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«Hears? 3 1293 01106 1714
LIBRARY

(416111232: State
Uh“ LI Sity

 

 

This is to certify that the

thesis entitled

The Magnetic Field Measurement
for the K500 Cyclotron

presented by

Hiroji Hanawa

has been accepted towards fulfillment
of the requirements for

Master of Science degmmin Electrical Engineering

 

 

 

. I
Major professor

O

[hue Aug. 8, 1984

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

MSU

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RETURNING MATERIALS:
Place in book drop to
remove this checkout from
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stamped below.

 

 

 

THE MAGNETIC FIELD MEASUREMENT

FOR THE K500 CYCLOTRON

BY

Hiroji Hanawa

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

198A

ABSTRACT

THE MAGNETIC FIELD MEASUREMENT
FOR THE K500 CYCLOTRON
BY

Hiroji Hanawa

This thesis describes the development of an apparatus which
measures the imperfection of the K500 cyclotron magnet.

The K500 magnet has three fold symmetry in its design. We
rotated a coil with its axis parallel to the magnetic field keeping
the same distance from the magnet center. The rotation speed was
regulated by the PLL technique. Therefore, by analyzing the coil
output voltage utilizing the Fourier analyzer, consisting of bandpass
filters, amplitude detectors.and phases meters, we could gain
important information concerning the magnet imperfection. For
example, the amplitude of the first harmonic component and the phase
data were closely related to the superconducting coil centering

problems.

ACKNOWLEDGEMENTS

This research was one of the many cyclotron laboratory projects.
Therefore, the success of this research is owed to all the laboratory
staff, especially to Jack Riedel.

I wish to express my gratitude to my advisor, Dr. Bon Ho, for his

review of the manuscript.

11

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

I.

II.

III.

INTRODUCTION

1.1

1.2

The Cyclotron Overview
Focusing of the Beam
Relativistic Increase of Mass
Higher Energy Cyclotron

MSU Cyclotron

Cyclotron Magnet

REQUIREMENTS AND DESIGN ALTERNATIVES

2.1

2.2

System Requirements

Design Alternatives

HARDWARE ORGANIZATION

3.1
3.2
3.3
3.“
3.5
3.6

3.7

General

Coils and Coil Disk
Driving Mechanism
Bandpass Filter
Amplitude Detector
Phase Meter

System Calibration

iii

Page

vi

1“

1A

18
18

20

22
22
25
no
146
64
6A
68

IV. OPERATION AND RESULTS
14.1 . Operation
N.2 Results

V. CONCLUSION

APPENDIX

REFERENCES

iv

69
69
70
8A

85

91

1.1

3.2
3-3

3.N

LIST OF TABLES

The K500 cyclotron magnet parameters

The coil sorting results

The errors using the bandpass filters

The combination of the values for 1 Hz, 2 Hz, and 3 Hz
bandpass filters

The simulation for 1 Hz, 2 Hz and 3 Hz bandpass filtes

Page
15
32
36

51

60

3.7

3-13
3.1M
3.15

3.16

LIST OF FIGURES

The principle of the cyclotron

Radially decreasing magnetic field strength required
for vertical focusing

K500 cyclotron 2 Kilo Gauss contours

The K500 Cyclotron

The K800 Cyclotron

Prespective view of the magnet for the 500 MeV cyclotron
The whole view of this system

Hardware organization

The coil disk

The test circuit for DC resistance

The flipping coil mechanism

The integrator for the flipping coils

The arrangement using the filter

Two coils relationship

Two coils cannot completely cancel each other
The block diagram of FOCUS 1

The DC amplifier and the phase detector

The frequency divider

The block diagram of this PLL sytem

The small motor with an encoder

Infinite-gain multiple feedback circuits

Multiple feedback bandpass filter

vi

Page

10
12
13
23
214
26
28
28
29
36
37
37
39
111

L12
13
an
117

A7

3.17 The

3.18 The

amplitude detector

phase meter logic for 1 Hz

3.19 Fourier components of a square wave

4.1 The
4.2 The
4.3 The
4.4 The
4.5 The
4.6 The
4.7 The

4.8 The

single coil output (R-15")

single coil output (R-26")

single coil output (R=25.5")

unstabe output due to damaged wire insulation
single coil output and the filter output

1, 2, and 3 Hz filter output for the single coil
bucked out signal from a pair of coils (R=12")

bucked out signal from a pair of coils

4.9 1 Hz square waves are fed to calibrate the system

4.10 Typical results

4.11 The

4.12 The

analyzed data from Figure 4.10

plotted data from Figure 4.11

vii

65
66
67
71
72
72
73
74
74
75
75
76
77
79
81

CHAPTER I

INTRODUCTION

1.1 The cyclotron overview

The cyclotron was the first practical accelerator to produce high
energy particles without the use of extremely high voltages.The
principle of the cyclotron was discovered by E.O. Lawrence in 1929;
the first small cyclotron was built in 1930. It produced 13 Kev H2
ions.

The arrangement of a typical cyclotron is shown in Figure 1.1.The
ion source S is an arc struck in the appropriate gas, for example H2
to provide protons. It is placed between two hollow metal boxes
called "dee" by reason of their shape. A large magnet provides a
nearly uniform magnetic field across the whole area of the dees and
perpendicular to their plane. The dees are connected to a radio
frequency OSCillator so that their potentials relative to ground vary
from positive to negative. When one dee is positive, the other is
negative. The dees are placed inside an evacuated tank (not shown in
Figure 1.1).

Consider the path of a positive ion which is formed at S at a
time when the right dee in Figure 1.1 is negatively charged. The ion

will be accelerated towards the dee, but at the same time the magnetic

Radio {requenCy

T T518812 N OSCI ”OSLO?

 

 

 

 

 

 

 

 

 

 

 

Magnetic field .

Figure 1.1 The principle of the cyclotron.

field will force it to move in a curved path. Inside the dee, rm)
electric «field acts on the particle which, however,will continue to
move in a circular path under the influence of the magnetic field.
While the ion is inside the dee, the oscillator reverses the
polarities so that the left dee of Figure 1.1 becomes negative and the
right dee positive. The ion is therefore accelerated again as it
crosses the gap between the dees, and the whole cycle is repeated many
times (SO-500). Each time the ion crosses the dee gap, it gains
Binetic energy equal to the product of its charge and the potential
difference betweeen the dees.

Let an ion of charge q and rest mass m be moving with velocity

V. The force exerted on it by the magnetic field is:

F = qVB (1.1)

B is the magnetic flux density in webers per square meter.This force
causes the particle to move in a circular orbit of radius r such that
the centrifugal force is equal to F. Thus, ignoring the relativistic
mass increase:

2
qVB= g!_ (1.2)

The distance traveled in a complete circuit is 21rr so that time t
required is:

2hr 2hr
t = rrrrr or V= ‘**‘-

Substituting this value of V into equation (1.2)

qB 2n 2nm (1.3)

——— . -__ or t . -———

m t qB

The operation of the cyclotron depends on the circumstance that the
time t required for a complete revolution of an ion of given rest mass
and charge is independent of the velocity of the ion as long as the
veLocity is low enough that the relativistic mass increase can be

ignored. From equation (1.2), the radius of an orbit is

r = ------ (1.4)

and although higher velocity ions travel in larger circles,tflmflr
higher velocity causes them to make a revolution in just the same time
as slower ions. Because of the result expressed in equation(1.3), the
cyclotron can be operated by the application of a constant
Badiofrequency to the dees, and the dee voltages will always increase
at the right time to cause further acceleration, regardless of the
velocity of the ion and the radius of its path.

The ions spiral out from the center of the cyclotron until they
approach the deflector D which is charged to a negative potential of
about SOKV. The deflector pulls the ions from their orbits and causes
them to leave the dee system. The energy of the particles, from

equation (1.2), will be

r’qu2 (1.5)

where r is the radius at which the ions are extracted from their
orbits by the deflector. Targets may be inserted at T, or the beam may
travel down an evacuated pipe for use at some distance from the
cyclotron.

Equation (1.3) shows that the oscillator must have a frequency v

given by:

1 qB (1.6)
V = --- a -----

1'. 21m

Equation (1.6) gives u in Hz when B is given in weberstxn'square
meter, q is in coulomb and m is in kilograms. In most cyclotrons, the
frequency is adjustable only over a small range so that the magnetic
field strength B is the quantity which is adjusted to satisfy equation
(1.6) for the q/m of the particular type of particle which it is
desired to accelerate. Acceleration of deuterons or helium ions (+2
charge) requires a magnetic field twice as strong as that required for

the acceleration of protons.

1.2 Focusing of the Beam

To obtain a useful beam intensity, the motion of the particles
Inust be confined to a horizontal plane in the center of the dees (the

median plane). lx'there is no focusing of the beam in the vertical

 

 

 

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O

 

 

 

 

tan pct-5E)

 

 

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Akznemcflh%f

 

Distance fmn ”I?“ Center

Figure 1.2 Radially decreasing magnetic field
strength required for vertical focusing.

direction, the particles will wander away from the median plane and
eventually be lost by striking the top or bottom surfaces of the dees.
The required vertical stability of the orbits can be achieved as the
magnetic field decreases by a few percent between the center and the
edge of the magnet.The magnetic field lines thus obtained are shown in
Figure 1.2. A particle traveling in spirals in the plane A-B will
experience:a.force downwards to restore it to the median plane, since
it is not crossing the field lines at right angles. This type of
focusing is similar to the focusing of particles in the fringing field
of magnets. If the magnetic field is drastically reduced to permit
the acceleration of protons, the fractional reduction in the magnetic
field strength at large radii is reduced, so that vertical focusing is
lost. In; is for this reason that many cyclotrons accelerate H2 rather

than proton.
1.3 Relativistic Increase of Mass

The frequency and magnetic field required for acceleration,
equation (1.6), are a function of the mass of the particle. When the

velocity of the particle becomes high, its relativisitic increase of

mass can no longer be ignored. As the particle spirals outwards, a
greater magnetic field is required to satisfy equation (1.6) with the
greater mass of the particle, but then the vertical stability is lost.
For this reason, conventional cyclotrons cannot accelerate particles
to velocities greater than about 0.2 c. The relativistic increase in
mass at this velocity is about 2%; the kinetic energy is about 20MeV

(for a proton).

Figure 1.3

 

 

Higher energy cyclotron magnet
field is not uniform because of
the three radial ridges in the
form of spirals on the faces of
the poles. (K500 cyclotron 2
kilograuss contours)

1.4 Higher Energy Cyclotron

Two ways of obtaining higher energies from cyclotrons have been
devised. In the first, the magnetic field is allowed to increase with
increasing radius to compensate for the increasing mass of the
particles without losing focus of the beam. This is done by suitable
shaping of the pole faces. Vertical stability is then obtained by the
use of radial ridges in the form of spirals on the faces of the poles,
so that the particles pass alternately through regions of higher and
lower magnetic field as shown in Figure 1.3.

The pole gap is smaller between the ridges, so that the magnetic
field strength is greater there. Since the magnetic field lines are
not perpendicular to the median plane in regions where the magnetic
field is increasing or decreasing, vertical forces act on the
particles with the result that they are strongly confined to the
median plane, even though the average field strength is increasing
with increasing radius. This focusing is called the fixed field
alternating gradient and those cyclotrons are called the sector focus
cyclotron (SF cyclotron) or the azimuthaly varying field cyclotron
(AVF cyclotron). MSU cyclotrons are those kind.

In the second, the frequency in equation (1.6) can be changed as
the mass of the particles increase. The constantly changing frequency
permits a group of particles to go through their accelerating cycle
until they are at full energy. In the meantime, though, no more
particles can start from the ion source because frequency is too low
for slow particles to satisfy equation (1.6). As soon as a group of

particles has reached full energy, the frequency of the oscillator is

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.4 The K500 Cyclotron

10

 
             

- REM”

w .I .9...
ammuimn-AW

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Figure 1.4 (cont'd.)

 

 

 

 

 

 

 

 

 

12

The K800 Cyclotron

Figure 1.5

SLPERCGDUCTING CYCLOTRON MAGNET - K - 500 HOV, K; I 160 Nev

 

   

 

OUTER “QQEFNNGS

 

 

HELNJI<UUU

 

 

 

 

 

 

 

 

NbTilN Cu
VWNO"«3

Figure 1.6 Perspective view of the
magnet for the 500 MeV

cyclotron.

13

changed back to its maximum value to permit another group to start
from the-ion source. Thus the beam from a frequency modulated
cyclotron consists of bursts of particles. Those cyclotrons are

called the frequency modulated (FM) cyclotron or synchrocyclotron.

1.5 MSU Cylclotron

MSU Cylotron Laboratory has three cyclotrons. One, which was
called 56MeV, is no longer in use. Another one, which is called K500,
is in operation. The last one is called K800 and is under
construction. K500 and K800 are similar in construction except for
the size difference. Figure 1.4 shows K500. Figure 1.5 shows K800.
These have the sector focus magnet with superconducting coils. With
such a coil, magnetic fields of 50 kilograuss are feasible which is
about three times higher than typical in present cyclotrons, and the
Energy from a structure of given physical size is then nearly Mai
times higher.Thus the K500 MeV cyclotron magnet is approximately the
same overall size and weight as MSU 56MeV cyclotron magnet. The
attractive features of such a cyclotron are small size and low cost“
K500 and K800 cyclotrons also have three dees instead of two. There
are three gaps between three dees so particles can be accelerated

three times instead of two from the radiofrequency voltage.

1.6 Cyclotron magnet

Maj or features of the K500 Cylotron magnet can be seen in Figure

1.6. The basic cyclotron layout is a dee-in-valley design with three

14

Parameter Sheet--500 MeV Cyclotron Magnet

Coil:
# of turns short coils 36 layers x 32 turns/layer = 1152
long coils 36 " x 64 " ” = 2304
total 4 coils = 6912
Nominal current density coil avg. 3,500 amps/cm;
conductor 5,000 amps/cm
Conductor size 0.110"x0.196" = 2.8m5.0m‘n
Design current 700 amps
Stored energy (with iron yoke) 16.9 Mjoules
Inductance (full field) short coils l3.8 Henry
long coils 27.6 "
mutual 13.8 "
Basic winding dimensions
Radial 60" 1.0., 71" O.D. (Ar=5.5")
Axial median plane to stall coil 1.425”
small coil ht. 6.465"
small coil to large coil .375"
large coil ht. 12.930"
total overall 42.390”
Magnet Yoke
Nominal weight 190,000 lbs.
Maximum size 120" dia x 86" high
Material cast 1020 Steel
Magnetic Field:
Average field at extraction radius 4.95 tesla
Max. hill field 5.9 tesla
Max. field in winding 4.4 tesla
Bp (at extraction radius) 3.22 tesla-meter
Magnet bending limit . 5:500 MeV (QZ/A)
Magnet focusing limit E/A=160 MeV (Q/A)
Refrigerator

CTI 1400 with 2 compressors
closed metal system (no gas bag)

Table 1.1 The K500 Cyclotron magnet parameters

15

sectors and three dees. The cyclotron magnet consists of a
cylindrically symmetric yoke and iron ridges with 120 degree symmetry.
The magnet operates at high fields where the steel is approximately
fully saturated. The coil design for the MSU magnet uses a layer-type
winding which is more compact and less expensive than the pancake
winding which has been used in bubble chamber magnets. A listing of
major parameters is given in Table 1.1.

In addition to the main magnet, there are 13 sets of trimming
coils on each hill, which are not superconducting magnet. To bring
lower energy particles out to the extraction radius requires a
reduction both in the oscillator frequency and in the magnetic field.
Reduction of the magnetic field reduces the amount that the field
falls off as a function of radius, and therefore reduces vertical
focusing. It is therefore necessary to build on the pole faces of the
magnet supplementary coils whose currents can be adjusted to give the
right magnetic field profile.

Immediately after we ran the beam in the K500 cyclotron it became
clear that the imperfections in the magnet had a significant
importance in how we were operating the cyclotron. We then started a
detailed study of the imperfections and their origin. There are two
kinds of origins. In the first, the imperfections come from
construction and assembly errors. The pole tips are split in two
parts at a radius of 14 inches. At the extraction radius of 26.0
inches, the pole tip ends and continues with the iron piece attached
to the cryostat. In the second, the coil is supported by nine
symmetrically located support links (three upper vertical, three lower

vertical,three horizontal at the median plane). .The relationship

16

between the coil and a yoke can be adjusted by the nine links. The
incorrect.relationship creates the imperfections of the magnetic

field.

17

CHAPTER 2

REQUIREMENTS AND DESIGN ALTERNATIVES

2.1 System requirements

The intensity of the magnetic field is maximized to more than 50K
gauss, and we need to measure the intensity with the accuracy as small
as 1 gauss. There are four methods to measure the magnetic field.

(1) NMR method: Utilizing the principle of nuclear magnetic
resonance “MUD, we can convert magnetic field intensity into
frequency with high accuracy. This method is the most reliable method
because the accuracy only depends upon the quantum mechanic principle.
Since each measurement needs many steps and adjustments, it is
difficult to apply this method for the automatic high speed
measurement system.

(2) Hall effect method: Utilizing the Hall effect of a
semiconductor, this method converts the intensity of the field into a
voltage. Because a semiconductor is sensitive to temperature, the
accuracy may be as great as 0.1%.

(3) Flip coil method: When we flip a coil in the constant steady
magnetic field, we will get a voltage according to the Faraday's law

of induction. Integrating the voltage over one cycle, we will be able

’18

to measure the field intensity. A flipping coil mechanism and good
integrator. are required.

(4) Moving coil method: A moving coil with its axis parallel to
the magnetic field induces a voltage only if the field changes by time
or space. By this method, we can only find out the field variation.

In deciding the method, we had to consider the special
circumstances. K500 high density magnet design turned out to be very
difficult for us to assess inside when the pole cap was lowered and
the magnet was on. The only space for an ion source is the hole
leading from the outside to the inside of the magnet. Besides this
there is only a 1 inch gap existing between the lower and upper
magnet. The measuring instrumentations have to be placed in this gap.

We decided to choose the moving coil method because we are only
interested in the imperfection of the magnet at this moment. The
magnet was designed to have a perfect three fold symmetry. Any
imperfection of the magnet would end up disturbing this three
fold symmetry. Suppose we were to rotate the coil with its axis
parallel to the field keeping the same distance from the center of the
magnet with the speed exactly 60 RPM, we should get only 3Hz and
higher frequency components from the output voltage of the coil. If
there are 1 or 2 Hz components, this means the magnet is “out of
symmetry. In this way we can simplify the study of the imperfection
of the magnet. Our objective becomes finding 1 and 2 Hz
components(first and second harmonic components) at the same radius.

This moving coil travels along the circular orbit similar to the
orbit which the particle beam travels in the cyclotron. Thus the

magnetic field which this coil is experiencing during traveling is

19

very similar to the magnetic field which the actual charged ion would
be experiencing at the particular radius while the cyclotron is
operating. The 3 Hz component contributes to the focusing beam while
the 1 and 2 Hz components disturb the focusing. This method of
decomposing a signal into harmonic components also eliminates all.tnua
absolute amplitude value drift problems which cannot be avoided in the
absolute amplitude measurement system.

We also arranged the two moving coils 120 degrees apart and
connected opposite polarity so that the main 3 Hz output would cancel
tout, which enabled us to measure 1.2 Hz components with higher

accuracy.

2.2 Design Alternatives

If we assume a coil is rotating at 60 RPM, the output from the
coil will have mainly 3 Hz components and small 1,2,4,5,6,... Hz
components. If we feed this output into a Fourier transform analyzer,
we will get an amplitude which corresponds to the size of the
imperfectiontof each frequency and phase which corresponds to the
position. There are three methods to analyze a signal into Fourier
components.

(1) FFT method: Convert the signal into digital data and then
feed it into the digital computer capable of doing fast Fourier
transformation (FFUO. THlis method requires the high accuracy coil
rotating mechanism.

(2) Lock-in amplifier method: A lock-in amplifier is a
signal recovery instrument, as are also, for example, signal

averagers,correlators, photon counters and electrometers. A lock-in

2O

amplifier perfroms Fourier tranformation using analog multipliers.
Signal recovery instruments can detect even a signal buried in a noisy
enviroment. All signal-recovery instruments can be thought of as
sophisticated filters which accept signal frequencies but reject most
noise frequencies. This method can accept rotating speed change.

03) Active filter method: 1 Hz, 2 Hz and 3 Hz bandpass filters
can be made using operational amplifiers, capacitors, and resistors
only. This method requires accurate speed control.

We chose the active filter method, because this seemed to be less

expensive and to give reasonable accuracy.

21

CHAPTER 3

HARDWARE ORGANIZATION

3.1 General

The first‘step is to divide this large system into smaller
functional blocks. Several functional blocks become one circuit
board. We have to be careful when we divide into physical boxes. Easy
testing, noise probems and interconnecting wiring are things which
have to be considered. Also a completely new system like this usually
needs a lot of modification and addition during the development. So
it is wise to reserve space for those changes. The whole view is shown
in Figure 3.1 and the hardware organization list is shown in Figure
3.2.

Weluuithree sets of 50 coils at 0.5 inch radial increments,
spanning from 2 inches to 26.5 inches. Sets were 120 degrees apart in
azimuth on the disk.

A 150 twisted pair cable was threaded down the 5/4 inch shaft to
a jumper box. In this rotating box we had the option of connecting
any pair of wires to a 100 contact slip ring assembly. The normal
connection was to connect pairs of coils at a given radius in such a

way tnuat the 3 Hz component could be cancelled. On the other hand, we

22

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23

The Magnetic Field Measurement System

 

r-— Mechanical Coils and disk
w—- Driving mechanism (motor and gears)
1— Encoder

1)— Jumper box

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—— Pipe
.— Electrical —— Motor controller Dn'ver PCB
p— Time-marker (TEX 2901) -—- Frequ PCB
1— Power supply 30V 5A —— 12 Bit ADC
1— Analog multiplexer 64 MPUX
APRX
.— Bandpass filters Panel
—— Computer
Filter box
--— Peak hold Sample PCB
y—- Phase meter , Phase PCB
L W
-— DAC 12 Bit DAC

Figure 3.2 Hardware organization

24

could alsoconnect the coils at a given azimuth directly to the slip
ring assembly.

The disc was driven at exactly 60 RPM rotation using the phase-
locked loop DC servo motor technique.

The raw signals are fed to a 64 position reed relay multiplexer.
One output signal was selected out of 50 signals. The signal was then
fed to unethree stage 1,2 and 3 Hz bandpass filters which can be
switched to have gains from 1 tx>10,000 in decade increments.
Following these are the digital phase detectors and the peak hold
circuits. Finally, the maximum amplitude from the peak hold was fed to
an analog-digital converter and to the main VAX-750 computer witnl the

phase data.
3.2 Coils and Coil Disk

We ordered 200 coils wound by a commercial coil winder. These are
honeycomb type coils using #38 wire. The coil dimensions were 0.25
inch ID, 0.5 inch 00, and 0.5 inches high. The mean value of NA(turn x
area) was 0.033 m2 turns. DC resistance was about 33 ohm.

Twenty-five coils were mounted on each of six azimuths of a 0.625
inch thick 010 epoxy glassfiber disk in such a manner that,
equivalently, we had three sets of 50 coils at 0.5 inch radial
increments, spanning from 2 inches to 26.5 inches. Sets were 120
degrees apart in azimuth. The coil disk is shown in Figure 3.3. In
this way, the entire field inside the cyclotron can be measured
Bithout positioning coils each time. To suppress the 3Hz output,

ideally all 150 coils must be identical (at least coils of the same

25

 

 

 

 

Figure 3.3 The coil disk. (150 coils)

26

radius). In reality, those coils are all different physnnnly and
electrically.The coils are sorted according to their characteristics“
The sorting methods are:

1. Using DC standard voltage supply and a digital voltmeter, we
could get 4 digits value ranging from 30 ohm to 33 ohm. 'Nuetest

circuit is shown in Figure 3.4.

DC resistance - -Y;_ = V2-—Bl- (3.1)
I v,- v2

2. By a digital impedance meter (Model 253 Electro Scientific
Industries) we could get a 3-digit accuracy ranging from 1.20 mH to
1.25 mH.

3. Coils are flipped inside a constant magnetic field which was
adjusted to 1K gauss using the NMR equipment. The output voltage is
then integrated over half of a cycle.

We concluded that method 3 is the most suitable for our purpose.
More details will be discussed below. According to Faraday's law of
induction, a.change with time in flux through a coil with N turn will
induce an EMF.

d0

EMF = — —-—- (3.2)
dt

The flux through the coil is given by
0 = NABocose = NAB (3.3)
Where

27

 

 

 

 

 

 

 

 

 

 

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60R PM

 

The flipping coil mechanism.

Figure 3.5

28

.m—wou mcwaa_~w one Low copmemmuew one

 

w

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SEQ eke /_

 

v.0—

e.m ac=m_l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

hm %
se¥s111fiaseseTlllllmL
iQIll .
hagegfi it
e52. .203 immaogxousx
3.0:. is
S .Efim
Raid

. 9
2

6 - angle between the coil axis and the field.
N - turn
A . area

Boa maximum magnetic flux density

The output voltage is

es — —99-- - + NABO sine -99‘ (3.u)

dt dt

Integrating this over a half cycle,the integrator output voltage

kdf “if o-n
I e dt = — ——3—dt . - 0 = 21111130 (3.5)
o oat 0:0

As we can see, the integrator output voltage is independent of the
rotating speed. If we rotate at 60 RPM, the integrator ouptput

voltage, Vout, can be put in terms of R, C, B and NA by the following

equations:
DESEC ~ +10%“:
1 1 dB NA ZBNA
Vout = --*- e dt = *r‘“ NA-*'* dt a ‘--‘{BB = ------- (3-6)

RC 0 RC dt RC J'WKG RC

RCVout 1
NA = ------ = -*- VoutRC [m2] At B=10Kgauss

28 2 ‘

30

The RC constant can be obtained by using the arrangement shown in
Figure 3.5. The RC value is measured to be 0.0113641 second.

The flipping coil mechanism and the integrator are shown in
Figure 3.5 and Figure 3.6. Actual movement of the coil becomes wobbly
instead of the ideal flipping. But the wobbly movement can be
considered as a combination of the ideal flipping action and a simple
parallel movement.A simple parallel movement does not induce any
voltage under a constant magnetic field, as a result, we may ignore
the wobbling, and regard the movement as a simple flipping.

Each coil was measured by two steps. ( 1 ) flip the coil andread
this single coil output.( 2 ) connect the coil to the reference coll
at opposite polarity and flip again, then read this serial coil

output. The outputs should satisfy the following equation.

Single coil output = Reference coil output

+ Serial coil output (3.7)

Typically, the variation is within 0.01%. If the above condition is
not met, there may be unstable contacts at the slipring or the coil
may be insecurely fixed. The measurement result is shown in Table 3.1.
200 coils had been measured and sorted according to the single coil
value. We made 55 groups which consisted of three closely matched
coils.

We tried a different method described below, which was closer to

our final measurement scheme to confirm our result.The result of this

31

n
0
H
r.

condemnation-o

10

(OHM) (MH)

32.260 1 250
31.850 1 240
31.840 1.230
0.000 0.000
31.950 1.240
31.900 1.240
31.370 1.200
31.620 1.230
31.930 1.230
32 730 1.230
32.670 1.250
32.840 1.250
32.780 1.250
32.750 1.250
32.790 1.250
32.870 1.240
32 790 1.250
31.590 1 230
31.860 1 250
32 790 1.250
32.740 1.240
31.850 1.240
31.770 1.240
32.570 1.230
32.530 1 240
32.640 1 230
31.660 1 230
31.690 1.240
32.570 1.230
31.910 1.240
32.120 1.240
31.850 1.240
32.380 1 230
31.510 1.220
32.670 1 240
32.320 1.220
33.060 1.230
32.770 1.230
33.010 1.240
31.970 1.250
31.990 1.240
31.920 1.230
32.560 1 230
31.880 1.240
31.930 1.250
33.130 1.240
31.890 1.250
32.730 1.240
32.500 1.240
32.820 1.250
32.810 1.250
32.720 1.140
32.740 1.250
32.700 1.250
31 890 1 240
37.710 1.250
31.750 1.230
31.540 1 220
31.700 1 240

Table 3.1

V

(VOLT)

.93180
.85540
.85270
.00000
.89020
.88870
.70840
.85170
.83900
.87330
.94610
.96970
.92140
.95350
.95740
.87940
.97470
.86150
.92630
.96360
.91360
.87390
.90510
.87870
.87820
.83450
.86600
.86860
.87600
.93010
.89740
.91670
.83060
.83820
.88130
.83850
.75410
.89800
.81090
.94990
.91230
.86470
.88430
.91010
.91600
.93660
.95630
.86140
.88410
.96720
.96090
.86340
.96470
.97910
.91780
.94680
.85940
.79490
.92180

mmmwmmmmmmmmmmmmmmmmmmmmmmmmmmmmm1110101010101mmmmmmmmmmmmmmmmommm

The coil sorting result

DV

(MV)

'77

'40
'41

13
11
'53
41

'7

'51
'52
'96

'51

'94.
.64999
'34.
.98000
.09800
'23.
'73.
'48.

14

'22
'17

'71

33
31
'65
35
48
'12
16
'71
'135
'9

32

.00000
.64300
'77.
.00000
.05700
.02300
.96400
'78.
'90.
'59.
.08900
.82800
.78200
20.
23.

10400

70300
67000
77000

01700
73000

.81800
.34000
'72.

69100

.20800
30.
'15.
'56.
'26.
.54300
.92500
.85100
'65.
'62.
'54.
'2.
'36.
'18.
'102.
'95.
.54500

25100
12400
09400
03200

86200
45000
16400
06800
63500
10200
67700
88500

06700
37000
67600

76100
78300

.69900
.86000
.55600
22.

57400

.51700
'48.

38300
94000
09800
68900
50400
97700
66000
20400
52600
94000
93000

E

(%)

0.

'1
'1

0.
'0.
'0.
'3.

'1
'1
'1

II I
OO-‘OOOOOOO

0000
.3089
.2998
0000
6753
6916
7419
.3268
.5285

.0076
.2207

.6040

.1986
.3375
.4000
.9073
.6969
.2254
.1215
.5100
.2550
.9456
.4389

.8689
.8922
.6327
.1103
.0528
.9131
.0349
.6176
.3052
.7310
.6165
.8690
.5858
.8769
.5794
.0395
.2377
.3991
.2435
.8224
.3827
.3011
.0599
.3806
.2057
.8157
.5722
.5243
.1074
.5985
.8257
.2134
.2732
.2058
.2917
.1674

OOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO000000000COCO

NS

SQUARE METER
.06738525
.06651735
.06648667
.00000000
.06691267
.06689563
.06484742
.06647531
.06633104
.06672069
.06754770
.06781579
.06726710
.06763176
.06767606
.06678998
.06787259
.06658664
.06732277
.06774650
.06717850
.06672750
.06708194
.06678203
.06677635
.06627992
.06663776
.06666730
.06675136
.06736594
.06699447
.06721371
.06623561
.06632195
.06681157
.06632536
.06536657
.06700128
.06601182
.06759086
.06716373
.06662299
.06684565
.06713873
.06720576
.06743978
.06766357
.06658550
.06684338
.06778739
.06771582
.06660822
.06775899
.06792258
.06722621
.06755565
.06656278
.06583006
.06727165

60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

32.

31

32.

32

32.
32.

32
32
31

32.

32
32

32.

31
31
31

32.
32.

31
31

32.
33.

32

32.
32.
32.
32.
31.
33.

32
32

33.

32
31

32.

32

32.
32.
32.

31

32.

33

32.

32

33.
32.
32.
32.
32.

32

32.

31
31

32.
32.
33.
32.

810 1.230
.000 0.000
.760 1.240
580 1.240
.820 1.240
.940 1.260
750 1.250
570 1.240
.820 1.250
.930 1.220
.750 1.240
810 ' 1.250
.820 1.260
.900 1.250
560 1.230
.850 1.240
.780 1.230
.830 1.230
660 1.230
570 1.250
.910 1.250
.820 1.240
520 1.230
150 1.240
.440 1.230
130 1.260
740 1.240
830 1.250
600 1.240
740 1.230
090 1.230
.420 1.240
.570 1.230
030 1.280
.940 1.260
.620 1.230
730 1.240
.000 0.000
.490 1.230
630 1.230
610 1.240
640 1.250
.940 1.240
770 1.250
.040 1.230
530 1.230
.790 1.260
040 1.230
710 1.250
850 1.250
860 1.250
710 1.240
.480 1.230
710 1.250
.910 1.240
.040 1.270
.990 1.250
270 1.220
730 1.250
220 1.240
790 1.250
Taille :3.1

UImmmmmmmmmmmmmmmmmmmmmmowwmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmom

.87760
.00000
.84730
.90470
.89930
.99390
.94960
.88090
.94940
.73170
.87460
.92560
.98850
.98730
.86990
.88660
.82840
.83780
.86000
.91540
.94580
.95920
.83250
.79100
.82890
.01740
.88440
.97400
.85940
.83180
.79660
.84900
.84670
.08700
.97920
.89010
.90630
.00000
.86190
.86380
.90370
.90620
.94470
.94310
.76510
.84910
.96560
.74180
.91650
.96410
.97030
.91110
.84010
.93280
.88760
.02130
.93850
.80900
.96890
.80580
.95610

'53

17

57

'103
'92

'99

85

'71

'41

'69

11

-189

31

'21

37

(cont'd.)

.03100
.00000
'83.
'29.
'32.

62.

18.
'50.

80700
89000
04200
28400
67800
01800

.48400
'198.
'56.
'5.

38000
40300
48300

.30000

56.
'59.
'44.

23100
94700
58600

.56200
.67400
-71.
'15.

13.
.46500
.06400
.44000
'102.

17300
86600
42100

35200

.35000
'46.
.56100
.39200
'99.
.13000
'82.
'84.
155.
47.
.52800
'24.
.00000
.96300
'67.
'28.
'25.
12.
.84800
'165.
'82.
34.

82600

47600

25000
24500
66000
87500

80800

32500
46300
73200
34100

88000
15700
15400

.64000
'15.
.95300
38.

47200

13000

.21500
-91.
.09900
-44.

89.
.39600
'123.

10100

78100
41600

08000

.06300
'125.
23.

55000
87300

.8940
.0000
.4128
.5039
.5402
.0500
.3149
.8432
.2948
.3443
.9509
.0924
.9660
.9480
.0106
.7516
.7459
.5623
.1999
.2675
.2263
.4630
.6700
.3676
.7255
.4389
.7894
.7175
.2035
.6770
.2612
.3866
.4202
.6242
.8071
.7001
.4182
.0000
.1795
.1350
.4798
.4338
.2080
.1997
.7965
.3850
.5758
.1970
.2608
.5387
.6428
.3576
.5358
.0185
.7549
.5074
.1078
.0749
.6248
'2.
.4025

1166

OOOOOOOOOOOOODOOOOODODOODOOOODDOOOODOOOOOOOOOCOO0000000000000

.06676954
.00000000
.06642533
.06707739
.06701605
.06809070
.06758746
.06680702
.06758519
.06511211
.06673545
.06731482
.06802936
.06801572
.06668206
.06687178
.06621063
.06631741
.06656960
.06719895
.06754429
.06769651
.06625720
.06578576
.06621630
.06835766
.06684678
.06786464
.06656278
.06624924
.06584937
.06644464
.06641851
.06914832
.06792371
.06691153
.06709557
.00000000
.06659118
.06661277
.06706603
.06709443
.06753179
.06751361
.06549153
.06644578
.06776921
.06522685
.06721144
.06775218
.06782261
.06715009
.06634353
.06739660
.06688313
.06840196
.06746136
.06599024
.06780671
.06595389
.06766129

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181

.900 1
.030 1
.710 1
.230 1
.230 1
.200 1
.100 1
.000 1
.000 1
.900 1
.820 1
.950 1
.430 1
.650 1
.830 1
.860 1
.590 1
.950 1
.680 1
.770 1
.790 1
.890 1
.240 1
.830 1
.960 1
.690 1
.510 1
.170 1
.000 0.
.540 1
.940 1
.380 1
.080 1
.550 1
.700 1
.010 1
.960 1
.370 1
.850 1
.760 1
.720 1
.640 1
.540 1
.000 0
.800 1
.440 1
.490 1
.920 1
.640 1
.860 1
.020 1
.750 1
.970 1
.830 1
.130 1
.820 1
.480 1
.770 1
.760 1
.590 1
.680 1

Table

.240
.250
.230
.220
.250
.240
.270
.250
.250
.240
.240
.250
.230
.240
.250
.260
.240
.250
.240
.240
.270
.260
.250
.230
.240
.240
.240
.240

000

.230
.270
.230
.230
.250
.240
.230
.180
.210
.240
.240
.240
.230
.240
.000
.250
.230
.240
.250
.250
.240
.240
.250
.260
.220
.230
.240
.220
.250
.250
.240
.250

3.1

5.87980 -52
5.94520 13
5.85220 '80
5.74300 -188
5.96480 32
5.79770 '133
6.05960 126
5.89590 '36
5.92760 '5
5.89300 '39
5.88750 '45
5.99780 66
5.82150 '111
5.90970 '29
5.94530 13
5.97390 41
5.90270 '29
5.90270 '30
5.87760 '54
5.84980 '81
6.01250 79
5.98850 55
5.89050 '41
5.81600 '113
5.89130 '38
5.87180 '58
5.87110 '59
5.76140 '169
0.00000 0
5.85310 '78
6.00880 77
5.85480 '75
5.77730 '152
5.93820 6
5.93160 '0
5.75230 '17?
5.68260 '246.
5.78820 '142.
5.89230 '39
5.87720 '54.
5.93800 6
5.82830 '103.
5.89690 '34.
0.00000 0
5.91310 '19.
5.89400 '37
5.90170 '30.
5.91670 '15.
5.90160 '30.
5.90110 '30
5.86240 '69
5.89720 '33
5.96600 35
5.74570 '184
5.77720 '152.
5.88910 -42.
5.77910 '151
5.92900 -1
5.93770 6
5.91090 '20.
5.94890 17.

(cont'd.)

34

.84100
.45800
.09500
.64999
.24600
.57001
.88000
.90700
.52800
.94900
.12600
.35500
.15900
.92100
.08500
.25700
.53700
.23600
.61100
.30100
.51000
.76000
.69500
.43200
.90300
.82200
.49700
.00000
.00000
.18400
.94100
.93600
.58000
.69100
.31100
.53999

55000
89000

.36500

80000

.40500

33000
80500

.00000

63400

.84200

70800
39500
57300

.90200
.95400
.98600
.18900
.64000

95000
28600

.99001
.77700
.81500

13000
78000

.8908
.2269
.3503
.1803
.5436
.2518
.1390
.6222
.0932
.6735
.7607
.1186
.8740
.5044
.2206
.6955
.4979
.5097
.9206
.3706
.3404
.9400
.7029
.9123
.6558
.9916
.0030
.8491
.0000
.3180
.3140
.2802
.5722
.1128
.0052
.9930
.1564
.4089
.6636
.9238
.1080
.7420
.5868
.0000
.3310
.6380
.5177
.2595
.5154
.5210
.1793
.5729
.5932
.1127
.5785
.7129
.5623
.0300
.1149
.3394
.2997

OOOOOOOOOOOOOOOOOOOOOOOO000000000000OOOOOOOOOOOOOOOOOO0000000

.06679452
.06753747
.06648099
.06524048
.06776012
.06586187
.06883705
.06697742
.06733754
.06694448
.06688200
.06813501
.06613224
.06713419
.06753861
.06786350
.06705467
.06705467
.06676954
.06645373
.06830200
.06802936
.06691608
.06606976
.06692517
.06670365
.06669570
.06544951
.00000000
.06649122
.06825997
.06651053
.06563012
.06745795
.06738298
.06534612
.06455433
.06575395
.06693653
.06676500
.06745568
.06620949
.06698879
.00000000
.06717281
.06695584
.06704331
.06721371
.06704217
.06703649
.06659687
.06699219
.06777376
.06527115
.06562899
.06690018
.06565057
.06735343
.06745227
.06714782
.06757951

182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200

31

32.
32.
32.
.780
.760
32.
32.
.800
.740
32.
.860
32.
32.
32.
33.
.730
32.
.810

31
32

31
31

31

31
31

.800

660
710
440

950
670

760
840
380
610
250

530

dddflddfldddddddd‘d-‘

.240
.240
.250
.230
.240
.230
.260
.250
.240
.240
.250
.240
.250
.230
.250
.240
.240
.240
.210

mmmmmmmmmmmwmmmmmmm

.90620
.86090
.97690
.86520
.89260
.84450
.98960
.95920
.90170
.89770
.93530
.87660
.97670
.85600
.91630
.80100
.87960
.90100
.71540

'25.
'69.
45.
'65
'38.
'85.
59.
29
'28.
'32.
5.
'53
46.
'73
'13
128
'50.
'28.
'214.

35

27700
46200
50100

.69300

29600
48500
36000

.07400

81700
70000
55200

.87100

29500

.86700
.92800
.50000

95800
56100
67999

-1.

-1.
'0.

'1

'0.
'0.

'0.

'1

'0.
'2.
'0.
'0.

'3

Table 3.1 (cont'd.)

.4261
1710
.7671
1075
6456
.4411
.0007
.4901
4858
5513
.0936
9082
.7805
.2453
2348
1663
8591
4815
.6191

OOOOOOOOOOODOOOOOOO

.06709443
.06657983
.06789759
.06662867
.06693994
.06639352
.06804186
.06769651
.06704331
.06699787
.06742501
.06675817
.06789531
.06652416
.06720916
.06589936
.06679226
.06703536
.06492694

Figure 3.7

11

0%

Ge

 

 

3:de Rank 1513

The arrangement using the filter.

 

DvM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O . .
5 J
COi/ # reading rCadtpt expand W error 7,
1e] -1.99'72
#20 -2.0102 - 0.0199 - 0.0/3 0. 9%
#39 '1-949‘7 -0.62’W -e.ae/5 ? /-7f‘/.
#50 ;2.0063 'O-°/3,/ -a.689/ 0.2%
#35 —/.9855 +0835 +0-O/I7 3 292%
#7 '/°97-’77 +0.06% + 0.4675 0.03%
#17 -2. 8180 -o.0/34 -0.0/8P 0.06%
#15 -2.oo77 -0.95’W ~010/05 ? 2170/1
4:; -/.976/ 110.8329 +0.oo// ? L397,
Table 3.2 Using the bandpass filter, the errors

become as large as 2.3% which corresponds
to 6 = 1.6 mounting angle.

36

 

 

 

 

Figure 3.8 Two coils are not exactly parallel.

6°" )9

L911

 

 
  

‘4 L- PMJS error ¢
Wear)(ai/2-Ca,‘1 >

Figure 3.9 Two coils can not completely cancel each other.

37

approach was unexpected. It showed us the importance of mechanical
accuracy during the coil installation on the disk.

The diagram in Figure 3.7 shows the measurement arrangement. We
noticed that the data from this arrangement deviated from what would
be expected.ffiwnn equation (3.7). After careful examination we found
that the main cause of the discrepency came from the fact that the two
Boils are not exactly parallel even though we planned to mount them
so.

Suppose we have two identical coils which are mounted<n1the
probe in parallel manner. Due to the mechanical tolerance in making
the holes and the coil, an angle may exist between them as shown in
Figure 3.8. As a result, the output voltage will not be able to
cancel.thrlly as expected. As shown in Figure 3.9, the physical
mounting error angle produces a phase difference between the two

output voltages. The output from these two coils is:

A sin (mt+ 0) - A sin mt

= Aisin wt cos 0 + cos wt sin 6 - sin wt} , coso=1

= A sin 0 cos mt . A sin ¢ sin (wt - E ) (3.8)
2 .

where A is the amplitude of one coil.

'nlis equation says that the physical misalignment error anglee
introdces a small signal which has an amplitude of Asimp and a phase

delay of 90°. Table 3.2 shows the data of this measurement.

38

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39

Using the former measurement system with the integrator, we
integrated1from 0 degrees to 180 degrees. Consequently, this 90 degree
out-of-phase signal was cancelled by itself. However, for the system
with bandpass filters, this small signal is retained at the output.
One can conclude that if we consider only the amplitude of the signals
Blone, the checking equation (3.7) will not be satisfied. In the
final measurement in which the coils are not flipped, the results
should be more accurate since the error is proportional to 0050 rather

than sine .
3.3 Driving Mechanism

Since 1, 2 and 3 Hz fixed frequency active bandpass filters are
used to analyze the signal, a constant rotating speed is essential for
this system. This was one of the big unknown problems to be overcome.
First we tried a commercially available DC motor and its controller
FOCUS 1 from WER INDUSTRIAL. FOCUS 1 is using the current feedback
from a shunt resistor and the armature voltage feedback to regulate
its speed. The control circuit block diagram is shown in Figure
3.10. Unfortunately, we found that its regulation error was more than
2% and there was no possibility to improve it.

The only way to eliminate speed errors seemed to be the phase-
locked loop (PLL) technique. We added a rotary encoder which produced
5000 pulses per one revolution on the main shaft. By using Tektronix
2901 time-mark generator we got 5K Hz with 3 Ppm stabiltiy. The 2901
generator derives its stability and accuracy from a temperature

stabilized 10M Hz crystal. The final schematic for the DC power

40

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6 3.03 -1 M- L- 246
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TYP. I F?-_W MAX. \__EEJ__/_
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DIAMAX.

 

 

 

MAX. ll_. 235
DIAMAX.

Figure 3.14 The small motor with an encorder

44

:03

amplifier and the phase detector is shown in Figure 3.11. The
frequency dividers which produce 5K Hz, 1 Hz and 3 Hz from 10K Hz is
shown in Figure 3.12. Fifty percent duty cycle square signals were
produced by putting a flip-flop circuit at the last stage of each
signal. 1 Hz, 2 Hz and 3 Hz were used to test and calibrate bandpass
filters.

The coil disk and DC motor can be regarded as an integrator with
a long time constant. This PLL control system has a block diagram
shown in Figure 3.13. Because of many unknown characteristics, we
first tested this circuit using a small DC motor with a built-in
optical encoder (DTH-2250-V'1 Litton). The characteristics of the
small DC motor are shown in Figure 3.14. We expected that we could
find out the approximate value of the compensation circuit components,
even though the rotor inertia was much smaller than the coil disk
which we had to control. At first we could not make the stable loop
with this small DC motor. We changed the phase detector IC from MC
4044 to LM 565 and we tried to find out the appropriate values. By
using a C.R. BOX, we were able to select a range of resistor-capacitor
combinations. Finally, we found out that 6M0 and 0.001pF were the
best values. The closed loop became stable. The resistor value 6M0
indicated that the phase detector gain is very high. D

For the next step, we used the final driving mechanism with the
encoder but without the disk. We found that 4 flip-flops were
required to reduce the detector gain and noise from the gears before
the phase detector.

After the entire installation of the disk, pipe, and driving

mechanism, we tried the system again. On the first try, the DC motor

45

needed 10A at 25V to rotate the disk at 60 RPM. We found out that the
bearing for the disk was binding. After a small modification of the
bearing, the power reduced to 0.5A at 15V. Then we found the optimum
compensating R.C. values using the same R.C. Box. Those were 1M0 and
0.1uF. At the same time we removed the PNP transistor at the power
amplifier. The original power amplifier had the NPN-PNP complementary
output to reduce the output impedance. While the disk was rotating,
the friction changed at a certain angle and the PNP transistor changed
the state from off to on abruptly. This made an abrupt current
change. This large instantaneous change of current produced a noise
which affected the measurement because this noise had 1, 22,.and 3 Hz

component.
3.4 Bandpass Filter

1 Hz, 2 Hz, and 3 Hz bandpass filter can be implemented using
Only capacitors, resistors and operational amplifiers. Figure 3.15
illustrates the infinite-gain multiple-feedback connection for a pair
of complex conjugate s-plane poles. The amplifier is used in its
inverting configuration, with the + input grounded. Each element Yi
represents a single resister or capacitor. The voltage transfer

function is:

E0 -Y1Y3
Bin 1
Y.<Y.+Y.+Y.+r.>+r.r.+-e-[<Y.+¥.><!.+Y.+Y.>+Y.r.]

46

Em P—

 

Figure 3.15

 

 

 

 

 

 

 

 

 

 

1?
G) 1
a 111.—
EN
R.
’9.
Figure 3.16

47

 

Multiple feedback bandpass filter.

 

Infinite-gain multiple feedback circuit.

In the limiting case as A0 approaches infinity we have:

so - r,r,

8113’ ' ‘1;Tij:§;:§j:§:3‘:‘§;§;“"

If these five elements are chosen as indicated in Figure 3.16, this
circuit becomes a bandpass filter.The voltage transfer function is

then:

-s(""')
Eo RICI
————(s) = ————————————————————————————————————————
Ein 1 1 1 1 1 1
82+s("')("' + "') + ( """ )("' + "')
R5 c, C. 8.0.0, B, R,

Iterms of the bandpass network function:

H°=--—-—v———e ———————————
R: C4
(———)(1 + ——— 1
R. C.

48

 

Tuning this filter appears rather formidable. In practice R1>>R2 and
so R2 can be used to trim the Q. Then, to adjust the center
frequency, R2 and Rs can be simultaneously adjusted by the same
percentage with negligible effect on the Q. The sensitivities of the

network parameters with respect to the elements are shown below.

0110 1

“’0

sw°= s = s

49

S a ———————————————
R2 2(R,+R2) 2
Q 1

s . «—

R. 2
Q Q 1
s - ——————————

In designing, we first chose Ho, C = C3 = C... 1110, Q and

calculated
Q
Ri= .......
HowoC
Q
32.. ...............
(ZQZ - Ho)woC
2Q
R5= ------
01°C

50

FREQ. Q C R1 82 RS

 

 

 

 

 

(or) (roan) (can) (scan)
5. 5.000 34.289 3508.823 318.309
5. 2.500 66.577 7017.645 636.618
5. 1.667 102.846 10524.363 954.737
10. 5.000 68.577 1629.360 636.618
'” 10. 27500 I§7TI§5"32567720"12737237'
10. 1.667 205.691 4887.102 1909.473
20. 5.000 137.155 800.417 1273.237
20. 2.500 274.310 1600.834 2546.473
20. 1.667 411.383 2400.771 3818.946
30. 5.000 205.732 531.887 1909.855
30. 2.500 411.465 1063.774 3819.710
30. 1.667 617.074 1595.341 5728.419
5. 5.000 17.144 1754.411 159.155
5. 2.500 34.289 3508.823 318.309
5. 1.667 51.423 5262.182 477.368
10. 5.000 34.289 814.680 318.309
_;. 10. 2.50 68.577 1629.360
2. 10. 1.667 102.84 « 44 .551 954.737
2. 20. 5.000 68.577 400.208 636.618
2. 20. 2.500 137.155 800.417 1273.237
2. 20. 1.667 205.691 1200.385 1909.473
2. 30. 5.000 102.866 265.943 954.927
2. 30. 2.500 205.732 531.887 1909.855
2. 30. 1.667 308.537 797.671 2864.209
3. 5. 5.000 11.430 1169.608 106.103
3. 5. 2.500 22.859 2339.215 212.206
3. 5. 1.667 34.282 3508.12l 318.246
3. 10. 5.000 22.859 543.120 212.206
3. 10. 2.500 45.718 1086.240 424.412
_3. 10. 1.567 68.564 1629.034 636.491
3. 20. 5.000 45.718 266.806 424.412
3. 20. 2.500 91.437 533.611 848.824
3. 20. 1.667 137.128 800.257 1272.982
3. 30. 5.000 68.577 177.296 636.618
3. 30. 2.500 137.155 354.591 1273.237
3. 30. 1.667 205.691 531.780 1909.473

Table 3.3 The combination of the values of 1 Hz,
2 Hz, and 3 Hz bandpass filters (selected
values are underlined).

51

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65

Ho has to be smaller than 10 to get accurate results and also C values
are limited to less than 51117 because of the availability. We first
made finalist of Q, C, R,, R2,and R5 and chose the practical
combinations. Table 3.3 shows the values for 1 Hz, 2 Hz and 3 Hz
bandpass filters. we also simulated those results using SPICE

program. Those results are listed in Table 3.u.

3.5 Amplitude Detector

The amplitude detector consists of the peak hold circuits and one
12 Bit analogsto-digital converter. The peak voltage of the sine wave
is sampled at exactly 90 degrees from the zero crossing point. A 90
degree sample pulse is generated using 5K Hz main clock and counters
because signal frequencies are precisely tuned by bandpass filters and
the disk driving mechanism.

Figure 3.17 is the schematic of 1 Hz, 2 Hz, and 3 Hz amplitude
detectors. 12 Bit analog-to-digital converter data will be sent to

the main computer.

3.6 Phase Meter

One Hz, 2 Hz, and 3 Hz sine waves from the filters are fed to the
zero cross detector, the square wave outputs of the zero cross
detector are then fed to the phase meter logic. The phase meter
counts the delay from the index pulse by the main 5K Hz clock. The
index pulse is generated in the encoder at zero degrees in each

rotation of the disk. The schematic is shown in Figure 3.18.

66

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Figure 3.19 Fourier components of a
square wave.

67

3.7 System calibration

Bandpass filters are made of R, C, and IC operational.amplifiers
and those components have temperature coefficients and time drifts
which degrade the analyzing accuracy. We fed 1 Hz, 2 Hz, and 3 Hz
square waves to those three filters periodically in place of coil
signals. Efince we knew accurately the input signal amplitude and
phase, we should be able to calibrate the system operation. A 1 Hz
square wave consists of 1 Hz, 3 Hz, 5 Hz, 7 Hz... components. A 1 Hz
bandpass filter rejects all frequencies except for the 1 Hz component.

Figure 3.19 shows those relationships.

68

CHAPTER U

OPERATION AND RESULTS

”.1 Operation

All installation and mapping of the system was completed in
September 1983. It took one week for the installation of the disk and
a week of about 100 maps.

The operation of the system was as follows:(1) Set the cyclotron
magnet<nument to the predetermined value. (2) Select 50 pairs of
coils by selecting cables in the jumper box. (3) Rotate the disk at 60
RPM. (A) Multiplexer select one pair of coils out of 50 pairs. (5)
Read the phase and amplitude of 1 Hz, 2 Hz, and 3 Hz components.
Repeat (A) and (5) until all 50 pairs are finished. Steps (A) and (5)
are controlled by the main computer and all data are stored in the
main computer.

The computer program controlled the operation through
instructions initiated at the terminal. During a run, calibrations for
amplitude and phase were made by feeding 1, 2, and 3 Hz square waves
into the filters. Then the outputs were sampled every three seconds,
and the new values were compared with the previous values. If the
amplitude differences were less than 1%, and the phase difference was
less than 2 degrees, the program will direct the multiplexers to the

next set of inputs.

69

The calibration takes about 50 seconds per step. Since the

difference in amplitude and phase between adjacent radii is

quitesmall, only twenty seconds was needed per step. The total time

for a mapping was about 20 minutes.

M.2 Results

Figure 11.1 is the single coil output at a radius of 15 inches.

The magnetic field changes rapidly along the hills and valleys.

Figure “.2 shows the single coil output at a radius of 26 inches.

It can readily be seen that there are two peaks for a single coil.

These peaks change shape sharply as the radius changes. Figure 11.3

shows a single coil output at 25.5 inches.

We had about 10 coils which had unstable outputs as depicted in

Figure M.A. It had been found in this situation that the output wires

from the coil were touching the pipe due to the damaged wire

insulation.

Figure N.5 is the picture of the raw
inch radius and the outputs of the three
coil and the main 3 Hz components are not
output is highly distorted from the 3 Hz
the details of the filter outputs.

In Figure 4.7 and Figure “.8, two

120 degrees apart are connected to cancel

signal for the coil at a 26
filters. The signal from one
cancelled. We see that 2 Hz

component. Figure A.6 shows

coils at the same radius and

out the 3 Hz component. In

this way, we can measure 1 Hz and 2 Hz components with much higher

accuracy.

70

 

+1.... r

 

(R=15”)

The single coil output.

Figure 4.1

 

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Figure /'3 )

(Ease

 

 

71

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Figure 4.2 The single coil output. (R=26')

We .

 

 

Figure 4.3 The single coil output. (R=25.5")

72

IS

 

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Figure 4.4 The unstable output due to
damaged wire insulation.

73

 

 

 

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3’33? ’rfi‘ni’): '

 

2H2 OU‘E

3Hzout

raw Signal

 

Figure 4.5 The single coil output and
the filter output.

//7/2 O'QV/dl'v

2H, 2%“,

3y; . $VA,‘V

 

Figure 4.6 The 1, 2, 3 Hz filter output
for the single coil. The
filter gain 1000 for 1 and 2 Hz,
10 for 3 Hz.

74

//-/z adv/aw
9pm 1000

2H2 2v/dw
H.=3aH~Iooo

3H2 2 v/éuv
ga:nlooo
rau) Omnv/aw

 

Figure 4.7 The bucked out signal from
a pair of coils. (R=12")

/Hz 0.2vAiw

gam‘looo
2 H2 /v /d-‘v

(gain Iooo

2v/div
3"" 3am IOOO

raw 0.02V/d.‘v

 

 

 

Figure 4.8 The bucked out si nal from
a pair of coils. ?R=2")
One of the trim coils is on.

75

le 0.2V/dw

2H2 2V/d-‘v

3hb 1Wflfiv

3%M4A3
5.30141 (H941 V)

 

 

 

Figure 4.9 1 Hz square waves are fed
to calibrate the system.
(All gain are 1000)

76

Q-SEP-1933 13153141471

413
823

1236
2467
113
139
233

RUN234 13/133733/7334 OLL TC'S OFF.
4444444444444 108 2 3 4444444444
SCYCLO
ICONNECTION : 54
I69!“ 3 3.3 4
100L133: : 342334 34433.
CURRENTIIG : 733.3333 4
CURRENTLITTLE = 733.3333 4
H1 3 54.4
32 : 33.4
H3 : 5324
H4 : .4
H5 2 35 14
H6 : 3734
H7 : .4
H3 : .4
C 1 = 35‘ 4 3333 4
C2 : 3.333333334334
TCA : 3.333333324334
TCB = 3.333333324334
ch : 3.333333364334
TC3 : 3.3333333E+334
TC1 : 3.33333332433.
TC2 : 3.333333324334
rca : 3.333333324334
TC4 : 3.333333364334
TCS : 3.333333324334
Tcs : 3.33333336433.
TC? : 3.333333384334
TCB : 3.333333354334
TC9 : 3.333333324334
TC13 : 3.333333324334
Tc11 = 3.3333333E+33o
TC12 : 3.333333324334
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TC19 : 3.333333324334
TC1B : 3.333333324334
TC1C : 3.333333324334
TC13A : 3.33333332433.
TC133 : 3.333333324334
TC13C : 3.333333334334
IROTATION : 1
SEND
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-1 433.3 2439 4963 3 1216-
-2 233.3 2 293 1215 1233
-2 433.3 1 $33 2426 1233
-3 233.3 2 376 2 775
-3 433.3 1 742 3 773
1 2.3 44 4977 536 1992
26 2.5 34 4793 693 1333
2 3.3 23 2314 633 1977
Figure 4.10 Typical results

77

1652
1652
2331
1997
1235
1235
1349
1334
1.76

42

34
126
169
211
253
296
323
362

27 3.5 73
3 4.3 63
23 '445 33
4 5.3 92
29 545 132
5 643 134
33 645 113
6 743 111
31 7.5 134
7 343 134
32 345 133
3 9.3 99
33 9.5 34
9 13.3 93
34 13.5 33
13 11.3 34
35 1145 33
11 12.3 39
36 12.5 93
12 13.3 133
37 1345 117

'2 433.3 1
-3 233.3 2
-3 433.3 1

-1 43343 2439

216

431

773

967
1377
1243
1234
1169
1366

914
1231
1337
4963
4962

312

522
3693

639

497
427
423
423
429
427
417
413
436
393
375
357
337
312
293
265
233
234
173
163
193
233

1215
2426
2

3
333
323
233
252
224
193
133
173
173
169
174
1
133
193
235
217
222
223
236
256
339
2
597
733
923
3

2
1216
2426
2

3

1363
1363
1652
1665
1511
1562
1412
1464
1336
1394
1273
1336
1233
1276
1146
1213
1379
1133
933
967
737
796
1122
1217
1233
1233
731
775
694
775
649
695
541
562
337
393
234
216
33
917
2374
2413
2232
2271
2135
2117
1924
1372
1645
1121
1433
1541
1633
1193
1225
1233
1233
773
777

Figure 4.10 (cont'd.)

78

154
131
173
124
133

1411

117
214
134
133
273
62
123
412
323
2

5
1236
2463

1536
347
1372
1331
533
1636
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673
735
799
546
593
753
613
1563
543
635
1391
556
192
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373
1652
1652
2339
1993
1235
1235
1291
1541
662
955
792
522
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793
533
734
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596
1546
1657
1469

133

335

433

233
1339

436
1696
1652
1652
2325
2339
1235
1235

395
426
459
493
523
556
537
623
651
634
717
743
731
312
345
376
939
942
973
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1373
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1329
1372
1435
1436
1469
1532
1535
1563
1599
1632
1665
1693
1729
1762
1795
1323
1361
1392
1925
1953
1991
2322
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2121
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81

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82

733.3

733.3

In Figure 4.9, 1 Hz square waves are fed to the filters in
placeof the coil signal. Only 1 Hz and 3 Hz components are existing.
This is used to calibrate the system.

The data in Figure ”.10 are typical measurement results. The
first column consists of coil numbers and negative numbers which
Bndicate the calibration inputs of 1 Hz, 2 Hz, and 3 Hz. The data from
Figure 11.10 is analyzed in Figure )4.11. The analyzed data are plotted
in Figure H.12. We can see the imperfection of the fused pole tip
construction at a radius of about 15 inches.

B1: 1 Hz component amplitude [gauss]

82: 2 Hz component amplitude [gauss]

PHASE 1: phase of 1 Hz component [degree]

PHASE 2: phase of 2 Hz component [degree]

83

CHAPTER 5
CONCLUSION

This method of mapping the harmonic field worked very well.
Repeatability was better than 1 gauss and 2 degrees. This method
does not require the complicated coil positioning mechanism or
extremely stable integrators or the complicated computer software for
Fourier analysis. For those reasons, this method can be the least
expensive and quickest method. Data from this method was used to
adjust the superconducting coil bobbin links.

The method used gives only the harmonic field components and is
lacking the absolute value information. For a complete mapping, which
gives absolute values, other methods have to be used in conjunction
with the methold described. The main purpose of this project was the
centering of the coil and the verification of results of the previous
flip coil arrangement measurement performed during January 1981.

For the K800 cyclotron, we are planning a different scheme. This
scheme involves two steps. The first step measures the center .of the
magnet using the NMR method. The second step involves the movement of
one coil from the center to the periphery. scanning the entire
field.The output signal from the coil is fed to the VF converter.
Integration is done digitally by counting the VF converter output

pulses. Fourier analysis will be done by a computer program.

84

APPENDIX

 

A.1 The pole cap of the K500 is
raised for access inside.

86

 

A.2 Inside of the K500 Cyclotron before mapping
disc is installed. (52" diameter)

 

A.3 Installation of the mapping disc. (150 coils
mounted)

87

oooooobooooooovo-gcao
00..
..‘mm00

 

A.4 Installation of the mapping disc continued.
(150 coils mounted) _

 

A.5 Adjusting the mapping disc rotating bearing.

88 ~

 

A.6 Measurement electronics (bandpass
filter on top in thermally isolated
box).

89

 

A.7 Measurement electronics (phase meter, ADC, peak
hold, multiplexer and DC motor controller).

90

REFERENCES

Blosser, H.G. The Michigan State University Superconducting Cyclotron
Program. IEEE'Transaction on Nuclear Science, Vol. NS-26, No. 2, April
1979. ‘ ‘

Marti, F. and Miller, P. Magnetic field imperfection in the K500
superconducting cyclotron. Tenth Intenational conference on
Cyclotrons, Michigan State UniVersity, 198M.

Graeme J.G., Tobey, C.R., Huelsman, L.P. Operational Mmflifiers-
Design and Applications. New York: McGraw Hill Book Co., 1971

CMOS Integrated Circuits. Motorola Semiconductor Products Inc., 1978.
Linear Databook. National Semiconductor Corporation, 1982.

Full Line Catolog. Precision Monolithics Inc., 1981.

Vladimirescu, A... Newton, A.R. and Pederson, D.O. SPICE Version 201

Users Guide. ‘Department'of Electrical Engineering and Computer
Science, University of California, Berkley, California 9H720 (1980).

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