Simple Analysis of my Induction Coil

<------  Feedback is very welcome !
When I started building my induction coil, looking around for information, revealed a bunch of practical information (- a number of books, written on the subject! - ), but no applicable, up to date "engineering theory" about the "obsolete device: induction coil". The knowledge about the subject, probably available in the automotive industry, is not within reach for me. So..., I made my coil based on  the traditional information, but kept in mind, the situation was not very satisfactory, from the theoretical viewpoint. The practical implication of this defect is: in designing modern versions of an interruptor, the designer is missing data, in order to size the semiconductors utilized, regarding voltage, current, (+ their time derivatives dV/dt, dI/dt) and power. The problematic part of the old induction coils beeing the interruptor (- from Wagner's Hammer, Mercury-Rotating Interruptors, to Wehnelt Electrolytic Breakers - ), the modern power-electronic devices offer a most attractive alternative: being it traditional style interruption of a DC-loaded primary, or an alternative capacitor discharge(-speak: dimmer-)  device. But many semiconductors are sent to "HV-heaven", just because of inadequate knowledge of the environment, where to operate them. An, even rudimentary, theory of the induction coil, allowing the simulation of the most important behavior of the coil,  would be most welcome.  The decision, I  took, was to follow the traditional line of a DC-interruptor, for my coil testing.  In order to gain an experimental base for modelling, 34 careful measurements were planned and carried out in November 2001. 

 click to see the induction coil's main data

On Dec. 23rd, 2001, I wrote: "This page is not yet finished; please have a look again in a few weeks."
Sorry, but I got stuck with the further development of "my" theory, which is based on the one of A.Bouwers, in his book "Elektrische Hoechstspannungen", Springer Berlin, 1939, pages 33 to 36 (Bouwers's text is downloadable as - 462kB -, containing .gif files of his text).  I also rederived his theory, in order to gain a better understanding (please contact me, if you like to see the 14 page handwritten derivation), finding some very few little errors. Then I tried to apply the theory to my experiments, by means of an Excel-spreadsheet: Well,...while is was a part success to explain the dominant 2 frequencies of the coil, I failed to generate the waveforms of my measurements, because the theory is for the lossless case only, and induction coils exhibit relatively high losses! Even the beginning of the waveforms didn't match the measured ones, which I was erronously expecting. And Bouwers's theory is never considering the spark as an element to take in account for modelling. Though, the modest semiempirical formulae below serve as a vehicle to correlate simple measured frequencies to coil parameters.   . 


3 typical scope-screenshots, out of the 34 experiments,
show the predominant waveforms.
operating the inductor without secondary-sparks. operating the inductor with secondary-sparks .
Looking at the scope-screenshots, it seems not quite obvious, how to to relate the waveforms to simple, experimentally easy to obtain parameters of the induction coil. 

At least 2 dominant frequencies f1, f2 can be observed, when the induction coil is producing sparks, or is otherwise loaded at the secondary (i.e. capacitively).

It proved possible to correlate these 2 frequencies to simple coil parameters. The result is shown in the two diagrams below.

operating the inductor without secondary-sparks , but 
added secondary capacitance, by connecting Leyden-jars.

f1 = 1 / { 2p * sqrt [ L1 * (1- k2) * C1 ] }
is the simple empirical formula, where

L1   primary inductance     [H]
L2   secondary inductance [H]
C1 primary capacitance     [F]
k coupling factor = M/sqrt(L1* L2)
M = mutual inductance     [H]

f2 = 1 / { 2p * sqrt [k 2* L1* ( C1+ n2 * C2 / k2)] }
is the simple empirical formula, where. 
The black dots are the calculated values.

L1   primary inductance    [H] 
C1 primary capacitance     [F] 
C2 secondary capacitance [F]
where C2 = C2,o + C2,add
C2,o   secondary self-capacitance      [F]
C2,add secondary added capacitance [F]
N1 number of primary turns    [-] 
N2 number of secondary turns [-]
n   turns ratio = N2/N1           [-] 


Last Updated on 7.9.02 / 15.12.01
By Kurt Schraner