ELECTROMAGNETIC RADIATION

FROM AUTOMOTIVE
IGNITION CIRCUITS

Thesis for the Degree of MSEE
MICHIGAN STATE UNIVERSITY
THOMAS LEE SCHALLHORN .

I976

 

.
'NQ'VI";PPQ\- .9".-
UJ' 9‘ has E‘Ly -‘

 

 

 

ABSTRACT

ELECTROMAGNETIC RADIATION FROM
AUTOMOTIVE IGNITION CIRCUITS
By

Thomas Lee Schallhorn

Radio frequency interference (RFI) has been studied nearly (75) years,
as documented by a review of the literature. This thesis addresses a
specific RFI problem: modeling the automotive ignition circuit to predict
the radiated electric field.

The selected ignition circuit model uses lumped elements for the re-
sistance, capacitance, and inductance in the secondary of the ignition
circuit. The spark plug and distributor gaps are shown as capacitances
which are shunted when the gaps break down, and the coil is represented
by its effective capacitance.

Analysis begins with an initially charged circuit, and predicts the
current and voltage waveforms as a function of time for a single spark
plug firing. Examples of the theoretical waveforms obtained from computer
solutions are shown to be in general agreement with observed behavior.

The transform of the theoretical ignition circuit current was ob-
tained to show frequency information. While these equations are somewhat
complicated, it is demonstrated that the separation, Af, between recurring

maxima observed in frequency domain is

Af * -—— (4.43b)

H

Thomas Lee Schallhorn

where fl is the time in seconds between the distributor and spark plug
gap breakdowns, and AI is the separation between maxima in Hertz.

General agreement between the theoretical amplitude density of the
transform of the ignition circuit current and the observed current den-
sity is also demonstrated using computer solutions.

Using the theoretical current amplitude density in a circular loop
antenna model, the electric field is predicted. The field strength is
shown to be significantly reduced in frequency domain by the additiOn of
resistance to the circuit, and examples demonstrate reasonable agreement
with known behavior.

Finally, the maximum field strength is predicted as a function of

time. The peak value of the electric field is given simply as

n ono r
for ‘tz- (5.25)
r c
where n = characteristic impedance of free space (=120fl ohms)
wo = cutoff frequency of current in frequency domain, radians/
second
Io = low-frequency amplitude of current in frequency domain,

amperes per radian/second
r = distance from the antenna in meters

c = speed of light in free space (=3 x 108 meters/second)

ELECTROMAGNETIC RADIATION FROM

AUTOMOTIVE IGNITION CIRCUITS

By

Thomas Lee Schallhorn

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Electrical Engineering and Systems Science

1976

ACKNOWLEDGMENTS

I am especially grateful to Dr. K. M. Chen, Professor of Electrical
Engineering at Michigan State University, for his guidance and patient
assistance in the preparation of this thesis.

I am indebted to my wife, Lynn, for her understanding and support,

and also thank Cindy Beard for her careful typing of the final manuscript.

ii

TABLE OF CONTENTS

Chapter Page
I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . 1
Background . . . . . . . . . . . . . . . . . . . . . . 1
Statement of Problem . . . . . . . . . . . . . . . . . . 2
General Procedure. . . . . . . . . . . . . . . . . . . . 2
II. REVIEW OF LITERATURE. . . . . . . . . . . . . . . . . . . . 3
Ignition Circuit Operation . . . . . . . 3
Typical Ignition Circuit Values. . . . . . . . . . . . . 6
Electric Field Measurements. . . . . . . . . . . . . . . 9
RFI Measurement Standards. . . . . . . . . . . . . . . 11
Some Early Ignition Circuit Models . . . . . . . . . . . 14
Transmission line approach. . . . . . . . . . . . . . 14
Treatment of RFI as an impulse. . . . . . . . . . . . 16
Lumped element approach . . . . . . . . . . . . . . . 17
Recently Published Research. . . . . . . . . . . . . . . 19

State variable model of ignition
system. . . . . . . . . . . . . . . . . . . . . . . 19

Experimentation with new suppression

techniques. . . . . . . . . . . . . . . . . . . . . 19

Alternative characterizations of
ignition noise. . . . . . . . . . . . . . . . . . . 20
RF current distribution on car bodies . . . . . . . . 22

III. SPARK PLUG CURRENT AS A FUNCTION OF TIME. . . . . . . . . . 23

Ignition Circuit Model . . . . . . . . . . . . . . . . . 23

Circuit Equations Before Spark Plug Fires. . . . . . . . 25

Circuit Equations After Spark Plug Fires . . . . . . . . 31
Numerical Examples . . . . . . . . . . . . . . . . . . . 34

Results using Newell's values . . . . . . . . . . . . 34

Effect of changing R. . . . . . . . . . . . . . . . . 35

Effect of changing E2 . . . . . . . . . . . . . 37

Effect of cnanglng Cdg and E1 . . . . . . . . . . . . 37

IV. FREQUENCY SPECTRUM OF SPARK PLUG CURRENT. . . . . . . . . . 40
Derivation of Amplitude Density Equations. . . . . . . . 40

Amplitude Density-Spark Plug Gap Only . . . . . . . . 41
Amplitude Density-Distributor and Spark

Plug Gaps . . . . . . . . . . . . . . . . . . . . . 42
Check of Equations. . . . . . . . . . . . 49
Significance of Time Between Gap Breakdowns . . . . . 51

iii

Chapter

V.

VI.

Numerical

Results of using Newell

Effect
Effect

Effect

ELECTRIC FIELD FROM CIRCULAR LOOP ANTENNA MODEL .

Predicted Field Strength in Frequency Domain .
Numerical Examples - Frequency Domain.
Results using Newell's values .

Effect
Effect

Effect

Predicted
Method
Method

Numerical

Examples . . . .

of changing R. . . . .
of changing E2 . .
of changing Cdg and E1

of changing R. . . . .
of changing E2 . . .
of changing Cdg and E1

Field Strength in Time Domain.

#1 . . . . . . . . .
#2 . . . . . . . .

Examples — Time Domain .

Discussion and Recommendations .

CONCLUSIONS

LIST OF REFERENCES.

APPENDICES

NUOW>

Program IGNITI. .
Program IGNITII . .
Program ADP . . . .
Program EMAX
Program ENTBES. .

iv

'8 values.

Page

55
55
55
57
57
58

58
61
61
63
63

n

J

65
66
68
7O
71

7/;

76

79
81
84
88
9O

LIST OF TABLES

Table Page
1 Nominal Ignition Circuit Values. . . . . . . . . . . . . . 7
2 Significant Features of Two RFI
Measurement Standards . . . . . . . . . . . . . . . . . 12

LIST OF FIGURES

Figure Page
1 Typical Ignition System . . . . . . . . . . . . . . . . . 4
2 Typical Voltage Patterns During

One Spark Plug Firing. . . . . . . . . . . . . . . . . 8
3 Published Mea8urements of Electric

Field Strength . . . . . . . . . . . . . . . . . . . . 10
4 Comparison of Measurements with

SAE J551a Limits . . . . . . . . . . . . . . . . . . . 15
5 Newell's Current and Electric

Field Spectra. . . - . . . . . . . . . . . . . . . . . 18
6 Results of Recent Studies of Spark

Plug Current and RFI . . . . . . . . . . . . . . . . . 21
7 Proposed Ignition Circuit Model . . . . . . . . . . . . . 24
8 Theoretical Waveforms Using Newell's

Values . . . . . . . . . . . . . . . . . . . . . . . . 35
9 Theoretical Current Waveforms . . . . . . . . . . . . . . 36
10 Theoretical Waveforms for Constant Initial

Distributor Cap Charge . . . . . . . . . . . . . . . . 39
11 Theoretical Amplitude Densities of

Ignition Circuit Current . . . . . . . . . . . . . . . 53
12 Theoretical Amplitude Densities of

Ignition Circuit Current . . . . . . . . . . . . . . . 56
13 Coordinate System for Circular Loop

Antenna. . . . . . . . . . . . . . . . . . . . . . . . 6O
14 Theoretical Field Strength Limit in

Frequency Domain . . . . . . . . . . . . . . . . . . . 62
15 Theoretical Field Strength Limit in

Frequency Domain . . . . . . . . . . . . . . . . . . . 64

vi

Figure Page

16 Theoretical Field Strength Limit in

'Iime Iknnain. . . . . . . . . . . ... . . . . . . . . . 71
17 Theoretical Phase Angle of Transform

of Current Using Newell's Values . . . . . . . . . . . 73

vii

CHAPTER I

INTRODUCTION

Background

 

In 1902, observers detected radio frequency interference (RFI)
originating from automotive ignition systems [1], By 1930, when auto-
mobile manufacturers first installed radios at the factory, the search
was on for an effective means of RFI suppression [2].

Now, the widespread increases in television and FM services, and
the more recent popularity of Land Base Mobile Communication systems,
demand more effective management of the radio frequency spectrum [2,3].

Research in the problem of interference has been concentrated in
two complementary areas: 1) quantification of RFI and its effects, and
2) development of a theoretical model consistent with observations.

Experimentation has resulted in the inclusion of resistance spark
plugs, a widened distributor gap, and distributed resistance spark plug
wires on most American automobiles to reduce RFI [4]. Other ignition
circuit modifications have shown promising results in recent tests [5].

In developing models, researchers had to decide whether or not a
lumped element model could validly be assumed. Some writers in the sub-
ject area favored the lumped element treatment, and they manipulated
their circuit formulations to obtain favorable results [6, 7, 8].

Other authors attempted uniform transmission line models to achieve

greater accuracy [9. 10]. However, as recently as 1969, solutions for

current in the ignition circuit required so much computation that these
models are generally not employed in analysis.

While the lumped element model lends itself to an analytical solu-
tion, the state of the art models employ simplifying assumptions which
in some cases are not strictly correct. In particular, one model which
yielded favorable results assumed complete independence of the effects
of the distributor and spark plug gap breakdowns. Since these gaps
break down sequentially, the model can be improved by including this

fact.

Statement of Problem

 

The problem is to develop a lumped element ignition circuit model
which includes the sequential nature of the distributor and spark plug

gap breakdowns.

General Procedure

 

Solution of this problem required several steps. First, available
research on RFI reduction and ignition circuit modeling was studied.
This included a review of the characteristics of typical ignition cir-
cuits.

Second, the desired modification was incorporated into a lumped
element ignition circuit model, and the circuit equations were written
and solved using LaPlace transform techniques.

In the next step, the amplitude density of the LaPlace transform of
the spark plug current was obtained and compared with published results.

Finally, using a circular loop antenna model, limits on the magni—

tude of the electric field strength were predicted.

CHAPTER II

REVIEW OF LITERATURE

This chapter summarizes past approaches to the problem of managing
radio frequency interference (RFI) from automotive ignition circuits.

First, ignition circuit operation is described, and typical compo—
nent values and circuit measurements are presented. Next, published re-
sults of electric field strength measurements are given, followed by a
review of the development of RFI measurement standards.

Some early attempts at modeling the ignition circuit are discussed,

and a condensation of recently published research concludes the chapter.

Ignition Circuit Operation

 

The ignition circuit serves a dual purpose: first, it provides a
spark with sufficient potential to ignite the gases in the combustion
chamber, and second, it provides that spark at the proper instant. A
step—up transformer (commonly called the coil) develops the required vol-
tage; meanwhile, the opening and closing of a contact breaker times the
spark.

Figure 1 shows a typical battery-powered ignition system. The pri—
mary circuit consists of the battery, primary coil winding, and associ-
ated low voltage devices and wiring, while the secondary coil winding,
rotor, spark plugs, and high voltage wiring comprise the secondary cir-

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Mechanically, the crankshaft simultaneously rotates the rotor and
the contact breaker cam, so the electrical activity in the primary
occurs at the proper time to fire the desired spark plug.

The spark plug firing sequence is as follows:

1. To start the engine, the start position of the ignition switch
bypasses the ballast resistor, RBR’ and compensates for reduced battery
voltage during starting. With the engine running, inclusion of the bal—
last resistor limits the maximum current, and keeps the current constant
for varying engine speeds when the contact breaker opens [11].

2. With the contact breaker closed, the battery voltage and the
ballast resistance determine the steady state value which the primary
current approaches.

3. As the rotor aligns with a spark plug terminal, the contact
breaker opens. This abruptly interrupts the steady state current, caus-
ing a voltage to appear on the coil. The condenser, shown as CCON in
Figure l, reduCes the effects of bounce in the operation of the contact
breaker. Also, the condenser assures an adequately rapid change in cur-
rent necessary to attain the desired voltages.

4. With the opening of the contact breaker, the coil secondary
voltage rises until the breakdown potential across the distributor gap
is reached.

5. For normal operation, the flux in the coil continues to collapse
after the distributor gap breakdown; thus, the secondary potential still
rises until the spark plug voltage is sufficient to fire the spark plug.

6. As the gases in the cylinder ionize, the potential required for

conduction in the gap drops to about half of the breakdown potential.

7. With the contact breaker still open, the coil voltage drops
until the voltages at the gaps become insufficient to maintain conduc-
tion. The energy in the secondary then dissipates through resistance in
the circuit.

8. While the rotor advances, the contact breaker closes. The volt—
age induced by this closure attenuates before the contact breaker opens
again.

9. Steps 2 through 8 repeat for the next spark plug.

Typical Ignition Circuit Values

 

Similarities in the performance of different ignition circuit de-
signs allow the indication of typical values, as shown in Table 1.

First, the times associated with the spark plug firing cycle are of
interest. The camshaft,which operates the rotor and contact breaker,ro-
tates once for every two revolutions of the crankshaft. Since the rotor
passes each spark plug terminal once in each revolution, four spark plug
firings occur during each crankshaft revolution for an eight cylinder car.

Table 1 shows thecycle times associated with different engine speeds.
A dwell of 300 is used, where dwell refers to the length of time in de—
grees of camshaft rotation that the contact breaker is closed.

Next, Specification of the operating conditions of an ignition sys-
tem is desired. Based on a wide range of sources, the remainder of Table
1 gives nominal values for discrete components and for selected circuit
parameters.

A final area of interest is the time variation of the currents and
voltages in the ignition system. Figure 2 on page 8 shows some of the

more important waveforms documented in the literature.

 

Table 1. Nominal Ignition Circuit Values

Cycle Times for 8—cy1inder Engines

 

 

Time Between Time Contact Time Contact
Engine Speed Spark Plug Firings Breaker Open Breaker Closed
(RPM) (Seconds) (Seconds) (Seconds)
500 0.030 0.0100 0.0200
1,000 0.015 0.0050 0.0100
1,500 0.010 0.0033 0.0067
3,000 0.005 0.0017 0.0033

 

 

 

Primary Circuit Values

 

Condenser capacitance
Current
Ballast resistor

Contact breaker gap

.18 to .30 microfarads [12, 13]
4 amperes, maximum [14]
135 ohm—8 cyl, 180 ohm-6 cy1.[15]

0.019 inches [16]

Secondary Circuit Values

 

Distributor gap

Distributor gap breakdown

Spark plug gap

Spark plug gap breakdown
voltage

Time between distributor gap and
spark plug gap breakdowns

High voltage resistance cable

Total resistance added for
RFI suppression

Coil capacitance

0.031 inches (CM before 1969) [4]
0.094 inches (GM after 1969) [4]

3,000 volts (before 1969) [9]
10,000 volts (GM after 1969) [5]

0.030 to (L035 inches

3,000 to 25,000 volts (depending
on operating conditions)[9,14,17]

10 to 20 microseconds [5]

4,500 to 5,000 ohms/foot [3,5]

5,000 to 25,000 ohms [18, 19]

50 picofarads [9]

 

   

 

4,5
4 5
CONTACT BREAKER CLOSE S
6 7
8
2 3
I__ 3
CONTACT BREAKER OPENS
(a) Rectified Primary Coil (b) Spark Plug Voltage[21].

Voltage[20]

6 7 NOTE: Numbers in figures
correspond with description on
pages 5 and 6.
4,5

(c) Secondary Coil Voltage[22]

Figure 2 - Typical Voltage Patterns During One Spark Plug Firing

Figure 2(a) shows the primary coil voltage for one spark plug
firing cycle as it appears on a commercially available cathode ray tube
ignition analyzer, and Figure 2(b) and 2(c) show the secondary spark
plug and coil voltages, respectively.

The patterns in Figure 2 give only a general indication of the
actual circuit behavior. They indicate when in the cycle oscillations
can be expected, without accurately showing the frequency of oscilla—
tion. Similarly, the relative magnitudes only approximate the expected

behavior.

Electric Field Measurements

 

Without the benefit of modern receivers and computers, the obtain-
ing and processing of data on the electric field strength of RFI re-
quires a prodigious effort. As a result, the literature contains a
limited number of reports on these data.

The earliest published results come from two sources: the work of
R. W. George [23], and the results of B. G. Pressey and G. E. Ashwell
[24].

George, working in the late 1930's,nmde peak electric field
strength measurements between 40 and 450 MHz. He calibrated the output
from knowledge of the aerial and receiver, and he treated his results
statistically. These results are shown in Figures 3(a) and 3(b).

Pressey and Ashwell made measurements for a four—cylinder and a
six-cylinder Vauxhall. Their results for the six-cylinder, shown in
Figure 3(c), represent measurements taken thirty feet from the center of
the car on the distributor side. Measurements made at three other 10-

cations around the car indicated no definite radiation pattern.

 

10

 

 

500 500
If e
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:1 ”.>
“ 1
,5 100 ' 100
u L
°° E’s
5 50 C 50
L m
u u
u: u I
U)
'o
,_4 "U
.3 10 '3 10
LL: 'f"'
g.
5 V 5
10 100 500 10 100 500
Frequency, MHz Frequency, MHz
(a) George—Results for Horizon— (b) George — Results for Vertical
tal Polarization [23]. Polarization [23].
m m
'0“ 1.00 "C: 100
.c .5
4.: 9O u
210 E E” E 90
3; a;
33 3 80 c‘n’ 3 8O
2 E2 3 2
m o 70 a) o 40 100 200 600
°H J3 .H '5
m m h m

40

100

200

Frequency, MHz

 

600

Frequency, MHz

(c) Pressey and Ashwell - Results (d) Pressey and Ashwell - Results

for 4-cylinder Vauxhall [24]

NOTES:
1. Figure
2. Figure
3. Figure
4. Figure

3(a)
3(b)
3(c)

3(d)

bandwidth

bandwidth

bandwidth

bandwidth

is

is

is

is

for single cylinder [24]

10 kHz, distance is 100 feet.
10 kHz, distance is 100 feet.
2.5 MHz, distance is 30 feet.

2.5 MHz, distance is 60 feet.

Figure 3 - Published Measurements of Electric Field Strength

11

Pressey and Ashwell also investigated thenwasurable electric
field for a single cylinder magneto and sparking plug. Figure 3(d)
shows measurements made in the horizontal plane at a distance of sixty
feet.

More recently, F. Bauer published the results of electric field
measurements made in June, 1965, on twenty vehicles [3]. The field
strength was found to increase with the compression ratio and the number
of cylinders, but no correlation was found between interference and

engine displacement.

RFI Measurement Standards

 

The diverse methods of quantizing radio frequency interference re-
quire adoption of a standard. At present, the two most prominent stand—
ards are: 1) SAE J551b, a standard of the Society of Automotive
Engineers used primarily in the United States [25], and 2) CISPR Recom—
mendation 18/2, an international standard defined by the Comite Inter-
national Special des Perturbation Radioelectrique and which has been
adopted by several European countries [26]. Table 2 lists significant
features of these procedures.

Both standards observe the EM radiation in the frequency domain to
avoid the complications of frequency dependence and limited bandwidth
from devices which measure in time domain [27]. The Foufier transform

describes the frequency occupancy of a signal from the definition

F(s) = I f(t) e'St dt (2.1)

“'03

Approximating equation (2.1) by a finite series.

 

Table 2.

Antenna Distance
Antenna Height
Antenna Type

Measuring Instrument
Distance from Vehicle

Scan Between Check
Frequencies

Characteristic
Reading

Statistical Technique

Test Site

Units for Readings

Limits

12

Significant Features of Two RFI

CISPR 18/2 [26]

Measurement Standards

SAE J551b [25]

 

(1970) (1973)

33 Feet 33 Feet
10 Feet 10 Feet
Dipole Dipole or Broadband

3 meters beyond an-
tenna, opposite car

No

In site, 10 feet minimum to
left or right of antenna

Yes

Maximum reading from horizontal and vertical mea-
surements taken on both right and left side.

80% confidence, 80% of vehicles conform

Ellipse - 20 meters
by 17.3 meters

uV/m, 120 kHz band—
width

40-75 MHz = 50 uV/m
rising linearly to
120 uv/m at 250 MHz

For comparison with
SAE standard, con—
vert above limit to
dB, add 20 dB to
.get limit for peak
measurements, then
subtract 41.6 dB
from peak limit to
get dB above luV/
m/kHz bandwidth.
Result is: 40-75
MHz = 12.4 dB ris—
ing linearly to
20.0 dB at 250 MHz.

100 foot radius

dB above luV/m per kHz
bandwidth

Curve passing through

20-75 MHz 12dB

100 MHz l4dB

150 MHz 16dB

200 MHz 18dB

250 MHz 20dB

300 MHz ZldB

350 MHz 22dB
400-1,000 MHZ 23dB

Subtract 20 dB for quasi-
peak

l3

[t1+ n(/\t)]

F(s) x 11m >: ml + n(/\t)]e—S (At) (2.2)

Alt->0

where At length of snbinterval of time used in obtaining

product for Summation

n(At) = length of time signal is observed
t1 = time when observation begins
8 = complex frequency

For physical measurements,tfluebandwidth is roughly inversely pro—

portional to the shortest detectable length of time, At. Thus,

-S[t + (in
1 BW (2.3)

n
E “‘1 + (fine
In making RFI measurements, the receiver samples the signal for a
time, n(At), while scanning a range of values of frequency, 5. The out-
put voltage represents the amplitude of the Fourier transform of the in—
put signal multiplied by the bandwidth.
Comparison of the receiver output with the SAE J551b standard uses

the relationship contained in that standard:

F = 20 log10 (R x H xB) (2.4)

where F field intensity in dB above 1 UV/m/kHz bandwidth

R = instrument reading in 0V
H = antenna and transmission line factor. This factor re—
lates a receiver's output in 0V to the field intensity

iII uVYnI at the antenna, and accounts for line losses.

B = bandwidth factor, 1 kHz/bandwidth of measuring set in
kHz.

14

The utility of the limits defined in the standards depends in part
on (lulettairudiilily ol Lluuu‘ limits;. Seleettul resIHtx: from In“) re—
searchers show that the limits are, indeed, reasonable.

In comparing the test results of RFI from single vehicles versus a
matrix of (21) vehicles, Doty [2] plotted the greatest upper bound from
these tests against the SAE standard (see Figure 4(a) and 4(b). The
results justify the SAE procedure of using the maximum of the vertically
and horizontally polarized readings, since neither polarization dominates
over the frequency range of the specification.

Bauer's results [3] also show the attainability of the SAE standard.
As shown in Figure 4(c), the substitution of resistance high voltage
cable for steel secondary ignition cable suppressed the RFI to within

the SAE limit.

Some Early Ignition Circuit Models

 

The task of modeling the interference from ignition systems attrac-
ted the interest of several researchers in the 1940's and 1950's. Sum—
maries of three unique approaches follow:

Transmission line approach. NethercOt [9] modeled the ignition

 

system as a uniform transmission line terminated by the spark plug at
one end and the secondary of the coil at the other.

Ignoring the distributor gap, Nethercot postulated that the break—
down of the spark plug gap initiates a traveling current pulse which is
repeatedly reflected at the coil and at the spark plug. Using the re-
flection coefficient for a uniform line terminated by a capacitor, he
predicted the current in the spark plug gap.

The addition of resistance for RFI suppression had been experimen-

tally established by the time of his article. To demonstrate agreement

Field Intensity dB, uV/m/MHz

(a)

15

   

N

E

\

E

\

>.

5E 1' 1

% 70 Vertica

.5 Jr

60

5 I

U

'5 50 orizont l
102 103 a 102 IO3

~H

e.

Frequency,MHz Frequency,MHz
Upper bounds of RFI from (b) Upper bounds of RFI from
single vehicles [2]. 21—vehicle matrices [2].

Steel Wire
+30
>.
U
gig. +20 L
Q) \
‘5 E +10 SAE
H :>
'u 1
_] . 0
m m
IZ'U _10 Resistance
Cable

 

-20
30 130 230 .330 430
FrequencyIMHz

(c) Suppression from changing igniticn wires [3].

Figure 4 - Comparison of Measurements with the SAE 3551a Limits

16

between this fact and his theory, Nethercot made two observations:
1) a resistor inserted by the spark plug reduces the initial magnitude
of fine current pulse and 2) a resistor placed near the coil alters the
reflection coefficient to reduce the radiation intensity.

Nethercot did not make any quantitative estimates of the radiated
fielci strength in his theory.

Treatment of RFI as an impulse. Eaglesfield [6] viewed the radiated

 

interference as a very short pulse which excites the impulse response of
a receiver. Replacing the Spark plug by a switch, he predicted the mag-
nitinie of the current surge due to the spark plug firing.

Then, viewing the cables as a magnetic dipole loop antenna, Eagles-
fielxi used equations for sinusoidally varying sources to deduce the mag-
nitude of the electric field pulse. Multiplying this expression by the
receiver bandwidth, Eaglesfield predicted an equivalent electric field
strength for comparison with experimental measurements as

u AVB

equivalent electric f1eld = ZE—EEE-mlcrovolts/meter (2.5)

where p permeability of free space (= 4W x 10—7 henry/meter)

c = velocity of light in free space (= 3 x 108 meters/second)

A = area of magnetic dipole loop, m2

V = breakdown voltage of spark plug, volts

L = inductance of ignition leads, henries

R = distance from magnetic dipole loop, m

B = receiver bandwidth, Hz

In a Subsequent article [7], Eaglesfield extended his treatment to
allow an arbitrary impedance in the ignition cables, and he defined a

Suppression ratio to describe its effect.

17

Finally, Eaglesfield considered the effects of a uniform line. He
concluded that the use of lumped elements is reasonable, and he demon—
strated agreement of this theory with published results.

Lumped element approach. Newell [3] Suggested modeling the ignition

 

secondary as an RLC circuit with switches replacing the distributor and
spark plug gaps. Assuming that the spark plug current flows uniformly
through the secondary, he used simple circuit theory to solve for the
current after the gap breakdowns.

From the known solution of a step voltage applied to a series RLC

circuit, Newell assumed the ignition current to be of the form:

.__ E —at .
1 - EE—e Sin(gt) (2.6)
where 2 =-34 a = 11- and = v 2 - a2

“’0 LC ’ 2L ’ 3 mo

He then claimed that the peak amplitude of the current measured by

a receiver would be

 

2EB '
I(peak) = (2.7)
L »/(w2 - w02)2 + 4w2az

where B ' receiver bandwidth

Next, Newell assumed that, for a narrow band receiver, the peak cur-
rent would be the sum of the amplitude contributions from each gap break-
down.

To test his theory, Newell constructed a dummy engine block with
variable air pressure in the cylinders. Combustible mixtures were not
used, and a comparison of the theoretical and measured results is Shown

in Figure 5(a).

18

 

o
u C
m --—-==Theoret1cal
>
-H ———-==Measured
Ltm
m'o
.I—l
m a
s-a
m N
'03-‘-
21.54
H\
-a
a?
043
EH

1 10 100
Frequency, MHz

(a) Current spectrum for distributor and
plugs at atmospheric pressure [8].

75 lbs/in2 I

Atmospheric Pressure

Amplitude relative to
1 OuV/m/kHz 1n dB

 

1 10 100
Frequency, MHz

(b) Theoretical radiated field strength [8].

Values for Theoretical Results:

B (Each Gap) = 2,500 volts L = 1.4 x 10-6 Henries

R = 90 ohms (selected to provide best fit)

C when distributor gap breaks down = 7.35 x 10—-12 Farads
C when spark plug gap breaks down = 40.0 x 10-12 Farads

A = 0.037 m2 D= 30.48 m

Figure 5 - Newell's Current and Electric Field Spectra

19

Finally, Newell regarded the ignition system as a loop antenna
carrying a uniform current, where the field strength due to a single

Spectral component(fl’angu1ar frequency, w, is:

n A I w2

4TIc2 D

E = (2.8)

II

where E field strength, volts/meter
n = intrinsic impedance of free space (120w ohms)
A = area of loop, m

D = distance from loop, m

I = amplitude of spectral component

Substituting his expression for the peak amplitude of the current in
equation (2.8), Newell obtained an expression for the peak field strength
for a receiver. Figure 5(b) shows his theoretical result when the cylin—
der pressure is atmospheric (spark plug breakdown voltage = 2,500 volts),
and when the cylinder pressure is 75 lb/in2 gauge (Spark plug breakdown

voltage = 9,000 volts).

Recently Published Research

 

I
Continued crowding of the radio spectrum has maintained interest in

RFI from automobiles. Some recent investigations are summarized below:

State variable model of ignition system. McLaughlin [10] developed

 

the state equations for a uniform transmission line model of the ignition
system. However, excessive computations were required to solve these
equations for the time interval between point opening and Spark plug gap
breakdown, and no results were given.

Experimentation with new suppression techniques. In 1969, General

 

Motors began installing its Radio Frequency Interference Suppression,

20

(RFIS), package on automobiles to meet the limits of the SAE standard.
The package involved three modifications [4]: 1) the use of distributed
resistance ignition cables, 2) an increase of the distributor gap from
0.031 inches to 0.094 inches, and 3) the use of specially designed re-
sistor type spark plugs.

Hsu and Schlick. [28]nmde measurements on a simulated ignition sys-
tem with a variable distributor gap, and observed the form of the spark
plug current to be similiar to that shown in Figure 6(a). From the
Fourier transform of the current equation, they demonstrated reduced
interference for increases in the distributor gap (which appear as de—
creases in the time, T1).

Burgett et. al. [19] investigated the effects of different spark
[plug designs on RFI, and measured the interference for different spark
plug gaps as shown in Figure 6(b). Noting the influence of the gap on
the interference spectrum, they recommended further Study without draw—
ing a specific conclusion on their data.

At Stanford Research Institute, Shepherd et. al.'[5] demonstrated
significant Suppression improvement of two different vehicles already
equipped with the General Motors RFIS package. Their technique involved
low-pass filtering to restrict the radiation associated with the gap’
breakdowns and contact breaker operation.

Alternative characterizations of ignition noise. Alternative methods

 

of representation are continually being sought to accurately depict igni-

tion noise. Research at General Motors has concentrated on pulse height
. . . 1 . . . . . .

distributions which, for identically equ1pped vehicles, were approxi~

mately found to be Weibull distributions [29].

 

PHDs plot the number of detected pulses against their peak amplitude.

dB above 1.0 microvolt per

i(t)
(8)
+40
+30

1: +20
1.)
'U
'9
Ti +10
CO
.0
N
:I.‘
.y.
H
(1)
CL
H
(D
‘63 —30
e

 

21

—t/T3

-t/T
B +_0Ce

% %
Time

Hsu's approximation of spark plug current waveform [28].

 

SAE LIMIT

 

 

«0.035 in.

, gap
. {—0.060 in.

88?
{-0.080 in.

gap

 

,1IIIII++II#
20 30 40 60 80 100 200 250 4I00 600 800 1000

(b)

Frequency, MHz

Interference for different spark plug gaps [19].

Figure 6 -Results Cd recent studies of spark plug current and RFI.

Shepherd [30] investigated amplitude probability distributions,
(APDS), and found these distributions to be part Rayleigh and part
Weibull.

RF current distribution on car bodies. Minozuma [31] observed
several aspects of automobile radio noise, including a unique study:
the measurement of radio frequency currents on the surface of a car.

Using a sliding current probe, Minozuma made measurements along
a vertical line just behind both front doors of a small van, and at
constant heights around the body. He observed resonance patterns
in the horizontal directions, and a 3/4 wave-length antenna current
distribution in the vertical direction at 220 MHz for the unsuppres-
sed vehicle. With the application of suppression techniques, some
resonance was Still observed, but the amplitude of the current was

noticeably reduced away from the neighborhood of the engine.

 

CHAPTER III l

SPARK PLUG CURRENT AS A FUNCTION OF TIME

This chapter presents a model for predicting current and voltage

waveforms in an ignition circuit. First, the assumptions are stated.

 

Next, solutions of the circuit equations are obtained for two time
periods: between the distributor and Spark plug gap breakdowns, and
after the spark plug gap breakdown.

Finally, numerical examples compare the theory with published re—

sults.

Ignition Circuit Model

 

A circuit model provides a simplified means for understanding an
observed physical event and for anticipating future behavior. In doing
this, a model should be analyzable, and it should accurately portray
the modeled event.

Using distributed elements and transmission line theory undoubtedly
results in an accurate model of the ignition system. However, as shown
in the previous chapter, the complexity of such a model generally pre-
cludes a researcher from performing a complete analysis. The objective
of the following research, then, is to enhance the accuracy of a state
of the art, lumped element ignition circuit model.

Figure 7 shows the proposed model based on the following assumptions:

1. Whether the system employs a conventional contact breaker or an

electronic switch, the purpose of the primary circuit is the same: to

23

24

interrupt the primary current and cause the coil secondary voltage to
rise. Therefore, details of the primary circuit are not given.

2. As shown in Figure 2 on page 8, the secondary circuit reaches a
steady state just prior to the opening of the contact breaker. With
negligible current in the secondary, the voltage builds rapidly at the
coil, and the distributor gap immediately breaks down. These events are
represented by an instantaneous charging of a coil capacitance, CC,
while the secondary current is zero immediately before the distributor
gap breaks down.

3. The high voltage secondary ignition cables are assumed to be
resistive and inductive only. The components R1 and L1 represent the
coil-to—distributor cable, while R2 and L2 represent a spark plug cable.

4. When not broken down, the distributor and Spark plug gaps are
essentially capacitive, as shown by Cdg and ng, respectively.

5. The gaps are assumed to be either open circuits or short cir-

cuits, with zero transition time from one state to the other.

 

 

+ DISTRIBUTOR GAP

 

 

lL_

II
C)

(A SPARK
C 7‘: v PLUG v

C —-——- sg sg

 

 

 

 

Figure 7 - Proposed Ignition Circuit Model

25

Eijtyit Equations Before EBQIEUPI”B Fires

 

Analysis of the ignition circuit model Shown in Figure 7 entails
the solution of differential equations for the time variation of all
pertinent voltages and current. First, the solution for the voltage,

v is sought following breakdown of the distributor gap, but before the

c9
spark plug gap breaks down.

Using Kirchoff's voltage law,

91.01

1 dt gilEl- + v (t) (3.1)

vC(t) = R11(t) + L 2 dt 88

+ vdg(t) + R21(t) + L

At any given time, the current through the capacitors is given by:

de(t) dvsg(t)

“”hcc—a‘r‘ =+ng—_dt

 

(3.2)

where the change in Sign results from the requirement of conservation of
charge.

Also, equation (3.2) may be differentiated, since the voltages are
continuous; that is, the voltages across the capacitors do not change
instantaneously due to finite current inputs [32]. Then, equation (3.1)

becomes (uSIng R = R1 + R2 and L = Ll + L2):

de(t) dva(t)
vc(t) = — R C -——-——' - L C —-———- + vdg(t) + ng(t) (3.3)

c dt c dt2

Also, integrating equation (3.2),

t de(t) CS dvsg(t)
] dt dt = ' CC [ dt dc (3'4)

0

 

26

from which

VC(t) - vC(O) = -

CLO
O U:

[ng(t) — vsg(0fl (3.5)

The initial conditions required in equation (3.5) come from evalu-
ating equation (3.1) at t=0. By assuming that the current in the igni—
tion circuit has attenuated to zero just before the distributor gap
breaks down, and further, if the time rate of change of the current is
assumed to be zero at t=0, then equation (3.1) becomes:

vC(0) = Vdg(0) + vsg(0) (3-6)

Totally discharged capacitors which charge at the same rate build

their voltages inversely to the ratio of their capacitances, so

_...._...___ = jg (3.7)

The distributor gap is assumed to break down instantaneously once

it has an arbitrary voltage, E1, across it, so

vdg(0) = E1 (3.8)

Substituting equations (3.7) and 3.8) into equation (3.6),

Cd
5g

VC(O) = El

 

27

Substituting equations (3.7, (3.8), and (3.9) into equation (3.5)

and solving for the Spark plug voltage,

 

 

 

CC Cc ng + Cc Cdg + CSngB_
ng(t) = - C vC(t) - El C C (3.10)
sg C 58
Finally, defining
1 — 1 1 1 — Cc ng + CC Cdg + ng ng
.__ _ __ + _‘_ + —— .. A (3.11)
c C C C C C C
X c dg SE C dg sg

and combining equations (3.3), (3.10), and (3.11),

CC de(t) dva(t)
l +-ET- vC(t) = - R CC —~—-——' - L C -——§*—- + vd (t) +
sg dt C dt g
E1 Cc Cd
8 (3.12)
C C
sg X

The differential equation given above may be solved by either of

two methods: 1) the homogeneous/particular method of solution, or 2)

the LaPlace transform method. Both methods were used to insure accurate

results, but only the LaPlace transform solution follows.
Using the definition of the one—sided LaPlace transform to trans-

form each term in equation (3.12), the first term is:

28

+
co 0 00
—st ~st —st
v t = v t e dt = v t e dt + v (t)e dt
gldgfl [Odgm [_dg<> [+dg
0 0

(3.13)

. + .
In the interval [0 < t < 00], v (t) equals zero from the assumption

dg
that the distributor gap remains broken down for positive time.

For the interval [0- < t < 0+], vdg(t) is well-behaved, changing
value from E1 to zero. In the limit that the distributor gap voltage
changes instantaneously (as has been assumed), the LaPlace transform of
vdg(t) becomes identically zero.

The LaPlace transform of the constant term is obtained from the

definition as:

E C C m E C C E C C
3 C1 2:: dg = [ ‘1: chg e-st dt = (i) 1 chg (3.14)
sg x 0 sg x sg x

Transformation of the remaining terms in equation (3.12), combined

with the preceding results, gives the equation

C

c _ _ _ _ 2 _
1 + C—— VC(s)— RC [SV§S) vC(0)] LCC s Vc(s) s vc(0)

58
dv (O)

c l C C
- ——aE——' + E. El C dg (3.15)
C C
sg x

Using equation (3.9) and its derivative for the initial conditions

and rearranging, equation (3.15) becomes

29

Cd Cd E C Cd
1+——£- 1+—4g 1—9—8
R C E C + sLC E. C + —~ C C
_ c l sg c l

Vc(s) - 2 C

(3.16)
3 LC +sRC +(1+—C-—
c C

C
38

Equation (3.16) may be written as the partial fraction expansion:

 

 

 

 

 

 

K1 Kn K3
V (s) = ——- + ———é~—- + —————- (3.17a)
C S S " S S " S ,
l 2
where
_ B _ _£+_ i.
x (L) (..)(+ C ) (3.17.)
c sg
s =-5—+1/2/i (317C) 3 =_B__16,/§ (317d)
1 2L ' 2 . 2L '
E C C
l c dg
K1 - C (C + C ) (3.17e)
x sg
R 2 R l
(81 + L) E1 Cdg [:81 + 81(L)+ LCX—J
K2 = ( - s ) + E1 C 3 s (s - s ) (3°17f)
S1 2 sg 1 l 2
2 R l
(52 + %) El dg [:2 + 82(1) + LCX]
3 (s2 - 81) 1 ng 32(52 81)

Equation (3.17a) Shows Simple poles at s = 0, s = 81’ and s = $2.
The inverse transform is then easily calculated using the residue

theorem [33h

vC(t) =

"MUD

{Residue of [VC(S)eSt] at the ith simple pole} (3.18)
i 1

30

where the residue of a function at the isolated singular point, 80’ is

given by

RCSldue (s = so) = lim [(3 — s0)VC(s)] (3.19)

s+s
0

After some simplification and rearrangement, the solution for the

coil voltage is:

 

E C C E C s t s t
unwise. . +~1——(§—)(a—%s—) (.1 -.2)
x c sg ZMR sg c
El CS ( slt szt)
+ —2- ——_‘g——C +C e +e (3.20)
sg c

The current in the secondary of the ignition circuit is obtained
using equation (3.2). Performing the indicated differentiation and Sim—

plifying,

' "‘ t l/ -1/ R 2 A C
i(t) = i 8 2L (82!)? t _ e 2&- t) for (__) > __ <1 + ES.— (3.21)
LI)? 8g

When the radical term is imaginary, equation (3.21) may be rewritten

 

 

as:
‘ 12L t
2E e 2 C
R 4
i(t) = 1 sin [>27le t] for (L>< ——LC (1 + CC > (3.22)
LVIXI C 8g

To emphasize the form of the solution given in equations (3.21) and
(3.22), define

C
a=__ (,2 =; f2 = 1+L> (3.23)
c sg

 

 

 

 

_ 2 2 _ 2 2
£11 - I/a (foo) 22 - I/(fmo) - a (3.23)
Then
E1 —at glt ’git R 2 4 CC
1(t) = 'ZLgl e (e - e ) for (IT) > i—C— ]. + C (3.248)
c sg
E 2 C
. = l -at . R, 4 c
1(t) Egg- e Sin(g2t) for (L) < LC; 1 + E;;— (3.24b)

The current excited in the secondary of the ignition circuit by
the closing of the distributor gap behaves either exponentially or as
an exponentially decaying sinusoid. Note that the form of equation

(3.24b) agrees with the solution assumed by Newell in equation (2.6).

Circuit Equations After Spark Plug Fires

 

The next step in the analysis determines the form of the ignition
circuit current after the spark plug gap breaks down. The circuit
shown in Figure 7 still applies, except that the distributor gap is now
assumed to be perfectly conducting.

Kirchoff's voltage law now yields:

§3I£2.+ V (t) (3.25)

= ' +
vC(t) R 1(t) L dt sg

Combining the above with equation (3.2),

de(t) dZVC(t)
v (t) = - R C ——~——-— - L C -——-———- + v (t) (3.26)
C c dt c dt2 sg

Using the LaPlace transform method of solution, the transformed

equation is:

32

dVC(0)

dt

2

VC(S) = - R CC[%VC(S) - vC(0fl - L CC 8 VC(S) — st(0) e (3.27)

Using an approach similar to the solution of equation (3.13), the
transform of ng(t) is identically zero for an instantaneous spark plug
firing.

In equation (3.27), the time scale is shifted so that t = 0 when
the spark plug gap breaks down. This breakdown occurs at a time t = t1
after the distributor gap has broken down, and coincides with the build—
up of a specified voltage, E2, across the spark plug gap.

The initial conditions for equation (3.27) are determined by com-

bining equations (3.20), (3.21), and (3.25) to get:

R
--—t
V (0-312” 211%-LL _R__ ,1 ga/iu _R_ _1
sg ng + Cc Cx 2 L/K L/R
-1/
e z/i t (3.28)

which is the expression for the spark plug voltage after the distributor
gap breaks down (t=0) and before the spark plug gap breaks down (t=tl).

The Spark plug gap breaks down when the spark plug voltage equals
By setting equation (3.28) equal to E2, the

value of tl may be determined. Then, the values of vC(t) and de(t)/dt

a specified voltage, E2.
when the spark plug fires are determined from equations (3.2), (3.20),
and (3.21) as follows:
S t' s t s t s t
ECG ER<ell-e21)c EC(ell+e21)

1) = Cl é dg+ C l sg + 1 sg
x( g ) ZL/R 2(ng + Cc)

 

 

 

(ng + CC)

(3.29)

33

dvc(tl) = -1(tl) = —Ele
dt C

 

(3.30)
c LCC/K

The values determined in equations (3.29) and (3.30) above are di-
rectly substitutable into equation (3.27) as the initial conditions

vC(0) and de(0)/dt. Combining terms and rewriting,

 

R v (t ) dv (t )
S"(ti)+[ 131+ 51:1]
v (s) = C (3.31)
C 32 + 5(3) + —l-
L LCC

Using the residue theorem to obtain the inverse transform, the
voltage across the capacitor, CC, after the distributor and spark plug

gaps have both broken down is

s’t

 

 

3 dv (t )
v (t) = e (E-+ /T) VC(tl) + 2 ——§E—l—-
C 2.4?
s t
4 dv (t )
- e (% - J?) v (t1) 4' 2 ——Ca‘E—;—- (3-323)
2/f C
2
_ B_ _ ._i_
where Y — (L) LC (3.32b)
C
= .. £- 1/ = - —B— - 1
s3 2L + M? (3.32c) s4 2L a/f (3.32d)

Time, t, in equation (3.32a) is measured from the instant the
spark plug breaks down, and the values of vC(t1) and dvc(t1)/dt are
given in equations (3.29) and (3.30).

Again, using equation (3.2) and simplifying,

34

 

— —— t
RC dv (t ) 2L 1 1
1(t) = veal) + C < C 1) -——————e e’ZVY t 43‘5” t

Finally, if the radical term in equation (3.33) is imaginary,

R
' dv (t ) - 2L-t
1(t) = 2 vc(t1) + RCC “’32-“;— 3————— sinQ/z fl?! t)
L I/l—Yl

2
_ Cc ——EE———- e cos (% VIYI t) for (B) < -3- (3-34)

Numerical Examples

This section presents the results obtained by substituting selected
component values into the equations from the preceding sections.

A computer program (see Appendix A) was written to Solve equations
(3.10), (3.20), (3.21), and (3.22) for the current and voltage waveforms

prior to the firing of the spark plug. The output of this program facili-

tates determination of the parameter, t1, for a given spark plug gap

breakdown voltage.
Another computer program (see Appendix B) was written to solve equa-
tion (3.32), (3.33), and (3.34) given the value of t1, and the plots which

follow utilize the outputs of both programs.
Results using Newell's values. Figure 8 Shows the predicted behavior
of the voltage and current for component values originally used by Newell

[8]. While Newell used his values to obtain good results in the frequency

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 4,000
vC
3 000 ‘ 3 R-90
15 . W '
F~“* —6
\N L=1.4 x 10
m IO 2,000 , "‘
AI u: ng // i E =2,500
.‘i‘. S \ 7 l '1
A c> 12’ . —12
5 > 1 000 —- C =40 x 10
E . ’ F”, I 1\\ C
e? u: _,¢” _ —12
z u» C =2 x 10
IE 5 0 d3
m 0 ._I l . 1"
D O C =9 x 10- 4
o > [ 38 U
l
-5 —1,000 .- ‘\4
-10 -2,000 1 10-6
I x 10’9 8 1 x 10'7 x

1 x 10'
TIME, SECONDS

Figure 8 - Theoretical Waveforms Using Newell's Values

domain (see Figure 5(a) on page 18), he gave no consideration to the time
behavior of the circuit.

Serious objection may be raised to the time between gap breakdowns,
t1, of 5 x 10-9 seconds. This is nearly a thousand times faster than the
value for modern ignition systems indicated in Table 1 on page 7.

Further, Newell used his equations with a spark plug gap breakdown
voltage of 9,000 volts to compare his theory with data from a pressurized
cylinder [8]. However, the maximum value of the spark plug voltage using
Newell's values is under 4,100 volts.

The remaining examples demonstrate the changes in behavior attain-
able using different component values.

Effect of changing R. Increasing the resistance, R, slows the rate

 

of oscillation in circuits below resonance, and increases the time con-
stants of the exponential terms above resonance. Figure 9(a) shows the

current for a circuit above resonance.

 

rU 2 2 2
_ 1 l 1
0 _ _ .
.1 AU nU 0
l 1 1
0 X 0 0
0 0 O X X X
0 l4 r) 5
9 o 9 3 O n/_ 9
l l 2 2 I... = =
= = = = = g g
R L I. 2 C d S
E E C C C
[[IllIIlll IIIlrlIllI I IIHIIII

I'll II[9.I‘.[IIICIII[III .li.ll-l-

 

I.IIII|[OIIIIIIII[O IIl [lull-l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mummaz< .szmmmso

1 x 10.-6

1 x 10’7

1 x 10’8

1 x 10

TIME, SECONDS

Current for a Circuit above Resonance

(a)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o o 2 2 2
6 1 ii. 1
_ _ . _
0 C O 0
.l . 1 l 1
0 O 0
X 0 oo 0 X X X
5 5 0
l4 3 a a O 2 9
0 . 2 l 4 4 __ _
9 l = = __ = 00
= = 1 2 C d
R L E E C C C
.I W .WII Hull
. l. [a [4:31- Il....l [III
4 I H - ITIIIIIIII [1.
31.1.1 I. III .SIQIIIII III [I-_T.[I..III filliavllll
[1m Il.llllmv.iI|-I-Oll-[
l T p L.
_ _ — .
b c A
._ I w ._
XII
01 H
VK 4
.1 IL I
M
mr\ n
N1
. /
MT
5 0 5 O 5 0
l l . l...

mommmz< .szmmmao

1 x 10"8

1 x10”9

Effect of Change in Spark Plug Gap Breakdown Voltage

(b)

Figure 9 - Theoretical Current Waveforms

37

With higher values of resistance, the spark plug voltage takes longer
to reach the same value, so t1 increases. Also, the amplitude of the
current is reduced, with a corresponding reduction in the radio frequency
interference associated with the circuit operation. However, for exces-
sive values of resistance, so much energy dissipates through the resis—
tance that the spark plug can not fire.

Effect of changing E2. Reducing the estimated spark plug gap break-

 

down voltage, EZ’ directly snortens the time between gap breakdowns.
Also, the peak amplitude of the current is affected, as shown in Figure
9(b).

Effect of changing Cdg and E1. Capacitance describes the ratio of

 

the magnitude of charge on either of two plates to the potential dif-

ference between the plates, or

(3.35)

(‘4
ll
<po

For two parallel plates, each with area, A, and separated by dis—

tance, d, equation (3.35) reduces to [34]:

_ e A -
C _ ._d_._ (5.36)

where E, is the permittivity of the medium between the plates.

By analogy to the parallel plates, increasing the distributor gap
should reduce the distributor gap capacitance. Further, if the initial
charge on the distributor gap is the same both before and after the gap
is changed, then the value of the distributor gap breakdown voltage should
increase. This agrees with the observations listed in Table 1 on page 7

for General Motors' change of the distributor gap width in 1969.

38

Figure 10 shows the effect on the voltage and current waveforms for
simultaneous changes in the distributor gap capacitance and breakdown
voltage using the constant charge assumption. Whereas Newell's original
values resulted in a restricted range of values for spark plug firing
voltage, Figure 10(a) shows that voltages to 15,000 volts can be readily
predicted.

Also, Figure 10(b) shows a considerable increase in the magnitude of
the current. Although the charge on the distributor gap prior to break-
down remained unchanged, the energy varies with the square of the voltage.
Therefore, the energy in the circuit at the time the distributor gap
breaks down is noticeably increased.

Finally, an increase in the width of the distributor gap shortens
the time between gap breakdowns for the same spark plug firing voltage.
This agrees with the observation of Hsu and Schlick [28] mentioned on

page 20.

VOLTAGE, VOLTS

CURRENT, AMPERES

39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R=90

L=1.4 x 10-5
CD

®

2

E1=4,000

=10.000
c =40 x 10’
C

-12
Cdg—1.25 x 10 (9
=0.5 x 10"12 ®

—12
ng=9 x 10

—6

R=90

L=1.4 x 10'6

®
=1o,000 (:)

12

E1=4,000

0 =40 x 10'
C

, _ - —12
tdg-1.25 x 10 ®

=0.5 x 10'12 (:)

csg=9 x 10-12

15,000 i Try}
®v
8%
10 000
’ F‘
@VC 2 74 r®vc
5,000 _-.-.,-- 4» 5F - ~- -
-/__....—+/ 17 I /\
0 ® I L ‘1
vSg NJ,
—5,000
-10,000
1 x 10'9 1 x 10‘8 1 x 10'7 1 x 10
TIME, SECONDS
(a) Voltage Waveforms
3O * r l I
(:>iw
20 _ l
/ N
10 / . f\ _,
7 . r
O 0 ’” tr
—10
\
-20
1 x 10”9 1 x 10’8 1 x 10'7 1 x 10‘

(b)

TIME, SECONDS

Current Waveforms

6

Figure 10 - Theoretical Waveforms for Constant Initial Distributor Cap

Charge

CHAPTER IV

FREQUENCY SPECTRUM OF SPARK PLUG CURRENT

The preceding development has resulted in closed form expressions of
the spark plug current as a function of time. Consideration of the radio
frequency interference which results from this current, however, requires
knowledge of the frequency variation of the spark plug current.

This chapter develops equations for the amplitude density of the
LaPlace transform of the current. Then, tests are performed to imply the
correctness of these equations.

The significance of the time between gap breakdowns is investigated,
and numerical examples using the amplitude density equations conclude the

chapter.

Derivation of Amplitude Density Equations

 

The amplitude density of the transform of a function expresses the
variation of the magnitude of that function in frequency domain. Phase
information, while not contained in the amplitude density, is available
from intermediate equations.

With the assumption of zero spark plug current for negative values
of time, the amplitude density comes from the one-sided LaPlace transform.
Substituting flu for s and writing the resulting expression in terms of

a real and imaginary part, the density is obtained as:

40

41

amplitude density = nge E I(jw) g]2 + [la $I(jw)?] 20 (4.1)

 

Calculations of the amplitude density follow for two cases of spark
plug current: 1) spectrum of the current arising from breakdown of the
spark plug gap only, and 2) spectrum of the total current due to both the

distributor and spark plug gap breakdowns.

Amplitude Density — Spark Plug Cap_0nly. The amplitude density of

the current follows from the LaPlace transform of equation (3.2):

I(s) = — CC [5 VC(s) - (initial value of vcil (4.2)

The initial value of vC in this case is the coil voltage at a time,
t1, after the distributor gap breaks down, or vC(tl). Also, using the

transform of the coil voltage from equation (3.31) and substituting in
equation (4.2),
($1.) E’c‘tfll ' (SCC)[dVCc(1:1)]

(4.3)

I(s) = i
s2 + 5%) + (EEC)

Substituting 3 = jw in the above equation, rationalizing the denomi-

nator, and simplifying yields
2 If

E;_ 1 _ wz _ w RCCK2 wc K 1 _ N2 + wRKi
1. LC L c 2 LC 2
c c L

 

 

 

 

 

 

 

I(jm) = 'j
1 _ 2 2 + 93- 2 1 _ wz 2 + £3. 2
LC w L LC L
t C 1 C
de(tl) (4'4)
where Kl = vC(tl) and K2 = —-EE——_

Finally, applying equation (4.1), the amplitude density of the igni—

tion circuit Current due to the spark plug gap breakdown only is:

42

 

 

JAl[m6 + A5014 + Afiwz + A4]
I 1(0)) I: 4 --.‘-.2.__. (4.5)
(11 + A3“) + A2
where A = (c K )2 A = (l/LC )2 A = (R/L)2 - (2/LC )
' l c 2 2 c 3 c
2
A4 - (KlAz/KZ) AS — (AA/A2) + A3 A6 — (A3A4/A2) + A2

Amplitude Density - Distributor and Spark Plug Gaps. The expres-

 

sions for the spark plug current when the sequential breakdown of both
gaps is considered are recalled as:

iO(t) = 0 for t‘<0 (4.6a)

 

 

11(t) — e - e for 0 < t < tl (4.6b)
L/E
where 2 C
- R _£L_ _£;_
X"(I) ' LC ]'+ C )
c sg
JL(t-t )
(RC dv (1:1)) 2L 1 #25, (H: )
1 (t t ) - v (t ) + e 1
2 1 1 2 dt 'L/? ‘J
-e/T (t-tl) Eg_ dvc(t1) 2L(t t1) k/Y (t-tl)
2 dt
+ e—%/§ (t-tl) for t > tl (4.6c)

L LC
c

2
where Y = (3) - ~9—

Using Heaviside unit step functions, the above may be written as:

1(t) = H(t)il(t) - H(t-tl)il(t) + H(t-tl)i2(t-tl) (4.7)

43

The desired transform is then
I(s) = g {H(t)il(t) - l-i(t-t1)il(t) + H(t-t1)12(t-tl)} (4.8)

From the linearity property,

I(s) = gimuilu); —%€{H(t-tl)il(t)} + g§H(t-tl)i2(t-tl)3

(4.9)

Each of the above will be evaluated separately.
A useful property of transforms concerns real translation in the
time domain. This property says that a time-shifted function experiences

a phase shift in the frequency domain. Thus,

_ 'Stl

g9 {H(t—tl)i2(t-tl)3 — e 12(5) (4.10)

Now, 12(5) is the transform of the current after the spark plug fires,

as given by equation (4.3). Therefore,

dv (t)
1
-st (—) v (t ) -sC [
gifl(t-tl)iz(t—tl)}=e 1 L+2[C 1; C1 dt (4.11)
s + s —- + ——-
(L) (ice)

The next term to be evaluated is g {H(t-t1)il(t)} . First,

 

equation (4.6b) is written as a time—shifted function:

121/)? R/x
E e("ZE'I—§_)(t_t1)e("EE'T'2_)t1 _ _§_

i'(t-t ) = -——
1 1 LC? L/i
R A? R A?
‘(ér+7)<t‘t1> (27'?) t1 “'12)
e e
Then

-st
geiH(t—tl)il(t)} =g€EH(t-tl)ii(t-tl)} = e 1 11(5) (4.13)

where 11(8) is the transform of equation (4.12).

44

By the principle of superposition,

R /x R A? . R A?
E (“2L+2\)t1 (”EE+7)‘ E "(213+7) t1
11(5) = ———-e e - ————e
LA? U)?
R A?
e-(2L+ 2 >t (4.14)

By definition of the one-sided LaPlace transform,

R R A?)
- ——-+ —— t m - s + ——-— ——- t
g e< 21‘ 2) = J e (2L 2 dt (4.15)
O

The complex variable, 5, may be written in terms of a real and imagi—
nary part as

s = O + jw (4.16)

Then, the integral in equation (4.15) is seen to converge when the real.
part, 0, is greater than —R/2L, so that

(.1: 4T),
g e 2L 2 = 1 for G>-2i (4.17)

 

Since the intent is to observe the frequency content of the ignition
circuit current, the real part of s is customarily taken as zero, and the
restriction required in obtaining the above transform poses no problems.

By a similar integration,

R

for G > — 2E. (4.18)

 

1
R f)?
s +[:2L-+ 2

45

Substitution of equations (4.14), (4.17),and (4.18) into equation

(4.13) yields

 

R A?
— ——-+ s t ——-t
g H(t_t1)il(t) =_E_e (ZL )1 e2 1 _
M)? 8+ _R__£
2L 2
A?
'7t1
e (4.19)

 

The last term to be evaluated isg£H(t)il(t)3 . This is easily

found to be

 

 

—
—.___

2L 2 —+—

2L 2

g H(t)il(t) =—E— 1 - 1 (4.20)
La “[1; a] “[12 a]

The desired transform of the ignition circuit current is obtained by

substituting equations (4.11), (4.19), and (4.20) into equation (4.9).

 

 

 

 

 

 

R )
- ——-+ s t
I(S) =_§_ 1 _ 1 __1;__e (2L 1
x _R_ g + _R_+ x 11/)?
2L " 2 3 2L 2
a? A? Ev (t )]
_ t — —- t 1 - C 1
e 2 l e 2 l + e-Stl (f) [vc(tl)] SCciT—fldt ,
" 2 R 1
R f)? R Q s + s(-) + (-——)
S + [Z—L — 7] S + [Z + 2 L LC

(4.21)

46

If the radical term in equation (4.21) is real, the circuit may be
said to be above resonance. Equation (4.21) may then be simplified using
the following definitions and substituting jw for s:

A cos wt A sin wt

 

 

 

 

 

 

 

 

 

I(' ) = 1 _ . 4 1
LC 3 L LC 3 L
c c
’A1t1
-j mAS cos wtl _ wAS Sin wtl _ A3e cos wtl
2 1 . 93 _ 2 1 . 93) (jw + A )
(‘w +LC)+J(2) (w+LC +J(L 1_
c c
—A tl -A t1 -A tl
+. A3e Sln wtl + A3e cos wtl _ . A3e Sln wtl + A3
3 (A + jw) (A + jw) J (A + jw) (A + jw)
1 2 2 l
A 2 C
_—(TA_—§~3—_j_w_)— “1(1) > TC 1 +_CC “'22)
2 c sg
where
/_,
A = .13. _ :2? A = ._R_ 1 _x
1 2L 2 2 2L 2
E Vc(t1)
A3 = —— A4 = T—
L/E
A = C de(tl)
5 dt
—jwt
e = cos(wtl) - J Sin(wt1)
Rationalizing the complex denominators and colleCting terms,
A-A wR. 1 2 wR 1_2.,"
4[(L)51nwtl — (LCC - w )coswtl] - wAS [(L)coswtl +(LCC (0)51nct1—l
I(jw) = —

 

2
4 2 R 2 1
(.1 +01 —-———— +
(L2 LCC> (LZCCZ)

"A1t1 "Altl
A A l—e coswt‘\ + wA e sin wt
1 3 1 3 1
+ 2 2 '
w + Al

47

 

 

-A t

1 .
coswtl) - A1A3e Sinwtl

w2 + A12

+ 2 2 (4.23)

58

The amplitude density is then obtained as

 

2 2 '
= real part of imaginary part
|I(u0| Jéquation (4.23)) + (bf equation (4.23)) (4'24)
2 C
R 4 c
for (I) > LC (1 + C j
c sg

Below resonance, the radical term in equation (4.21) results in an
imaginary number. Using the following definitions, substituting jw for

s, and rearranging, the complex expression for the current as a funCtion

of frequency is:

Alcoswtl ' Alainwt1 . Azcoswt1

- J - 1
1 2) (ij (1 2) .(wR
1_2 .wR —————-m+3— -———-w+3—
(ch; (u)+ 3L) (LCC L LCC L

 

10"») =

 

 

 

 

 

1M _-_.--_,_..1_1_.1__-_ - (4.25)

 

 

 

c sg
v(t) d(t) --B't
where A = C l— A = C _7C 1 A = 2L' 1
1 L 2 c dt 3 e
A = —E— A = J:- e—Jwt = coswt — j sinwt
4
Ldil 5 2L 1 l

Rationalizing the complex denominators, equation (4.25) becomes

 

 

 

 

 

 

 

- A1(chosmt1 - D151nwtl) - wA2(choswtl + D281nwt1)
104)) = 2
D1 + D2
+ A3A4D4e ‘_ - A3A4D3e - A4D4 + A4D3
2 2 2 2 2 2 2 2
D
A5 + D4 A5 + D3 A5 + D4 A5 + 3
+ j -A1(D1coswtl + D231nwtl) — wA2(D2coswt1 - D151nwtl)
2 2
D
D1 + 2
-jD t -jD t
A A A e 4 1 A A A e 3 1 A A A4A5
3 4 5 3 4 5 4 5 4
+ 2 2 =' 2 2 ’ 2 2 + 2 2 ( ’26)
.. l. + ,,
A5 + D4 A5 + D3 A5 + D4 A5 U3

where D =E£B D =-l; — w2 D = w +VIXT- D = w - [Iii

49

The amplitude density is then obtained as:

 

[I(w)l = real part of imaginary part of

equation (4.26) equation (4.26) (4.27)

Check of Equations

 

As a precaution against mathematical errors, three tests are per-

formed to imply the correctness of the equations in the preceding section.
1. The transform of a real function is Hermitian; i.e., the real
part of the transform is even and the imaginary part is odd. Apply-
ing this test to equation (4.4), the real part is seen to be even by
inspection.

For the imaginary part, the numerator is odd while the denomina-
tor is even, yielding an odd imaginary part. Therefore, the trans—
form of the current after the spark plug fires is Hermitian as
required.

2. The second test requires equation (4.21) to reduce to equation
(4.3) when t1=0. This condition occurs when the spark plug gap and

the distributor gap breakdown simultaneously.

From equation (4.21),

 

 

C ’3
I(S)t__=0 "' qz +";(E + l j (4.L8)
i ‘ L LC

Since the above equation equals equation (4.3) with tl set to

zero, the test is satisfied.

50

fl

3. The final test involves setting 8 equal to zero in equation (4.21).
The integration of a function over all time equals the value of that

function's transform to the frequency domain at s=0 [35]. Thus,

1(3) = J i(t) (it (4.29)

If the spark plug gap and distributor gap break down simultan—
eously, i.e., if tl=0, then the integral of i(t) is simply the sum-
mation of the flow of charge in the circuit over all time. But, the
total charge in the circuit with both gaps broken down is known to
be the charge on the coil capacitor, Cc’ when the gaps break down.
This is given by the equation:

total charge on : capacitance of x voltage across coil
coil capacitor coil capacitor capacitor when tl=0 (4.30)

From equation (4.21),

R
EC ’Zti {it -—/Xt
_ c R 2 l 2 1
1(0) — l - ————- ——- e -e
Cc VX 2L
1+C_
sg
fit fit
51 .__ _ _- .
VA 2 l 2 1 ,
+ 2 e + e + Ccvc(tl) (4.31)
and when tl is equal to zero
1(0) :0 = Cch(O) (4.32)

1

Satisfaction of the requirements imposed by all three tests supports

the amplitude density equations as written.

51

Significance of Time Between Cap Breakdowns

 

Because of the length of the equations for the amplitude density, a
simplified relationship is sought to explain the significance of the paraf
meter, t1.

For the following development, the current due to the distributor
gap breakdown is viewed as flowing only for 0<t<tl. The current is blocked
for time less than zero, and the current which flows after t1 is due to the.
spark plug gap breakdown.

The rectangle function,iifl(£%g), accomplishes the desired screening,

where h is the height of the function, c is the time at the midpoint of

the function, and b is the width of the function [36]. For this develop—

ment, a rectangle function with unit height, a base of width t1, and
centered at t = %t1 is desired. The function is written as
,_f_1
n—?—=H 2-1 (4.33)
t1 t1 2

From the Fourier series expansion, an infinite number of single fre«
quency components comprises the total current. Thus, observing the effect
of tl on the amplitude density of a single component lends insight to the
overall effect.

Using phasor analysis, a single component of the current may be writ-

jm t

ten as I e , where moiesthe angular frequency of the single component.

Thus, the current observed after the distributor gap breaks down is

i(t) = II E9 —% 1 e‘ (4.34)
1

Taking the Fourier transform,

1(s)‘ (Bank-‘1”) * (a? Ie O (4.35)
t 2
l
where the asterisk indicates convolution.

Using several theorems for Fourier transforms, the above becomes

NS) = e-jfisg H (i) * I g ejmfot

L1

e-jTTs l (J Il(t) u * I 1 (E: ej‘rrt?
IZfOI

 

 

 

 

 

——1 l
t s: S 8:...S_.
l 1U) 2f
-—- o
t.
l
= -jns [sin(fls t ) * I _
tle 3: §?—- 6(s f0) (4.36)
[fist o
1
From the definition of convolution,
m . sin(flut )
= -Jflu _ 1 I _ _
I(s) [ tle .-_REf—_—- §?—- 6(8 11 f0) du
_a) 1 o
I tl -jfl(s - f ) sin (8 - f )t n
= “f e O o 1 (4.37)
A o fi(s - f )t
o 1

Because of the form of the Fourier transform which was used, set s

equal to f, where f is frequency in Hertz. Substituting and rearranging,

I t
_ 1 . - -
I(f) — 2nf0(f _ f0)t1 Sln [fitl(t — f0)] cos [R(r - f0)]

 

ltl

" j ,
2Wf0(f f0)t1

 

sin[fltl(f - f0)] sin[fi(f - f0)] (4.38)

NEWELL ' S EXPERIMENTAL DATA 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o
\ 27 R = 90
. 1 . .__. _.

_ ‘1 _
(g 10 .__. .—-- \L/\ L = 1.4 x 10 6
E N \ E - — 2
43: _20 [ 1- 1.2— ,500
§\ \ C = 40 x 10‘12
%.§ Theoretical 1 c

o —30 _- - .l. .__-..11-,-1 _

' ° 1 C = 2 x 10 12
N dg .
:19 —40 -««L m—ng= 9 x 10-12
S if \ t1 = 5.22 x 10’9

-50 ,TP..-._..1.--_.,_.. 4- \—4F
-60
1 x 106 1 x 107 1 x 108 4 x 108
FREQUENCY, Hz
(a) Using Newell's Values
NEW'ELL'S EXPERIMENTAL DATA?
0 “V/ R = 200 6)
MA?
-10 _ - 1,000 Q)
m ‘*\ N
.’> ._
E: NK1\N L L = 1.4 x 10 6
<1 N _20 .
.4 :1: k r :-
Eé \ E1=E2= 2,500
93 E \ , . -12

.9 -3o \ CC = 40 x 10
m -—1 I -12
g Q 5 I , Cdg= 2 X 10
S H ‘40 ' 12
._1 =
g; sg 9 x 10

_50 ' -- t1 = 5.9 x 10’9 CD
0N = 1.9 x 10“8 ©

—60 - -

1 x 106 l x 107 1 x 108 4 x 108

FREQUENCY, Hz
(b) Effect of Change in Resistance

Figure 11 - Theoretical Amplitude Densities of Ignition Circuit Current

Taking the square root of the Sum of the squares of the real and

imaginary parts, the amplitude density becomes

(1 sinfflt1(f - fo)]

”IRE (f - f )
0 O

 

for (n — 1)2R<<ntl(f —f0) < (2n —1)n

where n l, 2, ... (4.39a)

|I(f)l=

 

(\:I Sin[ntl(r - fo)] for (Zn _ 1)” < ntl(f _ f0) < Znn

Zn fo(f - f0) 1, 2, ... . (4.39b)

where n

Maxima are found where the derivative is zero, which leads to the

requirement that

I (f — fo)cos[flt1(f - fo)](fltl) — sin[fltl(f - fo)]

 

 

= O (4.40)
20f 2
o (f - f0)
or
ntl(f - f0) = tan[th(f — f0)] (4.41)
Letting a = fltl(f - f0), the above equation becomes
tan(a) = a (4.42)
which has solutions at O=0, al= :4.49, a2= :7.73, a3= :10.90, et cetera.

For larger values of a, the maxima repeat approximately every N

radians, so

” + A - = . - ‘ + '.4“
nt1(r f f0) Rtl(f f0) N (4 5a)
or
.__1_
AI ' t1 (4.43b)

This simple result predicts that the current which flows after the
distributor gap breaks down but before the spark plug fires causes recur—

ring maxima in the frequency domain. These maxima recur at a difference

55

in frequency which is the inverse of the length of time between the gap

breakdowns.

Numerical Examples

 

This section presents amplitude density plots predicted by equations
(4.24) and (4.27) for different component values. The computer program
contained in Appendix C was used in solving the equations.

Results using Newell's values. Figure 11a shows Newell's experimen-

 

tal values [8] and the theoretical amplitude density obtained by using
Newell's values in equation (4.27). The curves agree below 20 MHz, but
discrepancies appear at the higher frequencies.

Most noticeably, the last two maxima from Newell's measurements occur
about 5.0 x 107 Hz and 8.4 x 107 Hz, for a Af of 3.4 x 107 Hz. Equation
(4.43b) predicts a time between gap breakdowns of 2.94 x 10-8 seconds.
However, Newell's values give a time, t1, of 5.22 x 10_9 seconds.

The remaining examples demonstrate the changes in the amplitude den—
sity attainable using different component values.

Effect of changing R. As observed in the previous chapter, increas-

 

ing the resistance, R, effectively increases the time between gap break—
downs for the same breakdown voltages and reduces the amplitude of the
current.

Figure 11b shows the effects observed in the amplitude density. The
amplitude is reduced, and the lengthened time between gap breakdowns
appears as more frequently occurring maxima.

A

As a check on equation (4.43b), tl is 1.9 x 10—0 seconds for the
curve with R = 1,000 ohms, so maxima are expected about 5.3 x 107 Hz

apart. Inspection of the results shows this behavior at the higher fre—

quencies.

AMPLITUDE, dB RELATIVE
T0 1.0 mA/kHz

Al‘lPLI'l'UDE, dB RELATIVE
T0 1.0 mZ/kHz

(a)

(b)

)()

NEWELL ' S (EXPERIMENTAL DATA 7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0~
fp/I R = 90
-10 « »lfi 4 {e- L = 1.4 x 10"6
,2
E1= 2,500
-20 - - L-L...- ....
®_ 5 E2= 1,580 @
N
—30 LN = 4,000 Q)
\\ CC= 40 x 10'12
-40 ,
N —‘1 C. = 2 x 10-12
\+-® “g
‘50 I: , ng= 9 x 10'12
_ —9
_60 _ c1 - 3.5 x 10 (:)
1x106 1x107 1x108 4x108 = 9.19 x 10'9(:)

FREQUENCY, Hz

Effect of Change in Spark Plug Gap Breakdown Voltage

+10

  
  
 

R = 90
0 L = 1.4 x 10-0
1 E1 = 4,000 ®
_ 0 —-
~ = 10,000 (2)
R=200 _5
_20 L=1.4x10 132 = 6,025 ®
El=2,300
24,150 = 14,250 Q)
-30 _ .12 —12
C - 4Cx10 C = 40 x 10
C _12 C
_40 Cdg- 2x10 Cdg:= 1.25 X 10-12 (:>
—12
ng‘ 9XIO = 0.5 x 10‘12 (:)
—50 -3 . . _
‘1' 2.95x10 0 = 9 X 10-12
8g
'60 t1 = 9.19 x 10'9
1x106 1x107 1x108 4x108
FREQUENCY, Hz
and E and for t = 2.95 x 10.-8

Results f r tan es in C.
o C. g 0g 1’ 1

Figure 12 - Theoretical Amplitude Densitites of Ignition Circuit Current

57

Effect of changing E Increasing the spark plug gap breakdown vol—

2.

 

tage directly increases the parameter, t This is evidenced in Figure

1'
123 by the appearance of additional maxima in the amplitude density.

The effect of the change in amplitude on the electric field is con-
sidered in the following chapter.

Effect of changing C Figure 12b shows the reSults of

 

and E .
dg --~l
simultaneously changing the distributor gap capacitance and breakdown
voltage while keeping their product constant. The increased amplitude
for the higher voltage circuit indicates the higher level of energy in
that circuit.

Figure 12b also contains a theoretical plot with a time between gap

A , —8 . . -
breakdowns of 2.93 x 10 seconds. While the max1ma recur at the proper
intervals to match those of Newell's experimental data, the first maximum
appears at too low a frequency, and the amplitude decays too rapidly.

The failure to precisely fit Newell's experimental curve emphasizes
the complexity of the equations involved. Obtaining an amplitude density
p10t with this model requires the following steps:

1. Specification of R, L, C , C , C , and E for solution of

c dg sg 1

equations for waveforms after the distributor gap breaks down.

2. Selection of time, for a specified spark plug gap breakdown

t1,
voltage using the results from (1) above.

3. Calculation of the coil voltage and its slope at t = t1 for use
as initial conditions in the amplitude density equations.

4. Solution of the amplitude density equations.

The above procedure requires numerous iterations when attempting to
match specific data points. However, the equations provide an effective

indication of the consequences of changes in particular component values

or operating conditions, as shown by the examples in this section.

CHAPTER V

ELECTRIC FIELD FROM CIRCULAR LOOP ANTENNA MODEL

The final step in modeling the ignition circuit involves the develop-
ment of a radiation model to predict the level of the interfering electric
field.

First, an upper bound on the electric field strength as a function
of frequency is found using a circular loop antenna model, and numerical
examples are given.

Next, the same model is used to predict the time variation of the
electric field. Two approaches to the solution of the equations are
given, along with examples.

Discussion of the validity of the ignition circuit model concludes

the chapter.

Predicted Field Streggth in Frequency Domain

 

. 'wt . . . .
Assuming an eJ time dependence, the electric and magnetic fields

can be expressed in terms of a vector potential as
+ +
B=VXA (5.1a)

+ +
E = -jw[A + fi%—V(V - A)l (5.1b)
where the vector potential is a space- and time-varying function which is
defined as [37]:

”A (it) = :7 jf LL.) ejwk'f‘”: ”(1w (5.2)

70

v
V

58

59

In the above equation, the integration is performed over a volume,

+

V' which contains all sources. The vector, r' indicates the source lo-
, 5

+

cation, while the vector, r, describes the field point. The distance be-
tween the source and the field point is R, and the volume current density
. -+-+"
is J(r ).

Using the conventions shown in Figure 13, the radiated (far zone)
electric and magnetic fields are found using the following assumptions:

1. The current in the antenna is independent of ¢'.

2. The antenna's dimensions are small compared with the wavelength;

0 r..—
i.e., amvue <<l.

3. The current in the antenna is uniform over the wire cross section,

- v
and is given by I ert .

4. Measurement of the fields occurs far from the antenna so R = r

for magnitude calculations.

Johnson [37] gives the equations for the fields as

E = -j (1) 11¢.) (5.3a)

jwv’fiE Ad) 0 (5.3b)

jw(t-Vue r)

and

_).
B

where A = jglé Jl(anuE sin0)e (5.3c)

0 2r

A A

The vector potential is zero in the 0 and r directions, and the nota-
tion, Jl( ), indicates the firsr order, first kind Bessel Function of the
parenthesized variable.

Substituting equation (5.3c) into equation (5.3a) and simplifying,

 

r
. 'U)(t _ _)/\
+ _ ulwa wa Slne J c
E ‘ 2r J1< c > e 4’ (5.4)
l . . . 8
where c = —-—-= propagation velocity in free space = 3 x 10 m/second.
we '

The maximum value of the electric field due to a single component of

. . 0 .
current w1th angular frequency, w, occurs when 0 is 90 and at time, t=r/c.

 

 

 

60

‘4 R=f-E'

[lot
0

 

 

 

 

 

 

Figure 13 - Coordinate System for CirCular Loop Antenna [37].

Thus, an upper bound on the magnitude of the electric field as a function

of frequency is given by

 

ma ,
Jl(j;) (3.5)

Writing the Bessel function as a power series,

4 6
ma 93 1 CB 1 ma . J (5.6)

_E. = _ L U§~ - _i ___ _ ______-
J1(c ) 2c [1 2(2c) F 12(2c 144(2c + '

Discarding higher order terms (which is consistent with assumption

number (2) on the preceding page), equation (5.5) becomes

+ 111002a2
M < —-—-— (5.7)
- 4rc

The above equation may also be written as

61

 

9
+ film‘A
[El < (5.8)
- , 2
4NDC
where n = uc, A = naz, and D = r. Equation (5.8) is identical to Newell's
equation (2.8) [8].
Numerical Examples — Frequency Domain

 

With the availability of Fortran software packages to calculate values
of the Bessel function, equation (5.5) was used to obtain the following
plots of the upper bound of the electric field versus frequency. The con-
puter program in Appendix C includes the solution of equation (5.5) in its
output.

Results usingfiNewell's values. Figure 14(a) shows the theoretical

 

limit of the radiated electric field strength using Newell's values in
equation (5.5). The loop radius of 0.1085 meters and the distance from
the antenna of 30.48 meters allow comparison with Newell's theoretical
result, shown in Figure 5(b) on page 18.

The approximation for the Bessel function used by Newell is accurate
within 3% up to 10 MHz. Therefore, the differences between Figure 5(b)
and Figure 14(a) arise from the different current amplitude densities
used (see Figure 5(a) and Figure 11(a), respectively).

Assumption number (2) requires (%?) to be much less than unity. For.
a loop radius of 0.1083 meters, the angular frequency should be much less

than 2.765 x 109 radians/second (f<<4.4 x 108

Hz). Therefore, theoretical
results are not shown above this frequency.
From equation (5.7), the limit of the electric field is proportional

2 . . . . -
to w times the current amplitude den31ty. This accounts tor the added

significance of the field due to the higher frequency current components.

AMPLITUDE RELATIVE TO

AMPLITUDE RELATIVE T0
1.0 uV/m/kHz, dB

1.0 uV/m/kHz, dB

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 R=90
L=1.4xio'6
10 V‘ge- ~——
\\ \ E1=E2=2 ,500
0 - “t'\**y “ C =40..10’12
C
1 \U4 C =2x10"12
-10 .... -}}u____ -4 “1 d8
/ C =9x10‘12
SE
-20 " t1=5.22xio'9
a=0.1085 m
-30 71
I / r=30.48 m
—40 (5
1x10 1x107 1x108 4x108
FREQUENCY, Hz
(3) Using Newell's Values
30
20
10
0
-10
—20
1x106 1x107 1x108 1x109 a=0.1035 m

FREQUENCY, Hz r=10 m

(b) Effect of Change in Resistance

Figure 14 - Theoretical Field Strength Limit in Frequency Domain

63

Effect of changing R. Adding resistance to the ignition circuit re—

 

duces the peak electric field strength, as shown in Figure 4(c) on page

14. Using a radius of 0.1085 meters and a distance of 10 meters, Figure
14(b) shows the theoretical results for two different values of resistance,
along with the SAE J551b limit. Significant improvement is predicted be-
low 100 MHz.

The theoretical results depict an upper bound on the electric field
strength from a single spark plug firing, while the SAE standard estab-
lishes a limit for the collective peak fields from numerous plug firings.
While their relationship was not investigated, the curves should show
reasonable agreement.

The preceding statement extends Doty's conclusion [2] that "a number
of discretely located random occurrence impulses do not significantly
phase—add in space when measured by an instrument having a broadband IF
and peak detector. While Doty compared results from a matrix of (21)
vehicles against those of a single vehicle, it seems reasonable to expect
peak measurements from the repeated firing of several spark plugs to be
similar to the model's predicted values.

Effect of changingiE Changes in the spark plug gap breakdown vol-

2.

 

tage, E2, alter the electric field spectrum as shown in Figure 15(a).
Since fuel mixture, cylinder operating conditions, spark plug gap,

and other factors determine the spark plug gap breakdown voltage, the time

between gap breakdowns is highly random. For the example shown, this ran-

dom time can cause successive readings to differ by nearly 15 dB at some

frequencies.

Figure 15(b) shows the reSults of

Effect of changing C and E

1.

 

dg

simultaneously changing the distributor gap capacitance and breakdown

64

 

30

 

  
  
 
 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R=90
—6
.L=-l.4 10
E, 20 ——--+- ~ - x
no 3 :-
E'U El 2,500
.4 “ 10 r««~1—- _
g g 132—1 .580 Q)
52%
E > 7
H 3' C —40 10'12
5°. c‘ X
n. .—1 -10 _ -12
E / dg-leO
-20 -.- =9x1012
. 8 8 S
7
1x106 1x10 1x10 4x10 tl=3.5xlO-9 ®
FREQUENCY, Hz _
=9.19x10 9 (:)
a=0.1085 m
r=10 m
(a) Effect of Change in Spark Plug Gap Breakdown Voltage
- R=9’J
40 R=200 _5 =
L=1.4x10 l L=1.4x10‘6
E =2,500 2'”
30 1 :
g E2=4,150 / ”,4 E1=49000 ©
-12
:1 l _
E98 20 Cc 'OXIO 12 vrlfl’ ‘109000 ®
e. ~ C =2 10“ ,
3 .2 .. 1222-6425 0
WM C =9x10
9‘\ 10 S ‘
S g -8 -14 250 (2)
g; t,=2.95x10 ' ,
:- -
E o C a=0.1085 . .. u C =40x10 12
v-l ' r=lO m C
n. .-+ 2 . .
7 ' C =1 25x10'12@
£3 -10. -.-. .. d8 °
/%1 =0.5x10’12 (2)
~20 - I , a 2 csg=9xio’12
6 7 8 .
{l 1 10 1x10 4x10 _
1‘ O X c =9.19x10 9
FREQUENCY. Hz 1
a=0.1085 m
(b) Results (0:8Changes in Cdg and El. and for =10
t =2.95x10 r m

1

Figure 15 - Theoretical Field Strength Limit in Frequency Domain

65

voltage while keeping their product constant. As expected, the higher
energy circuit produces more interference at all frequencies.

Figure 15(b) also contains a theoretical plot with an inductance of
14.0 x 10.6 henries (10 times Newell's value). The significant reduc-
tion in the bound on the electric field suggests that the inductance of
the spark plug leads should be increased, an observation which was also
made by Newell [8].

The model does not consider the near zone field, and the effect in-
creased lead inductance could have on other circuits in the vehicle.
Also, engine performance would have to be maintained. However, the in-

ference remains that the ignition circuit inductance can be optimized.

Predicted Field Strength in Time Domain

 

Equation (5.4) contains the time behavior of the electric field
strength. This section presents two approaches for predicting the peak
measurable electric field, using approximations for the current amplitude
density based on previous numerical examples.

For simplicity, let 0 = 900, so equation (5.4) becomes

. .E
Jw(t c) A

+ _ qua fig
- Jl(c) e ¢ (5.9)

2r

 

The measurable electric field is obtained by taking the real part

of the above expression, so

jw(t - E) A
(5.10)

e.

+ =___uwa .w_a
Re {E} 21' J1(C) Re Ie
Expressing the comples amplitude of the current, I, by a magnitude

and a phase term,

66

Re I e

r r
jw(t - —) .a jw(t --—) A
C2=Re |I|eJ e- C (1)

= III cos [..(t — E) + «1 cf) (5°11)

Assuming that the phase term is zero, the measurable electric field

becomes
ma ma , r. A
Re E 2 %— Jl(‘E- '1' C08 [NHL - 3)] (I) (5.12)

The above expressions apply for a uniform current of a single fre-
quency,(u. For a broadband current, i.e., one with a continuous frequency
spectrum, the total measured electric field is obtained by integrating

I

over all frequencies, where l1] varies with frequency.

Then

2 a m , a r A
Re 513? total 2 1;? I 00'1ka Jl(w?) cos[w(t -E-)] dw q) (5.13)

Two approaches are used in solving the above equation.
Method #1. This method uses the approximation for the Bessel func-

tion from the power series expansion:

L113 (U3 C r I
J1(c )-— 2c for w << a (J-lq)
Then

' 32 [w 2 r A
Re if? total 2 L4“: 00 w [100)] cos[w(t - 3)] doc (13 (3.13)

From the examples in Figures 11 and 12 on pages_53andffl3, respectively,
the current amplitude density is seen to be approximately constant up to
a certain frequency, after which it becomes roughly inversely proportional

to frequency. Thus, the amplitude density is assumed as

67

.I/ I for '41.) < (A) < U)
0 O

i1(m)| = (5.16)

(L) I
0 0

--- for<n < Iml
(D 0

Since the integrand is an even function,

A

2 m ‘
x N pa 2 _.E
Re E:E? total — I w |I(w)| cos[w(t C) dw] ¢

 

 

2rc
UaZIO {we 2 r m r A
= w cos[m(t — —)]dw + w w cos[w(t - —)]dw ¢ (5.17)
2rc J c o c
o w

0

Because of the approximation for the Bessel function, the integration
is not actually carried out to infinity. Using an upper value of integra-

tion, mm, and performing the integrations,

 

 

+ pa ono r r
= ' — —- + w t - —>
Re {E total I 2 coslw0(t c” cos[ m( c)]
2rc(t --—
c
2 sin[w (t — 11)] A
r . r o c , .
+ w (t - —) Sin[w (t - —)] - ¢ (5.18)
m c m c

r
wo(t - E)

The above equation satisfies six essential tests:

1. The predicted electric field strength is proportional to the
magnitude of the current, ono

2. The field is radiated and, therefore, varies as the inverse of
the distance.

3. The field is proportional to the area of the loop antenna.

4. The field is a maximum at the time, t = Eu This is expected,
since the current is nearly an impulse, and the maximum field from an
impulse is delayed only by the time it takes to travel from the antenna

to the field point.

()8

5. The field asymptotically goes to zero with time because of the

r 2 .
(t — —) term in the denominator.

c

6. The units are correct.

Using L'Hopital's rule, the numerator and denominator of equation
(5.18) can be successively differentiated to obtain an expression for the

. . . . . r -
largest predicted value of the electric field, which occurs at t = Eu The

reSulting expression is

2

. Ha w I A
x o o 2 2 . , .
Re 1E}total| — (3w -w )cp (5.19)
r
t = __
c
An obvious difficulty with equations (5.18) and (5.19) are their
dependence on the limit of integration, mm. This difficulty is circum—
vented with the second approach.
Method #2. This approach uses a continuous function similar to that

in equation (5.16) to represent the current amplitude density:

w I
|I(w)l =——9—9——— (5.20)
sz + w 2
0
Thus, equation (5.13) becomes
x Hawolo m w wa . r A
=_-___ __________ __ __~' I a
Re E total r [ Jl(<:) cos[w(t C)de ¢ (5.21)
2 2
O (U +00

0
Using a piece—wise continuous linear approximation for the function

L1)

9

w2 + w 2
o

+ 1J3ono O a) ma r
. < _______ __ - ___ _ __ .
Re {E} total ~ r (j (mo) J1( C) cos[u)(t CHaw

69

‘n A paw I m
ma r o 0 ma r
+ J .JICE—) (os[m(t — 2)]dw ¢ 5 r J J1(7?) cos[w(t — 2)]dw
w o
0
mo (n ma r A
- OJ (1 - {JD—0‘) Jl(—E:_) COS [w(t - 2)]dw Cb (5.1.2)

Setting the second integral equal to zero (this assumption is veri-

fied later),

>

R (E; (333339 {OOJ 93 I 3L11d <1> (523)
e total ~ r OJ 1((:) COS w(t _ c) w '

Using the solution to the above integral as given by Abramowitz and
Stegun [38], equation (5.23) becomes

Ucw I
o o

 

 

 

for 5 < t < a—il (5.24.5)
r C C
+ 2
-Ua w I
Re {Eitotal 5 - 0 0
2 2 2 2
r a r r 3
mm ‘. C) - (C) (t - C) + (t - C) - (C)
for t > 51—2—11 (5.2415)

The peak value of the electric field is predicted to occur in the

 

+
time interval-E < t <-§—;—£ , and is given by the simple relationship
+ nwOIO
R < .
e E total ' r (5 25)

where we cutoff frequency of current in radians/second

I = low-frequency amplitude of current in frequency domain,
amperes per radians/second

r = distance, meters
n = characteristic impedance of free space (=120W ohms)
Now, the assumptions in going from equation (5.22) to (5.23) is re-
viewed. First, the peak value of the field occurs vfimul t = E—, which

means that the cosine term is nearly unity. Using the approximation for

the Bessel function, the second

70

integral of equation (5.22) is approxi-

 

mately
“5 w m1 [ rmo H ma)
( 2:“ A. ‘ _ _ 2 " _ L __
J (I - (If) Jl( C) (-05 [m(t CHdm J (1 w ) (20 du)
o o
o 0
1m 2
2‘ :—2 (5026)
12c
Thus, the contribution due to this integral (for t 8 E) is
2 3-
pa mo 10
I .fi7
12 rc ‘5 ‘ )
Comparing equation (5.243) with equation (5.27),
equation (5.24a) 12 A
= ______. . 3
equation (5.27) 2 (J 2 )
w a
_2_

However, in using the approximation for the Bessel function (and in

developing the circular loop antenna equations), the assumption was al-

w a
o . . . . .
ready made that {-E—> is much less than unity. Tnus, the contribution of

the second integral in equation (5.22) is insignificant in determining the

peak value of the electric field, and was juStifiably discarded.

Numerical Examples — Time Domain

 

Figure 16 compares the maximum electric field strength predicted by

the two methods described in the preceding section. The computer programs

contained in Appendix D and Appendix E facilitate the caICulations required

by equation (5.18) and (5.24), respectively.

Method #1 relies heavily on the value selected for the upper limit of

integration, mm. Conversely, Method #2 allows a concise prediction of the

peak electric field and its Subsequent decay.

/

.__.

.I'
I
A»

l)...
1.14

0

.t...
~11

b shows

A

u inter

e1. ff

1
a

1H
1-

In d

W kev a

AMPLITUDE RELATIVE TO

71

 

 
    

 

 

 

t _ I
C ._ .12
' 1 2 3:2 .
60 . ' c a=0.1085 m
I
r0 ‘ 10 . r=30.48 m
J ‘ Method #1 w =lx10 8
I, m w =6.28x10
40 - I - ~“' rad/sec
I
m ‘ - _
'o 30 -_Jim .1 . .__”, -. . . IO=3.l6x10 8
g ' I i . amp-sec/rad
\\ I
> 20 _
‘3 a
'7 10 -nl-- - -
i
_1-. __ - _
0 2r . .-
-10 111.1; M _- Method #1 ,
':' w =lx109
_20 i. i m
0.101 0.103 0.105 0.107 0.109 0.111

TIME, MICROSECONDS

Figure 16 - Theoretical Field Strength Limit in Time Domain

The assumption for the current amplitude density used in Method #2
might result in an abnormally high predicted peak field strength (Figure
16 shows a peak electric field of about 250 V/m). However, equation
(2.25) does indicate the well-documented fact that objectionable levels

of interference arise from operation of an unsuppressed ignition circuit.

Discussion and Recommendations

 

While the preceding development emphasizes the sufficiency of the
model. this section suggests possible areas of improvement.

In determining the time variation of the ignition circuit current,
two key assumptions appear questionable. First, the assumption that the

secondary circuit charges instantaneously with the opening of the contact

72

breaker ignores any energy transfer through the coil after the distribu-
tor and spark plug gap breakdowns.

Selwiuil, tlle H|lek |)|lug )Ulp Innlllfilinbi u fill‘lt‘ Vtwltzlgt‘ uc'r1u4s It :Iftl‘r
breakdown, as shown in Figure 2 on page 8.

In spite of the above assumptions (which considerably simplify the
model). the current waveform shows a similarity to that measured by Hsu
and Schlick [28] and approximated in Figure 6 culpage 21-‘Therefore, while
further improvements to the model may improve the amplitudes predicted by
selected component values, the general shape of the solution should not
change drastically.

The amplitude density of the transform of the current requires no
additional assumptions over those made in time domain. Since this density
instrumentally determines the electric field strength, the field is limited
by the assumptions for the current in time domain.

Additionally, the assumption of a uniformly distributed Current in
a circular loop antenna limits the equations for the field strength to
frequencies such that w<<§. An antenna model with a non—uniform current
distribution would improve the treatment.

An apparently arbitrary assumption for the time varying electric
fields was the zero phase angle assumption in going from equation (5.11)
to (5.12). Figure 17 plots this angle for Newell's values.

Obviously, the phase angle varies with frequency, and inaccuracies
result from the assumption. However, for this development, the simplicity
resulting from the assumption was considered of greater benefit than the
potential gain in accuracy.

Finally, while the model incorporates some improvements over previous
models, the limited availability of supporting data suggests the need for

additional measurements of the predicted quantities.

73

 

 

 

 

 

 

 

 

 

 

 

PHASE ANGLE, DEGREES

 

180 . ~- ~ —~
1 ~)[ Vk\ R=90
—6
120 L=1.4x10
\
I E1=E2=2,SOO
60 ' —-0 _
» c =40x10 12
l c ,
-12
O Cdg-ZXIO
NH -
$\\. 1 c =9x10 12
83
-60 -9
1‘\ t1=5.22x10
-120 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, \ 1

-180 -

1x10 ' 1x107 1x108 4x10

 

 

8

FREQUENCY , Hz

Figure 17 - Theoretical Phase Angle of Transform of Current Using Newell's
Values

CHAPTER VI

CONCLUSIONS

The model presented in the preceding chapters successfully incorpor—
ates the sequential nature of the distributor and spark plug gap break—
downs. The following conclusions are drawn from the development of this
model:

1. The general problem of radio frequency interference requires con—
tinuing attention, as documented in the literature.

2. Prediction of the time variation of the ignition circuit current
satisfactorily approaches known behavior using this model.

3. The equations developed for the amplitude density of the trans-
form of the current predict recurring maxima in frequency domain, which
agrees with the experimental data of Newell [8].

4. The inverse of the time between the distributor and spark plug
gap breakdowns predicts the approximate separation in frequency between
the above-mentioned maxima. )v

5. Increasing the resistance in the ignition circuit decreases the
peak amplitude of the current in time domain, reduces the amplitude den-
sity of the current in frequency domain, and significantly reduces the
prediCted electric field strength.

6. The model can predict spark plug gap breakdown voltages of well

over 10,000 volts, which constitutes an improvement over Newell's model

[8].

74

75

7. The circular loop antenna model provides reasonable prediction
of the maximum electric field strength for frequencies to about 100 MHz.
8. The maximum measureable value of the eleCtric field strength as

a function of time is predicced to be less than

w I
n o o
r
where wo = cutoff frequency of current in frequency domain, radians/second
IO = low-frequency amplitude of current in frequency domain, amperes

per radian/second
r = distance from the antenna in meters
n = characteristic impedance of free space (=120 ohms)
9. The electric field at the observation point is predicted to

reach its maximum value a propagation delay time, t , after the peak

OIH

ignition circuit current occurs.

LIST OF

REFERENCES

 

 

[l]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[ll]

[12]

LIST OF REFERENCES

H. E. Dinger, ”RFI Measurements and Standards", Proceedings of
.2he IRE (Institute of Radio Engineers) May, 1962 pp. 1313.

 

A. C. Doty, "A Progress Report on the Detroit Electromagnetic
Survey", 1971 SAE Transactions No. 710031 pp. 107-119.

 

F. Bauer, "Controlling Radio Spectrum Pollution from Automotive
Engines — Ignition Suppression Updated", 1967 SAE Trans-
actions No. 670103 pp. 681—691.

 

Edward F. Weller, "Radio Frequency Ignition Interference Sup-
pression - 1969", GM Research Publication CHE-878, General
Motors Research Laboratories, General Motors Corporation,
Warren, Michigan.

 

Richard A. Shepherd, James C. Caddie, and Donald L. Nielson,
"Emission Impossible: New Techniques for Suppression of
Automobile Ignition Noise", Stanford Research Institute,
Menlo Park, California under contract FCC-072 with the
Federal Communications Commission January, 1975.

C. C. Eaglesfield, "Motor-Car Ignition Interference", Wireless
Engineer October, 1946 pp. 265-272.

C. C. Eaglesfield, "Car-Ignition Radiation", Wireless Engineer
January. 1951 pp. 17-22.

 

G. F. Newell, "Ignition Interference at Frequencies Below
100 Mc/s: The Mechanism of Its Production", British Broad-
casting Corporation (BBC) Quarterly Autumn, 1954, Vol. 9,
No. 3, pp. 175—184.

 

 

W. Nethercot, "Car-Ignition Interference", Wireless Engineer,
August, 1949 pp. 352-357.

 

Cleon C. McLaughlin, ”Suppression of Automotive Radio Frequency

Interference", Master's Thesis at Texas A & M, 1969. Copy
available at General Motors Institute, Flint, Michigan.

Walter B. Larew, Ignition Systems (Philadelphia: Chilton Book
Company, 1968), p. 131.

 

Ibid, p. 127.

76

[1'3]

[14]

[15]

[16]
[17]
[18]

[19]

[20]
[21]
[22]

[23]

[24]

[25]

[261

[27]

[28]

77

A. P. Young and L. Griffiths, Aytomgbile Electrical Equipment
(Philadelphia: Chilton Company, Inc., 1956), p. 225.

 

R. F. Graf and G. J. Whalen, Automotive Electronics (Indiana-
polis: Howard W. Sams and Company, Inc., 1971) p. 79.

 

Chiltoflls Repair and Tune-up Guide: Chevrolet/GMC Vans (Radnor,

 

Pennsylvania: Chilton Book Company, 1974), p. 184.
Ibid, p. 42.
Walter B. Larew, op. cit., p. 120.
A. P. Young and L. Griffiths, op. cit., p. 343.

Richard R. Burgett, Richard E. Massoll, and Donald R. Van Uum,
"Relationship Between Spark Plugs and Engine-Radiated
Electromagnetic Interference", IEEE Transactions on Electro—
magnetic Compatibility, Volume EMC-16, No. 3, August, 1974
p. 160-172

 

 

A. P. Young and L. Griffiths, op. cit., p. 375.

Walter B. Larew, op. cit., p. 133.

R. F. Graf and G. J. Whalen, op. cit., p. 69

R. W. George, ”Field Strength of Motorcar Ignition Between 40 and
450 Megacycles", Proceedings of the I.R.E., September, 1940
pp. 409—412.

B. G. Pressey and G. E. Ashwell, "Radiation from Car Ignition
Systems", Wireless Eggineer, January, 1949 p. 31—34.

 

"Measurement of Electromagnetic Radiation from Motor Vehicles
(20-1,000 MHz)", SAE J551b, Society of Automotive Engineers,
Two Pennsylvania Plaza, New York, New York 10001 (1973).

International Electrotechnical Commission, International Special
Committee on Radio Interference (CISPR), "Recommendation No.
18/2, Interference from Ignition Systems", (1970). Avail-
able from the American National Standards Institute, care of
the National Electrical Manufacturers Association, 155 East
44th Street, New York, New York, 10017.

H. Dean McKay and Kenneth W. Bach, "Basic Electromagnetic Inter—
ference Measurements on Automobiles", 1971 SAE Transactions
NO. 710027.

 

H. P. Hsu and D. C. Schlick, ”Effect of Distributor Cap on
Radiated Ignition Interference”, 1969 IEEE Electromagnetic
Compatibility Symposium Record Asbury Park, New Jersey
June 17-19, 1969, Published by the Institute of Electrical
and Electronic Engineers, Inc., New York, New York 1969,
pp. 319-324.

 

 

{31)

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

78

R. M. Storwick, D. C. Schlick, and H. P. Hsu, "Measured Statisti—
cal Characteristics of Automotive Ignition Noise", 1973 SAE
Transactions No. 730133.

 

R. A. Shepherd, ”Measurements of Amplitude Probability Distribu-
tions and Power of Automobile Ignition Noise at HF", IEEE
Transactions on Vehicular Technology Volume VT-23, No. 3,
August, 1974.

 

 

Fumio Minozuma, "Radio Noise Interference for Frequency Management-
Automobile Radio Noise and Its Suppression Methods", Received
through private communications.

Robert H. Cannon, Jr., Dynamics of Physical Systems (McGraw-Hill
Book Company, 1967), p. 202.

 

R. Saucedo and E. Schiring, "Introduction to Continuous and.
Digital Control Systems", McMillan Company, 1968 pp. 31-33.

N. N. Rao, Basic Electromagnetics with Applications, (Englewood
Cliffs, New Jersey) 1972 Prentice-Hall, Inc., pp. 373-376).

 

Ron Bracewell, The Fourier Transform and Its Applications, McGraw-
Hill, Inc. 1965, p. 136.

 

Ibid, p. 52.

C. C. Johnson, Field and Wave Electrodynamics, McGraw—Hill, Inc.,
1965 pp. 22-23.

 

M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions

 

with Formulas, Graphs, and Mathematical Tables", U. S. Depart-
ment of Commerce National Bureau of Standards, Applied Mathe-
matical Series 53, June, 1964, p. 487.

 

APPENDICES

APPENDIX A

PROGRAM IGNITI

Descri

APPENDIX A

Description: The computer program, IGNITI, solves equations (3.10),

(3.20), (3.21), and (3.22).

Input variables:

CC

CDG

CSG

CL

TB

TM

coil capacitance, farads

distributor gap capacitance, farads
spark plug gap capacitance, farads
resistance, ohms

inductance, henries

distributor gap breakdown voltage, volts
starting value of time, seconds

maximum value of time, seconds

multiplier, so that (tn+l) = (TM)x(tn)

Output variables:

T(I)
VSG(I)
VC(I)

CUR(I)

time, seconds
spark plug gap voltage, volts
coil voltage, volts

current , amperes

79

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APPENDIX B

PROGRAM IGNITII

9—4
T.)

APPENDIX B

Description: The computer program, IGNITII, solves equations (3.32) and

(3.33)

Input variables:

CC

CDG

CSG

TA

TB

TM

coil capacitance, farads

distributor gap capacitance, farads
spark plug gap capacitance, farads
resistance, ohms

inductance, henries

distributor gap breakdown voltage, volts
time when spark plug fires (t1), seconds
maximum value of time, seconds

multiplier, so that (tn+1) = (TM)x(tn)

Output variables:

RT(I)
VC(I)
CUR(I)
VCT1

DVCTl

time after distributor gap breaks down, seconds
coil voltage, volts

current, amperes

coil voltage when spark plug fires, volts

slope of coil voltage when spark plug fires, volts/second

81

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APPENDIX C

PROGRAM ADP

1f:

Description:

APPENDIX C

The computer program, ADP, solves equations (4.24), (4.27),

and (5.5).

Input variables:

RADIUS

DIST

CC

CDC

CSG

CL

VTl

DVTl

Tl

ZA

ZB

ZM

radius of loop antenna, meters

distance from antenna, meters

coil capacitance, farads

discributor gap capacitance, farads

spark plug gap capacitance, farads

resistance, ohms

inductance, henries

distributor gap breakdown voltage, volts

coil voltage when spark plug fires, volts

slope of soil voltage when spark plug fires, volts/second
time when spark plug fires, seconds

starting value of angular frequency, radians/second
maximum value of angular frequency, radians/second
multiplier, so that (mn

+1) = (2M)x<wn)

Output variables:

W(I)
ANS(I)

ANSDB(I)

angular frequency, radians/second

current, amperes/Hertz

= 20 loglO [ANS(I)]

84

 

F
PHASER(I)
Fl
EMAX(I)
EMAXDB(I)

ANDB(I)

85

frequency, Hertz

phase angle, radians

phase angle, degrees

maximum electric field, Volts/meter
20 loglo [EMAX(I)]

20 loglo [2 x ANS(I)]

 

 

 

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APPENDIX D

PROGRAM EMAX

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APPENDIX D

Description: The computer program, EMAX, solves equation (5.18).

Input variables:

J = data set number (first set, N=l,; second set, N=2; . .
N=O terminates program and prints output)

AA(J) = radius of loop antenna, meters

AR(J) = distance from antenna, meters

WB(J) = angular frequency (mo), radians/second

CURB(J) = current amplitude in frequency domain, amperes/Hertz
TA = starting value of time, seconds

TB = maximum value of time. seconds

TM = multiplier. so that (tn+1) = (TM)x(tn)

WM(J) = cutoff value of angular frequency (mm), radians/second

Output variables:

T(J,I) time, seconds

EMAXT(J,I)

maximum electric field strength, Volts/meter/Hertz

EMAXTDB(J,I) = 20 log10 [EMAXT(J,I)]

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APPENDIX E

PROGRAM EMTBES

 

APPENDIX E

Description: The computer program. EMTBES, solves equation (5.24).

Input variables:

J = data set number (first set, N=1; second set, N=2; .
N=O terminates program and prints output)

AA(J) = radius of loop antenna, meters

AK(J) = maximum value of current in time domain (ono), amperes
AR(J) = distance from antenna, meters

TB = maximum value of time, seconds

T = m lti lie 3 h th t t = ’ '

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Output variables:

T(J,I) time, seconds
EMAXT(J,I) = maximum electric field strength, Volts/meter/Hertz

EMAXTDB(J,I) = 20 log10[EMAXT(J,I)]

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