TX to Ae

Magnetics

Losses and Q

-


Inductor self-resonance and self-capacitance

The self-resonance and self-capacitance of solenoid coils
By David W Knight

Self-resonance and self-capacitance of solenoids .
DOI: 10.13140/RG.2.1.1472.0887

+ Open Document spreadsheets and coil data
F61-32T.ods ,
Medhurst.ods ,
CL_theor_test.ods ,
18T_scat_Howe.ods ,
CL_axial-field.ods .
Helical_vf.ods .
Maxi Spring Air Core Inductors. Coilcraft Document 185-1, 2004 (accessed 5th Jan. 2016)

velocity factor comparison

Abstract:
The data on which Medhurst's semi-empirical self-capacitance formula is based are re-analysed in a way that takes the permittivity of the coil-former into account. The updated formula is compared
with theories attributing self-capacitance to the capacitance between adjacent turns, and also with
transmission-line theories. The inter-turn capacitance approach is found to have no predictive
power. Transmission-line behaviour is corroborated by measurements using an induction loop and
a receiving antenna, and by visualising the electric field using a gas discharge tube. In-circuit
solenoid self-capacitance determinations show long-coil asymptotic behaviour corresponding to a
wave propagating along the helical conductor with a phase-velocity governed by the local refractive index (i.e., v = c if the medium is air). This is consistent with measurements of transformer phase error vs. frequency, which indicate a constant time delay. These observations are at odds with the fact that a long solenoid in free space will exhibit helical propagation with a frequency-dependent phase velocity > c. The implication is that unmodified helical-waveguide theories are not appropriate for the prediction of self-capacitance, but they remain applicable in principle to opencircuit systems, such as Tesla coils, helical resonators and loaded vertical antennas, despite poor agreement with actual measurements. A semi-empirical method is given for predicting the first self-resonance frequencies of free coils by treating the coil as a helical transmission-line terminated by its own axial-field and fringe-field capacitances.

This article is also available from ResearchGate.net
https://www.researchgate.net/publication/301824613

Additional comments and further work.

Some suggestions for modelling the dielectric effects of tubular coil formers are given by Prof. Tuck Choy:
On the effects of dielectric or permeable formers on the inductance and self-capacitance of solenoids. Tuck Choy. 2015.

The scientific data analysis methods used in this study are explained in a separate article:
Scientific Data Analysis. D W Knight. 2009.


Experiment & measurement

Coil resonance experiments

Inductor resonance and self-resonance experiments .
Photographs and practical details of some coil resonance experiments by DWK.

Solenoid self-resonance measurements by Alex Pettit, KK4VB

Self-capacitance of toroidal inductors.

Capacitor standardisation using a reference inductor.

Parallel resonance indicated using a neon strobotron tube

Evaluation and optimisation of current transformer bridges.



References & further reading

System of Transmission of Electrical Energy. N Tesla, 1900, US Pat. No. 645576.

On the construction of Tesla Transformers: Period of oscillation and self-inductance of the coil [Zur construction von Teslatransformatoren. Schwingungsdauer und Selbstinduction von Drahtspulen)], P Drude, Annalen der Physik 1902, 314(10 & 11), p293-339, 590-610.
English translation by David Knight and Robert Weaver. arXiv:1605.04196 .

The Calibration of Wave-Meters for Radio-Telegraphy, G W O Howe.
Proc. Phys. Soc. London. Vol 24, issue 1, 1st Dec. 1911, p251-259.

Systematic study on self-capacity of coils for radio use. I Yamamoto. JIEEJ, 45 (1925) No. 440, p259-277.

Die Grundlagen der Hochfrequenztechnik, Franz Ollendorff. Section 54, Pages 79-87,
Das dynamische Feld der mehrwindigen Spule [The dynamic field of multi-turn coils].

Remarks on the self-capacitance of coils [Remarques sur la capacité propre des bobines], P Cassou and J Cayrel, Comptes Rendus Académie des Sciences, Vol 198 (1934), p1305-1308.
English translation by Kate Knight and David Knight.

  H F Resistance and Self-C of Single-Layer Solenoids. R G Medhurst, 1947.

Travelling Wave Tubes. J R Pierce. BSTJ* 1950: 29(1) p1-59, 29(2) p189-250, 29(3) p390-460, 29(4) p608-671.

EM Wave Propagation on Helical Conductors, S. Sensiper, MIT Research Lab Electronics Tech Report No. 194, May 1951.

Some wave properties of helical conductors. J H Bryant. Electrical Communication 31(1), 1954. p50-56.

Coaxial Line with Helical Inner Conductor. W Sichak. Proc. IRE. Aug. 1954. p1315-1319. Correction Feb. 1955, p148. Reprinted in Electrical Communication, 32(1), March 1955. p62-67.

Wide frequency-range tuned helical antennas and circuits. A G Kandoian, W Sichak. Electrical Communication 30(4), 1953. p294-299. Correction: 31(1), 1954, p49.
Considerations Regarding the Kandoian & Sichak Formula, Andrés Esteban de la Plaza. (accessed 5th Jan. 2016).

Helical Antennas, Ref Data for Radio Eng., 4th edn. 1956, ITT corp., p682-687.

Helix Waveguide. S P Morgan, J A Young. BSTJ. 1956: 35(6), p1347-1384.
(Unfortunately, Bell System Technical Journal articles are no longer free from Alcatel-Lucent. The articles are available via IEEE Xplore (subscription required). Some whole volumes of BSTJ can be found on Archive.org.)

Folded-over helical resonator. P Vizmuller, US Pat. # 4422058, 1983. [see also Vizmuller's book 'Filters with Helical and Folded Helical Resonators' (1987) ISBN 0-89006-244-7 (not available online)].

Fields and Waves in Communication Electronics, Simon Ramo, John R.Whinnery, Theodore Van Duzer, 3rd edn. Publ. John Wiley & Sons Inc. 1994. ISBN 0-471-58551-3.
9.8: The idealized helix and other slow-wave structures. 9.9: Surface Guiding.

Stray Capacitances of Single-Layer Solenoid Air-Core Inductors, G. Grandi, M K Kazimierczuk, A Massarini, U Reggiani. IEEE Trans. on Industry Apps., Vol 35, No. 5, Sept/Oct 1999, p1162-1168.

Filters and an Oscillator Using a New Solenoid Model, Randy Rhea, Applied Microwave & Wireless, Nov 2000, p30-42.

RF Inductor Modelling for the 21st century. Leslie Green. EDN, Sept. 2001.

RF Coils, Helical Resonators and Voltage Magnification by Coherent Spatial Modes. K L and J F Corum, Microwave Review, Sept 2001 p36-45.
Class Notes: Tesla Coils and the Failure of Lumped-Element Circuit Theory, Kenneth and James Corum.
(now seems to be available again from: ece.k-state.edu/people/faculty/gjohnson/ )
Multiple Resonances in RF Coils and the Failure of Lumped Inductance Models. K L Corum, P V Pesavento, J F Corum. 6th International Tesla Symposium 2006.

Solid State Tesla Coil. Gary L Johnson, 2001.

Practical continuous funcs for internal Z of solid cyl. conductors. D W Knight 2010

A study of secondary winding designs for the two-coil Tesla transformer. R M Craven, PhD 2014.

Self-resonant frequencies of air-core single-layer solenoid coils calculated by simple method, Caio Marcelo de Miranda, Sergio Francisco Pichorim, Elec. Eng. 97(1) p57-64, Mar. 2014. Available from both authors at researchgate.net.

Paul Drude's Prediction of Nonreciprocal Mutual Inductance for Tesla Transformers, Bart McGuyer, 2014, PLoS ONE. 9(12):e115397. doi: 10.1371/journal.pone.0115397.


TX to Ae

Magnetics

Losses and Q

-


© D W Knight 2008 - 2016.