked with your idea of finding Φ(n). And that was heureka! Concerning capacitance: My calculations ignored the presence of any capacitance. In the paper [Funkamateur, Okt. 2013] Dr Hegewald limits the validity to 1/5 of the SRF. It would be nice to have it more universal. On the other hand I carefully measured the C_{0} of the sample coils and used the findings to correct the direct measurement values L and Q. That means the values in my file are true for coils having no C_{0}. In order to give the limit of ≤1/5 of the SRF some meaning, I give the simple formula of Medhurst for C_{0} and calculate the SRF. Then the C of the connecting wires has to be added. The measurement of C_{0} and the calculation agreed to approx. ±5% ±0.2 pF. To avoid additional losses I did not use any coil formers, and the coils were standing in free air on top of the measuring gear. Distance >D. [See p 1032 Funkamateur 10 2013, also see photo above]. " 




