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THEORY OF THE IGNITION COIL

BY

MATI LAL DUTT

B. S., University of Illinois, 1911

THESIS

Submitted in Partial Fulfillment of the Requirements for the

Degree of

MASTER OF SCIENCE

IN ELECTRICAL ENGINEERING

IN

THE GRADUATE SCHOOL

OF THE

UNIVERSITY OF ILLINOIS

19 12

O'

1*5* ft

UNIVERSITY OF ILLINOIS

THE GRADUATE SCHOOL

Way 31, 19£2

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY

MAT I LAL DUTT

ENTITLED TECCHY OF THE IGIIIT IOIT COIL

BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OP SCIENCE IU ELECTRICAL EIT CITIES?. TUG

In Charge of Major Work

ead of Department

Recommendation concurred in

%Committee

on

Final Examination

KM

CONTENTS

PagoI Introduction 1

II Physical Theory and Principles

of Operation 3

III Fundamental Equations in

Transients 8

IV Numerical Applications 16

VI Conclusions 26

THEORY OF THE MODERN IGNITION COIL

I Introduction

The modern ignition coil, otherwise known as

Induction coil. Induct orium, or Rhumkorff coil was regarded

a few years ago principally as a useful laboratory apparatus

and was chiefly used to illustrate the principles of electro-

magnetic induction. To-day it has become an article of ne-

cessity to thousands of people, and the industry of manu-

facturing induction coils has become a very important one.

Among the uses to which induction coils are put, may he

mentioned the wireless telegraph, the excitation of X-ray

tubes, igniting the explosive mixture of gas and gasoline

in the internal combustion engines of various types, electric

gas lighting, etc.

In spite of the extensive use of the induction

<Joil and the trouble arising from ignorance in the handling

of such coils, very little has been written regarding its

principles and operation from an engineering and practical

point of view. Of course, all text books on physics give an

elementary explanation of its action, and a few highly mathe-

matical articles, written more from the stand point of the

mathematician than from that of the engineer, have been

published. The practical engineer having ordinary mathematic

al knov/ledge, finds very little information on the subject

and his knowledge is limited to the usual text books. 3ven

z

this meager information is so scattered that it is quite be-

yond the reach of practical engineers. The attempt of this

thesis will be to present the whole subject in a logical

manner and develop some equations from fundamental principles

to be of use to the every day engineer.

3

II Physical Theory and Principles of Operation

When we examine the development of the ignition

coil, we find that the evolution followed the general law

"that improvements in experimental instruments advance along

definite lines "by a process of evolution in which rudimentary

forms are successively replaced "by more and more completely

developed machines." Most people who are interested in the

induction coil think that Faraday made the discovery of

electro-magnetic induction with his rude ring transformer,

"but the fact is that Joseph Henry, a young teacher in the

Albany Academy, was an independent discoverer of electro-

magnetic induction. This is proven "by an account of the

manner in which he had independently performed a similar

experiment in the previous autumn "before receiving an account

of Faraday's work.* But V/illiam Sturgeon, an eminent English

physicist, was the first person to construct a coil which

was practically the same in the general form as the induction

coil of to-day. The next great improvement was that of in-

serting a condenser across the ""break" of the primary cir-

cuit of the coil. This was rendered by Fizeau, French

physicist. This application of the condenser in the primary

circuit made possible the universal use of the induction

coil. The modern ignition coil is essentially the same as

the Rhumkorff coil or induction coil. It consists of two

coils, primary and secondary, and a central iron core. The

4

latter is usually composed of a "bundle of soft iron wires

(insulated from each other by shellac). The primary coil

which is wound around this core is made of a few turns of

thick insulated copper wire; the secondary coil which

surrounds the primary coil is made of very fine, well in-

sulated wire of considerable length having a lp-~ge number

of turns.

Fig. I represents

the picture of such a coil

showing the details. The cur-

rent flowing from the battery

B through the binding screw A,

the contact screw b and the

hammer h, enters the primary coil,

where it acts inductively on the

secondary coil. Having traversed the primary coil it comes

out at f , and returns to the battery through the binding

screw C. When the current flows through the primary coil it

magnetises the iron core which attracts the iron hammer or

vibrator h, thus breaking the primary circuit at e. This

interruption of the primary circuit causes the magnetic flux

to die away. The hammer is then released thus completing

the electric circuit, and the current flows again. This is

repeated at a great frequency which depends on the inertia

of the hammer and the constants of the coil. The repeated

appearance and disappearance of the current in the primary

coil induces an alternating electro-motive force of high voltage

Frg.1

in the secondary coil. The strength of this electro-motive

force depends on tho ratio of the number of turns in the

secondary coil to that of the primary coil. When the electro-

motive force is large enough to overcome the resistance be-

tween the needle points at p, a spark passes.

To make the break more sudden and to set up an

electrical oscillation in the circuit it is usual to put a

condenser across the "break points" of the primary circuit.

This condenser is thus so connected that it does not affect

the current rush in making but only in breaking. Owing to

the magnetic induction in the coil, the current in the primary

coil cannot rise suddenly to its maximum strength. It follows

the law,

where i = primary current in amperes

E = impressed electro-motive force in volts

r = resistance of primary coil in ohms

I self induction in henries

6 = 2.718

t = time in seconds

The current therefore requires an appreciable fraction of a

second to flow through the jprimary coil containing inductance

and resistance only. Consequently at the make of the primary

circuit the rate of change of flux is relatively slow. In the

case of the break, however, the primary circuit contains in-

ductance, resistance and capacity, as a consequence the rate

of change of flux in the case of break is greater than in the

€

case of make. Hence the maximum voltage across the terminals

of the secondary coil occurs at the time of primary "break.

The object of the condenser is primarily two-fold.

It enables the primary circuit to he broken more or less

8parklessly and it serves as a spring which absorbs the electro

magnetic energy, which is equal to — , at the time of the

break. This absorbed energy is sent back from the condenser

as a reversed current into the primary coil causing magnetic

lines to appear in the opposite direction. Thus the electro-

motive force in the secondary coil is increased and an in-

tensified spark occurs at the spark gap.

More clearly, if a condenser is connected across

the "break points" of the primary circuit, the energy in the

magnetic field dies down and charges the condenser for a short

time; the condenser then discharges sending a reversed current

through the coil, thus setting up an electrical oscillation.

The electro-motive force set up in the secondary coil is then

the result of the stoppage of the primary current and its

immediate reversal in direction, and this is equivalent to

the removal of a certain number of lines of induction from

the secondary circuit, and their immediate insertion into it

in the opposite direction. Hence when a condenser is used the

secondary electro-motive force would be just double the electro

motive force in the case when no condenser is used (neglect-

ing losses). "The condenser acts by setting up electrical

oscillations, and it does away with the spark or largely di-

minishes it, in virtue of the fact that the condenser acts at

7

at the moment of ""break" as if it were a shunt circuit of

negative self-induction, only with this difference— that

instead of dissipating energy like a circuit of resistance

and induction it returns to the primary circuit in the form

of a reversed current, and increases the total change of in-

duction through the secondary circuit"

5

e

FUNDAMENTAL BCffJAflONS IN TRANSIENTS

X P

F.g.2

The induction coil

stripped of all mechanical

detail may "be represented

diagrammatically "by Pig. 2.

E is the constant electromo-

tive force impressed, L and

r are the self-induction

and resistance of the primary coil. C is a capacity connected

across the switch or interrupter S. e is the electromotive force

of the condenser. Also, I^is the self-induction of the secondary

coil, and r4is the sum of the resistances, r^of the coil, and

r of the spark gap, and M is equal to the mutual induction of the

two coils, primary and secondary.

From the fundamental law that in a closed circuit the

algehraic sum of the electromotive forces is equal to zero, we

find at the instant after opening the switch S, that the fol-

lowing equations are true.

/^fo/fip/y /ny epu&S-i'orr f 6y L/ arte/ e^ca^/or? Z &y — f, ?

V* * I? L'M& + * L

<~ eL

'= ° ~~ 3

_ - - - -f

_ /

- ^

9

~cl* ~ [n f] J £&t x /va, cot- nr c

+ e — e

cut >

(^J^ *fe*^#^*f-' 7

= c

?V 3 -f am 2-

-r- bm + O = o _ __ _ _

to

o — —y + h + v

fu/e are :

-/-//JZ

/

5*jore

*»« y- froc As o-A /fie eocro-//c/7 9 <?re

^ = > - 43 "\3 3

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//

Sohs A//urir?0 ~7fre expresssons for g£ t

t ^naf <g/ "7 <?pc<,/,orr

M si.

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four** oy mi*i*t cc^Jorr ,*"* °*

/primary circuit" a/ faSVtlc/, Or in/vrrufter S,

£=<>• 77T<>r>

I = °

L,= c

£>tj/>s///t,//r7y 7#<? l/a/ves of /7f , /72 Gnat #3 "7 -e<pc/a~f/o/7s ft*

/ Z- One/ /3/

7%e €Xf?r>e sst'ons for Corraferrse*- C/rarpef

/pr/sr?ary

Ct/r re/771- ctrref seear?c/ary Career?/ /'rr ffms o^f ~£ cq/? <5e Co/pl//g/c

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.

C/7SE. 1 € -

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- ML,

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— <3 l+S-C

'7

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L - a /s

- — a7,——— ^ // t - ) /9

- o

r» — n = c

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3

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Lfi, +- M i - K C?onsfanj) — - — z I

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7f /Pr/rrrat-y ct/rre/771 600/A^r&rr c/o&eaf for 0/7 af>/>*-e c/aA/^

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• ; Ltit

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7 , if is :

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gats*/ Ac I t^S /?0 A as7 osc/AAa A/ftp ce/ry-e .

NUMERICAL EXAMPLES

To illustrate the use of the equations previously de-

duced, the constants of an induction coil were determined for

numerical application . The resistances of "both the primary

and the secondary coils were determined "by means of a re-

sistance "bridge which is familiar to every electrical engineer.

The method used in measuring the inductance was the well known

impedance method. Each of the primary find the secondary coils

was connected as shown in Fig. 4. An alternating electro-mot^ 9

force was impressed on the circuit,

The total current in the coil and the

voltmeter was measured in each case, 1 \Q \V)

and this current was later corrected

"by deducting the current taken "by the

voltmeter. The current flowing through ^'3' ^

the voltmeter was determined "by the

equation Jv = where r is the voltmeter resistance, and E is

the impressed electro-motive force. The frequency of the circuit

was also determined "by a frequency meter. The impedance of the

coil Z = -j- therefore the reactance, x » J7? - R2 where R =

xthe resistance of the coil, the self-induction L = where

2 ir ff * the frequency of the electro-motive force.

The unknown capacity was determined "by comparing the

deflection caused "by its full charge in a galvanometer with the

deflection caused "by a known capacity charged with same voltage

in the same galvanometer* The connections are shown in Fig. 5.

G is a galvanometer. The unknown capacity was charged by the

battery and then discharged into the galvanometer circuit and the

deflection noted. Then the standard capacity of a "known value

was connected in place of Cx and the de-

flection was noted egain. Then

where d is the deflection of the

#Fig 5

galvanometer and C the capacity.

The following constants were determined:

the primary resistance r = .1696 ohms

the primary reactance x = .612 ohms

the secondary resistance * 3060 ohms

the secondary reactance x-^ - 6580 ohms

the capacity C * .122 microfarads

the primary inductance L .0017 henry

the secondary inductance * 17.5 henries

and the mutual inductance M = ^/.75 L

• .1495 (assumed)

General Case

.

Substituting these constants of the coil under in-

vesitgation, previously determined, in the solution of the

general differential equation 8 and the auxiliary equation 9.

a =L,n -f-A.n, '7 5 X /(>?5 + OO/yx 3o(,Q

/e

for jb or7c/ <g tê. <?&f

f = (S^J _ + o) = - 3.67 x/o /z-

Scj6s^-/û/n^ Qâts7 ftrese \z&/c,es yo one/ ^> /<? y 3 y ?

one/ y fH/t? ye/

f

y = 3 oo•/

y - - /so -t- j. /3&ooo

y - - / 5~o -J.

/3s o o o

6a/ *? = y-f- One/ f = C^£. = 3^3.

T*? = / - 3 6-5" - - €5

?T)Z

= J£ - 3^5 - - 5/5 + J ' 3&ooo

7773

= - 3 6S = - S/S-* /3&000

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/s? e

So/ i — £*2L

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— /7Z € S /S£&"7 ('/ 3 8 000C + ATjj^ £J

Frem eyuaf/or? 5"

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_r /O S/o ff388 Cot ______ 4o

//7 ^'J- ~7$e Curves ore sAa^r?

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u- or t. s. s. roRM a

VI Conclusions

The curve q in Fig. 6 shows the condenser charge

after the primary circuit is broken at switch S Pig. 2. The

constant term - .61 x 10" 6 in equation 31 represents the

normal condenser charge corresponding to the impressed electro-

motive force. The two transient terms show how the condenser

charge varies from instant to instant. The vector sum of

these three terms is represented by the curve q. The electrical

oscillation is started by the energy stored up in the magnetic

field around the coil. At the instant of the primary break,

this energy is dissipated as a contact spark if no condenser

is used. But it charges a condenser when it is connected

across the "break points," and consequently a current flows

in the syrtem because the time-rate of the condenser charge

is the current flowing in the circuit. Hence this energy

charges the condenser to a higher voltage than the impressed

constant electro-motive force. This electrical instability

cannot exist and the condenser discharges pnd sends a reversed

current through the coil which sets up a magnetic field al-

most as strong as the original field, if we neglect the losses

in the resistance and the imperfect mutual induction. The

energy stored in the magnetic field thus set up charges the

condenser again which discharges and sends current through

the coil again and so on. Thus the electrical oscillation

is set up whose period is a very small fraction of a second

and generally depends on the constants of the circuit.

If we refer to the simpler case, when r-^ r = o,

we find from equation 17, the period of oscillation equal to

7 77- fTL <~ .- r/^jc^

% in a particular coil the terms

L, L^, and M remain constant. The deduction is that the

period of oscillation for the coil is directly proportional

to the square-root of the capacity. Therefore the frequency

is inversely proportional to the square-root of the capacity.

Hence smaller the capacity, the larger the frequency.

The period of the mechanical oscillation of the

vibrator of the induction coil is much larger than the period

of the electrical oscillation. As soon as the hammer is attract

ed, the primary circuit is "broken and the electrical oscilla-

tion, previously described, starts and goes on for some time

before the hammer completes the circuit again. It is a phys-

ical impossibility for a mechanical vibrator to have the same

period of oscillation as that of an electrical circuit of this

nature, therefore a series of reversals of magnetic lines takes

place in the coil and several sparks pass between the terminals

of the secondary coil during one break and make of the primary

circuit.

It might also happen that when the current dies down

in the act of charging the condenser, for the first time, the

hammer is released. But before it goes a reasonable distance

in the space between the attracted position of the hammer and

the contact screw, the reversed current from the condenser

magnetises the iron core in the coil. This magnetised iron

ZQ

iron core, though of reversed polarity, reattracts the hammer

to a certain extent and dampens or hinders its oscillation

and keeps it longer in the space . The reversed current dying

down charges the condenser and the hammer is released again

and so on.

This process continually repeated keeps the hammer

in space while sparks pass between the terminals of the sec-

ondary coil, until the strength of the current becomes so

small that it cannot hold the hammer any longer in space.

Then the hammer recompletes the primary circuit and some more

current flows through it, at the same time short-circuiting

the condenser. This phenomenon is possible because the

frequency of this oscillation is so great. Thus what happens

is almost equivalent to holding the hammer in space . This

is not noticeable when the frequency is great. But by in-

creasing the capacity, the frequency becomes smaller and it

is noticed that the hammer becomes sluggish. The action,

explained above, causes it as is evident from the discussion.

The most interesting feature of this phenomenon is

that the primary coil takes a fresh charge of energy only when

the oscillation cannot continue while working in unison with

the other mechanical factors involved in the operation.

The term .1762 x 1CT 6 £"*615 x Cos (138000 t)

of equation 31 represents the amount of the condenser charge

which causes the oscillation and = .000046 second138000

is its period. It is also interesting to note that the period- StSt -4>5t

being .000046 of a second, the exponential terms £ £

Z9

decrease very slowly and therefore the oscillations practical-

ly retain their initial strength for a large number of re-

versals of magnetic lines.

All this is true when ideal conditions are obtain-

able, but such conditions do not exist in practice. The break

of the primary current is always accompanied by a spark even

when a condenser is connected across the "break points".L i*

Thus a part of the energy --— is lost. The oscillation

therefore starts with a smaller value of q and i and dies

down faster than the theoretical curves.

Almost all ignition coils, which are seen in the

market today, are different modifications of the induction

coil. In the ignition of the explosive mixtures of gas engines,

the battery circuit is connected to a mechanical device mount-

ed on the engine support. Pig. 8 -shows the simplest arrange-

ment of such a device. In the commercial types a large variety

Fig. 8

30

of arrangements is found, and the connections are made in

many ways. The switch S could be thrown either on the battery

B or magneto M for the electrical current. The contact-maker

K fixed on the shaft revolves and makes the electrical cir-

cuit complete once every revolution at the point L. This

making of the circuit sends a current thru the primary coil,

and the action previously described takes place in the coil

and a series of sparks passes in the spark plug and ignites

the compressed gas. Since the oscillation in an average coil

is very fast, even a very small contact point at L permits a

large number of electrical oscillations to take place and a

large number of reversals of magnetic lines occur causing a

series of sparks to pass between the points of the spark plug.

If the contact-point L is large and the contact

maker continues to be in a position to send current through

the primary coil' a'fter the gas is exploded, the sparks continue

to pass in the spark plug and an unnecessary waste of energy

occurs

.

To sum up the different points regarding the con-

denser, we find that it minimises the contact spark at the break

of the primary circuit, it sets up the electrical oscillation

and causes a reversed current to flow in the primary circuit

thus doubling the change in the magnetic field consequently

inducing a double electro-motive force in the secondary coil.

It also controlls the period of the hammer by retracting it

by sending a reversed current. This controlling of the

hammer allows more time for the oscillations to continue and

•3V

to permit sparks to pass "between the terminals of the second-

ary ooil.

3Z

References Quoted.

X. Sullivan's American Jornal of Science July 1832

2. Comptes Rendus Volume XXXVI p. 418

3, Alternating Current Transformer Fleming.

Bibliography

1. Internal Combustion Engines H. E. Wimperis

2. Electric Ignition for Gas Engine J. A. Uewman

3. Induction Coil — action of condenser in Rhunkorff's

Coil Electrician, London, November 11, 1910

4. Secondary current of the induction coil,-- oscillograph

by Clyde Snook — Journal Franklin Institute, Oct. 1907

5. Induction Coils — B. F. Bailey — Electrical World

April 14 and 21, 1910

6. The Design of Induction Coils — W. M. 0. Eddy —Electrical World — Deo. 26, 1906; Jan. 5, Feb. 2, 1907

7. Induction Coil in Practical Work — Lewis Wright

8. The Design and Operation of Spark Coils F. W. Springer

Electrical World, December 14, 1907

9. Heating Effect of the Electric Spark — H, A. Perkins

Electrioal World, March 24, 1906

10. The Science of Jump Spark Coil — J. a. Williams — Gas

Engine, July 1909

11. Electric Ignition Jones

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