Non-magnetic slug-tuned inductors
by Charles L A Gies
A THESIS Submitted to the Graduate Committee in partial fulfillment of the requirements for the
degree of Master of Science in Electrical Engineering
Montana State University
© Copyright by Charles L A Gies (1952)
Abstract:
The determination of the effects of a nonmagnetic slug for tuning inductors at radio frequencies, to
facilitate the design of coils used in tuned r. f. circuits having a band-pass characteristic was the
primary purpose of this thesis.
The accomplishment of this purpose necessitated the ascertaining of the manner in which the reactance,
the resistance, and the Q of the coil varied with coil size, slug size,and slug position. Equipment
limitations prevented a complete analytical derivation of formulae for the design of non-magnetic
slug-tuned coils. However, sufficient information was obtained to serve as a basis for the design of
non-magnetic slug-tuned coils by use of graphs. NON-MLGiNETIC SLUG™TUNED INDUCTORS
by
.CHARLES L. A0 GIES
/»
A THESIS
S u b m itted to th e G raduate Committee
in,
p a r t i a l f u l f i l l m e n t o f th e r e q u ir e m e n ts f o r "the d eg ree o f
M a ster o f S c ie n c e in E l e c t r i c a l E n g in e e rin g
at
Montana S t a t e C o lleg e
A pproveds
C hairm an. Exam ining Committed
Bbzeman 9 Montana
Ju n e j 1952
'" * • <v,„;
'"O'! /I
N3 W
Ct
3 Li
(Lr^./L
—2 —
TABLE
OF
CONTENTS
Page
Acknowledgment ...............................
3
A b s tr a c t ............................................
4
I n tr o d u c tio n ....................................
5
L im its of th e I n v e s t i g a t i o n .
.
7
Method of I n v e s t i g a t i o n . . . .
9
M agnetic F ie ld T heory. . . . .
11
C o u p le d -C irc u it Theory . . . .
16
S h o rt C o il D is c u s s io n ..................
18
A»
R eactan ce Changes . . .
18
Bo
R e s is ta n c e and Q Changes
21
Summary o f R e s u lts . . . . . .
23
C o n c lu sio n s and Recommendations
25
L i t e r a t u r e C ite d and C o n su lted
26
A ppendix .............................................
27
I
4
103047
'«=*5«=»
ACKNOWLEDGMENT
The a u th o r w ish e s to e x p re s s a p p r e c ia tio n to a l l
members o f th e E l e c t r i c a l E n g in e e rin g S t a f f f o r v a lu a b le
h e lp and s u g g e s tio n s , and p a r t i c u l a r l y to P r o f e s s o r B„ 0 .
S e i b e l 5 u n d er whose s u p e r v is io n th e work was com p leted ;
P r o f e s s o r S . A. W hitt, o f th e I n d u s t r i a l E n g in e e rin g De­
p a rtm e n t and Mr,o- Theodore R 0 Murphy of th e M echanical En­
g in e e r in g D epartm ent.
C h a rle s L. A. G ies
< * 4 ; c =j
ABSTRACT
The d e te r m in a tio n o f th e e f f e c t s o f a .non­
m ag n etic s lu g f o r tu n in g in d u c to r s a t r a d io f r e q u e n c ie s ,
to f a c i l i t a t e th e d e s ig n of c o i l s used in tu n ed r . f .
c i r c u i t s h av in g a h a n d -p a ss c h a r a c t e r i s t i c was th e p r i ­
mary p u rp o se of t h i s t h e s i s .
The accom plishm ent of t h i s p u rp o se n e c e s s ita t e d
th e a s c e r t a i n i n g of th e manner in w hich th e .re a c ta n c e ,
th e re s is ta n c e ^ and th e % of th e c o i l v a r ie d w ith c o i l
s i z e , s lu g s i z e sand s lu g p o s i t i o n . Equipm ent l i m i t a t i o n s
p re v e n te d a c o m p le te ,a n a ly tic a l d e r iv a tio n o f fo rm u lae
f o r th e d e s ig n of n oh-m agnetie s lu g -tu n e d c o i l s . However
s u f f i c i e n t in fo rm a tio n was o b ta in e d to .serve a s a b a s is
f o r th e d e s ig n of n o n -m ag n etic s lu g -tu n e d c o i l s by use of
g ra p h s.
00
INTRQPnGTIPN
The u s u a l r a d io t r a n s m i t t e r c o n s is ts of s e v e r a l
cascad ed s ta g e s - o s c i l l a t o r , b u f f e r , m u l t i p l i e r s , d r i v e r ,
and f i n a l ,
N orm ally th e p l a t e c i r c u i t and o c c a s io n a lly
b o th th e p l a t e and g r id c i r c u i t o f each s ta g e , a r e tu n e d .
T h is tu n in g i s c u s to m a rily acco m p lish ed by v a ry in g th e
c a p a c ita n c e w hich i s in p a r a l l e l w ith an in d u c ta n c e .
In r e c e n t y e a rs th e m a n u fa c tu re rs of t r a n s m i t t e r s
■
have te n d ed t o use a v a r ia b le in d u c ta n c e and a c o n s ta n t
.
c a p a c ita n c e in th e low -powered s ta g e s .
T his h as been
acco m p lish ed by i n s e r t i n g a m e t a l l i c s lu g in to th e in ­
d u c to r and v a ry in g th e s lu g p o s i t i o n -to g e t th e v a r i a ­
t i o n o f in d u c ta n c e ,
At f i r s t , th e ty p e of s lu g m ost com­
monly used f o r t h i s p u rp o se was e i t h e r ir o n o r powdered
iro n .
These m ag n etic s lu g s in c re a s e d th e in d u c ta n c e and
th e Q, of th e in d u c to r , w hich r e s u l t e d in a sh arp r e s o n ­
ance curve an d , in t u r n , r e q u ir e d p r e c i s io n tu n in g . ■
When, a non-m agnetic s lu g , such as b r a s s , was used
th e in d u c ta n c e and th e Q df th e in d u c to r was d e c re a s e d .
Thus, th e reso n a n ce cu rv e was broad en ed and tu n in g was no
lo n g e r so d i f f i c u l t .
The ta n k c i r c u i t was no lo n g e r r e s ­
o n an t a t one fre q u e n c y b u t r e s o n a te d o v e r a s h o r t ran g e
o f f r e q u e n c ie s .
I t fo llo w s th e n , t h a t i f a t r a n s m i t t e r
were c o n s tru c te d u s in g non-m agneti e s lu g -tu n e d in d u c to rs
O
S0C3S
in a l l tu n e d c i r c u i t s e x c e p t th e fre q u e n c y d e te rm in in g
c i r c u i t o f th e o s c i l l a t o r and th e f i n a l s ta g e , o n ly th e
f i n a l s ta g e would r e q u ir e r e - tu n in g when..the fre q u e n c y
o f th e t r a n s m i t t e r was v a r ie d o v er th e s h o rt ran g e, a t
w hich th e s e c o i l s were re s o n a n t.
When t h i s t h e s i s was u n d e rta k e n , th e com m ercial
p r a c t i c e in d e s ig n in g non-m agnetic tu n e d in d u c to rs was
hy th e use of t r i a l and e r r o r m ethods f o r th e p h y s ic a l
s i z e of th e in d u c to r s and s lu g s .
T his t h e s i s r e s e a r c h
was u n d e rta k e n to d eterm in e th e r e l a t i o n s h i p "between
■c o i l and s l u g , s i z e s f o r a g iv e n in d u c ta n c e change and band­
p a s s w id th .
=Y= ■
LIMITS OF THE INVESTIGATION
To f in d th e r e l a t i o n s h i p betw een c o i l and s lu g
s i z e s . f o r a g iv e n in d u c ta n c e change and b a n d -p a ss w id th
th e p a ra m e te rs w hich had to be found w ere:
in d u c tiv e
r e a c t a n c e , e f f e c t i v e r e s i s t a n c e of th e in d u c to r o r c o i l ,
pow er, v o lta g e , a n d .c u r r e n t of th e c o i l ,
A r a d io f r e ­
quency s ig n a l g e n e r a to r , r a d io fre q u e n c y b r i d g e , and a
s u i t a b l e r e c e i v e r was used to m easure th e re a c ta n c e and
e ffe c tiv e re s is ta n c e
of th e c o i l s .
The c u r r e n ts in v o lv e d w ere of th e o r d e r o f te n th s
o f a m illia m p e r e , and th e v o lta g e s w ere o f th e o r d e r of
I v o l t a t a fre q u e n c y o f 2 m e g acy c les, ' T his p r e s e n te d a
d i f f i c u l t in s tr u m e n ta tio n problem w hich was n o t so lv e d
b e c a u se o f equipm ent l i m i t a t i o n s ,
. A ccording to P r o f , F-., E , Terman1-, th e b e s t c o i l
f o r use in a r a d io ta n k c i r c u i t i s one w ith a le n g th to
d ia m e te r r a t i o o f a p p ro x im a te ly o n e.
U sing t h i s r a t i o
and c o n s tr u c tin g c o i l s of th e s i z e t h a t a r e n o rm a lly found
in low -pow ered t r a n s m i t t e r s ta g e s , th e c o i l s used w ere a
o n e -in c h , a t h r e e - q u a r t e r - i n c h , a n d .a o n e - h a lf - in c h in
d ia m e te r.
The in d u c ta n c e o f th e c o i l s was sm all becau se
o f th e dim en sio n l i m i t s from th e J!/d r a t i o and d ia m e te rs ,
I , " T e m a n T F ,E , ,..1.9.37 .- RADIO ENGINEERING pp 5 8 - 4 l
:
MCGraw H i l l Book Compaftyf I n e , , New York and London
■-8 “
The sm a ll in d u c ta n c e r e s u l t e d in a h ig h s e lf - r e s o n a n t f r e ­
quency, w e ll above th e fre q u e n c y a t w hich m easurem ents were
made „
C o n s id e rin g th e fo re g o in g , t h e r e f o r e , t h e r e were
c e r t a i n re q u ire m e n ts to be met in p ro c e e d in g w ith th e i n ­
v e s tig a tio n :
■I 0
Use of a c o i l whose
S/d r a t i o was a p ­
p ro x im a te ly I .
2.
A -sm all c o i l s im ila r to th o s e u sed in com­
m e rc ia l t r a n s m i t t e r s .
3.
A: c o i l whose r e a c ta n c e was w ith in tb,e
ran g e o f th e b rid g e a v a i l a b l e .
W ith th e c o i l s u s e d , i t was n e c e s s a ry to use a fre q u e n c y
o f 2 m eg acy cles t o keep th e r e a c ta n c e w ith in th e ran g e
of th e b r id g e u se d .
T h u s, b ecau se of in s tr u m e n ta tio n d i f f i c u l t i e s ,
t h i s i n v e s t i g a t i o n was lim ite d to th e change o f in d u c ­
ta n c e s , change o f e f f e c t i v e r e s i s t a n c e s 5 and Q o f th e
c o i l s s e le c te d w ith non-m agnetic s lu g tu n in g .
—9 ==
METHOD
BTTESTIGATIOH
The a n a ly s is of th e non-m agnetic s lu g - tu n e d c o i l
by # s a n s of c o u p l e d - c ir c u it th e o ry was u n d erta k en f i r s t .
The la b o r a to r y i n v e s t i g a t i o n fo llo w e d .
The s e l e c t i o n o f c o i l s was made .so t h a t one s e t
o f c o i l s had th e same w ire s iz e and
4/d r a t i o ; a n o th e r
s e t had th e same in d u c ta n c e , barb d i f f e r e n t w ire s iz e s
and le n g th s ;
and le n g th .
and th e th ir d , s e t had th e same w ire s iz e
The s p e c i f i c a t i o n s f o r th e c o i l s a r e ;
.. C o il L en g th
in e h e s
C o n sta n t le n g th
a l l c o ils
1 035
C o n sta n t ^ d
I " d ia m e te r c o i l
3 /4 w d ia m e te r c o i l
l / 2 M d ia m e te r c o i l
I
3 /4
C o n stan t In d u c ta n c e
1 ” d ia m e te r c o i l
3 / 4 ” d ia m e te r c o i l
1 / 2 ” d ia m e te r c o i l
■W ire S iz e
gauge
, 24
1/2
24
24
24
1- 1 / 8
22
1 -3 /1 6
1- 1 / 8
24
28
A p r e lim in a r y i n v e s t i g a t i o n was made a s t o th e
e f f e c t s o f th e ch em ical co m p o sitio n o f th e s lu g on th e r e ­
a c ta n c e and r e s i s t a n c e v a r i a t i o n s o f th e s lu g - tu n e d c o i l .
Tke b r id g e re a d in g s o f th e r e a c ta n c e and r e s i s t a n c e were
i d e n t i c a l w ith in th e a c c u ra c y o f th e b r id g e , f o r th e th r e e
ty p e s o f b r a s s t e s t e d , 62 p e r c e n t, 65 p e r c e n t and 72 p e r
c e n t co p p er.
"3.0=
The v o lta g e a p p lie d to th e re a c ta n c e b rid g e was
c o n s ta n t a t 0 .5 v o l t s and two m egacycles f o r a l l e x p e rl
m e n ta tio n
=H=*
MAGNETIC EIElB THEORY
The in d u c ta n c e of an a i r - c o r e c o i l i s d i f f i c u l t
t o compute and ad d in g a non-m agnetic s lu g in c r e a s e s th e
d iffic u ltie s .
The in d u c ta n c e i s g iv e n "by th e e q u a tio n
w here
L i s in d u c ta n c e o f c o i l
N i s number, o f tu r n s in th e c o i l
gf i s th e m agnetic f l u x of th e c o i l
The d i f f i c u l t y i s in com puting 0 .
The ty p e o f c o i l in
w hich th e m ag n etic f l u x i s e a s i e s t to compute i s a lo n g
s in g le -la y e r c o il.
In t h i s ty p e of c o i l o n ly h a l f of th e
f l u x re a c h e s th e end o f th e c o i l ;
th ro u g h th e c o i l i t s e l f .
th e r e s t le a k s o u t
T h is c a u se s c o m p lic a tio n s in
com puting th e m ag n etic f l u x produced by th e flo w o f c u r­
r e n t in th e c o i l .
An assu m p tio n made by m ost a u th o rs
in th e tr e a tm e n t of lo n g c o i l s i s t h a t th e r e i s a Mc u r­
r e n t sh e e h " in th e c o i l .
T h is i s n o t t r u e w ith an a c tu a l
c o i l as round w ire s w ith i n s u l a t i o n a re u se d .
The use of
round w ire a ls o r e s u l t s in a w in d in g p i t c h w hich w i l l g iv e
a c u r r e n t component p a r a l l e l to th e a x i s .
Eor th e s e re a s o n s
th e g e n e r a lly ad o p ted tr e a tm e n t g iv e s an a p p ro x im a tio n , b u t
th e r e s u l t s a re w e ll w ith in e n g in e e rin g a c c u ra c y i f th e
d ia m e te r of th e w ire i s v e ry sm a ll compared to th e
d ia m e te r o f tHg. c o i l .
The m ag n etic f i e l d i n t e n s i t y o f an s i r - c o r e c o i l
(Hg ) a lo n g th e a x i s of th e c o i l l a
H° _
S trH I 0
." I
.. I " + b
^
l / r s + ^ | -f hj 2
i ~ b
{ r 2+ ( I _ h j2
where
5 i s le n g th of c o i l
h i s d is ta n c e frpm any p o i n t oh th e a x i s to
c e n te r of c o i l
r i s r a d iu s o f c o i l .
The m ag n etic f l u x on th e c o i l a x i s i s g iv e n hy th e equa­
tio n
Po =ZfdoAw here
L
A i s th e a r e a norm al t o th e d ir e c tio n , o f Hg
yU i s p e r m e a b ili ty O
Assuming th e c o i l i s an i n f i n i t e l y lo n g c o i l , th e
f l u x d e n s ity a c r o s s th e m id - s e c tio n i s u n ifo rm and
0 -
Jl
When th e t r a s s ,slu g i s i n s e r t e d in s id e th e c o i l ,
v o lta g e i s in d u ced in th e s lu g .
T h is v o lta g e i s
“1 3 -
The s e lf - in d u c e d v o lta g e in th e s lu g i s a p p ro x im a te ly
z e ro b ec au se th e in d u c ta n c e o f th e s lu g i s p r a c t i c a l l y
z e ro .
The c u r r e n t i n th e s lu g i s d eterm in ed s o l e l y by
th e induced v o lta g e and e f f e c t i v e r e s i s t a n c e o f th e s lu g .
The c u r r e n t,
(eddy c u r r e n t) i s
-r __
e
18 Hi
and i s p r o p o r tio n a l to th e f i e l d o f th e c o i l
The eddy c u r r e n t ( I e ) in tu r n c r e a t e s a f i e l d aro u n d th e
s lu g in o p p o s itio n to th e o r i g i n a l f i e l d and c a u se s a
d e c re a s e in th e o r i g i n a l c o i l f i e l d , .
The s m a lle r
0O
r e s u l t s i n a d e c re a se in 0 S ( s lu g f lu x ) w hich ca u ses th e
c o i l f lu x to in c r e a s e s l i g h t l y and u ltim a te ly a p o in t of
e q u ilib r iu m i s re a c h e d g iv in g a c o n s ta n t r e s u l t a n t f l u x .
W ith no s lu g in th e c o i l , th e f lu x d e n s ity i s un­
ifo rm and p a r a l l e l t o th e a x is a t th e c e n te r s e c tio n of
th e c o i l and d e c re a s e s i n m agnitude and Changes d i r e c ­
t i o n a s th e p o in t in q u e s tio n moves from th e c e n te r t o ­
w ards e i t h e r end of th e c o i l .
c h a n g e s .th is d i s t r i b u t i o n .
The a d d itio n o f th e s lu g
When c u r r e n t flo w s i n th e
s lu g i t flo w s o n ly in th e o u te r p e r ip h e r y b ecau se o f s k in
e ffe c t.
W ith c u r r e n t o n ly in th e o u te r p o r tio n of th e
-1 4 -
s lu g , th e f l u x l i n e s w i l l d i s t o r t due to th e eddy c u r r e n t
a c t i n g as an in s id e boundary o f th e m ag n etic f i e l d .
T his
was p ro v en to be so by th e r e a c ta n c e c u rv e s of a s o li d
s lu g and a .h o llo w s lu g (F ig . 4 ) .
Based on th e fo re g o in g f in d in g s , th e assu m p tio n
can be made t h a t th e t o t a l H v a r i e s as th e H a lo n g th e
c o i l a x is b ecau se a l l th e f lu x goes th ro u g h th e p o r tio n
o f th e s lu g w hich i s c a rr y in g th e c u r r e n t „ W ith t h i s .as-*
su m p tio n , th e f l u x around th e b r a s s s lu g due to eddy
c u r r e n t s sh o u ld be p r o p o r tio n a l to. the- H o f th e c o i l ,
(0 e '
Then a s
00) °
L0 —
Ndgf0
di
B a / ''
—
Lg0
^
s)
Lo
— di 1
and
<
"
1
AL
=
Il
0
Li
0 o " 0e
d (0o
0 e .)
di
th e n
- agfe
^ ~gj
but
0e ^
00 = yvHA of 0e
th e r e f o r e
A
l
=
it
-
w|j.ere K i s a p r o p o r t i o n a l i t y c o n s ta n ts
T his i s s u b s ta n ­
t i a t e d by th e g rap h s ( F ig s . I , 5 and 6 ) o f th e computed
H and th e p e r c e n t AL*.
These c u rv e s have a p p ro x im a te ly
th e same s lo p e in th e l i n e a r p o r tio n Of th e c u rv e Ss
"16==
COUPLED" GIRQUIT THEORY
U sing c o u p l e d - c ir c u it th e o r y , w ith th e b r a s s s lu g
b e in g th o u g h t o f as a s h o r t - c i r c u i t e d c o i l in s id e of th e
a c tu a l c o l l , th e b r a s s s lu g has an impedance o f
Sg =
Rg 4-
juy Lg
and th e c o i l h a s an impedance o f
—
R
+■
juyL j
Then, u s in g Tang’ s 8 c o u p l e d - c ir c u it s o lu t io n , e q u a tin g
r e a l s and im a g in a rie s
PU —
z 12
rn l
4- I 2 2
Rq "h
and
£
X? ™
The unknowns a r e
xLq "
8M
-h
Hg, and Xg and none of th e s e can be
m easured d i r e c t l y w ith p r e s e n t eq u ip m en t.
v a r ie s w ith
s lu g p o s i t i o n b ecau se th e m u tu al in d u c ta n c e betw een two
c o i l s v a r ie s w ith th e f l u x lin k a g e betw een them , and in
t h i s in s ta n c e , i t i s im p o ssib le to d eterm in e th e f lu x
lin k a g e w ith th e equipm ent a v a i l a b l e .
The d . c . v a lu e of
R2 can be found and an approxim ate v a lu e of a . c . r e s i s t ­
ance can be computed by f in d in g th e d ep th of p e n e t r a t i o n
a t S m e g acy c les.
U sin g th e e q u a tio n R — ^©A/J2
and
Tang, K".' Y .T T 9 4 9 , ALTERNATING-CURRENT CIRCUITS,..pp'7
£08-211, The I n t e r n a t i o n a l Textbook Company, S c ra n to n
P e n n s y lv a n ia . ■
-1 7 -
knowing th e d ep th o f p e n e t r a t i o n , Hg can be computed a p ­
p ro x im a te ly .
An ap p ro x im a tio n f o r Lg can a l s o be made
knowing th e d ep th o f p e n e tr a tio n , u s in g o n ly t h a t p o r ­
t i o n o f th e s lu g w hich c a r r i e s c u r r e n t a s a s i n g l e - t u r n
c o i l and com puting th e in d u c ta n c e from
L =
0.0595 r 8 N8
K
w here K i s found fro m .T a b le s d ev elo p ed by Nagaoka3 .
Rg and Xg co u ld be assumed c o n s t a n t , th e
so lv e d f o r d i f f e r e n t s lu g p o s i t i o n s .
If
co u ld be
T h is c a l c u l a t i o n
was made, and th e r e s u l t s showed, t h a t Xg and Rg d id n o t
rem ain c o n s ta n t.
The v a lu e o f Xg w i l l change w ith th e
f l u x o f th e c o il.w h ic h l i n k s th e s l u g .
T h e re fo re , Xg
w i l l be g r e a t e s t when th e s lu g c e n t e r i s a t th e c o i l
c e n te r.
R2 w i l l v a ry o n ly s l i g h t l y w ith a v a r i a t i o n in
s lu g p o s i t i o n .
5.
U . 8 . D epartm ent o f Commerce N a tio n a l Bureau of
S ta n d a rd s , 1937, RADIO INSTRUMENTS MD MEASUREMENTS
CIRCULAR C74, T ab le 10, page 285. U n ite d S t a t e s
Government P r i n t i n g O f f i c e , W ashington, D. 0 .
=18“
SHORT COIL DISCUSSION
Ao
R eaotance Changes
The p h y s ic a l d im en sio n s of th e c o i l s Used in t h i s
r e s e a r c h w ere d eterm in ed upon th e b a s i s of th e fo llo w in g
fa c to rs :
th e
J?/d r a t i o s , equipm ent a v a i l a b l e , and th e
d e s ir e to u se com m ercial ty p e c o i l s .
The ch o ic e o f slu g
was d eterm in ed by e x p e rim e n ta l d a t a .
The in d u c ta n c e
change w ith le n g th of s lu g , Fige- 3$ was found to be a p “
p ro x im a te ly l i n e a r when th e le n g th o f th e s lu g was b e ­
tw een f i v e - s i x t e e n t h s o f an Indh and f o u rte e h “ S ix te e h th s
o f an in c h .
To s im p lif y th e p ro b lem , s lu g le n g th s were
chosen in th e l i n e a r p o r tio n of th e c u rv e .
The manner in w hich th e d ia m e te r of th e s lu g
v a r ie d th e c o i l in d u c ta n c e , F ig , 5 , was found by e x p e r i­
m e n tal d a ta to be a p p ro x im a te ly
- —g- »
The s lu g diaim-
e te r S were chosen so t h a t an a p p r e c ia b le change in in d u c t­
ance would be o b ta in e d .
w e re i
The th r e e slu g d ia m e te rs chosen
s e v e n -e ig h th s o f an in c h , f i v e e ig h th s of an in c h ,
and th r e e - e i g h t h s o f an in c h .
I t was p r e v io u s ly shown, page 14, t h a t th e change
i n in d u c ta n c e o r re a c ta n c e Was p r o p o r tio n a l to th e mag­
n e t i c f i e l d i n t e n s i t y (H0 ) o f th e, c o i l ,
As H i s depend­
e n t upon th e le n g th and d ia m e te r o f th e c o i l s , th e in ­
d u c ta n c e change w i l l a l s o be d ep en d en t upon th e
^ /d
=19=
r a t i o of th e c o i l s .
T h is i s in d ic a t e d by F ig . 5 and
F ig . 6 o • B oth s e t s o f c u rv e s have th e same slo p e in th e
l i n e a r p o r tio n of th e c u rv e « F ig u re 5 i s f o r a c o i l one
in c h in d ia m e te r and one in c h in l e n g th .
has th e ^ame
F ig u re 6 a ls o
J^/d r a t i o , b u t th e d ia m e te r o f th e c o i l i s
t h r e e - q u a r t e r s o f an in c h .
F ig u re 7 a ls o shows t h a t w ith
th e same. I / d r a t i o , th e slo p e of th e re a c ta n c e c u rv e s i s
th e same when th e same d ia m e te r of s lu g i s u se d .
F ig u re s 7 th ro u g h 11 Show how th e in d u c ta n c e v a r ­
i e s w ith le n g th of s lu g , d ia m e te r o f s lu g and
^ /d r a t i o s
o f th e c o i l s i n th e p r o p o r tio n s s t a t e d e a r l i e r *
The in d u c ta n c e o f a c o i l i s d eterm in ed by th e
f l u x ^Linkage.
T re a tin g th e s lu g a s a o h e - tu r n c o i l , as
th e plu g moved tow ard th e c e n te r of, th e c o i l , th e f lu x
lin k a g e in c re a s e d and th e eddy c u r r e n ts in c r e a s e d .
T his
produced an. in c r e a s e in s lu g in d u c ta n c e and s lu g r e a c t ­
ance.
The m u tu al in d u c ta n c e a ls o in c re a s e d a s th e f lu x
lin k a g e betw een th e p o l l ,.and ..slug in c r e a s e d .
e q u a tio n
X1 -
IijiHl2_is.
Eg2
+
Zg2
th e change in r e a c ta n c e i s due to th e term
In th e
"SO*™
WitH % 5 Xg and R 2 v a r y in g , i t i s im p o ssib le to so lv e f o r
any o f them w ith th e d a ta o b ta in e d .
If
power m easurem ents
co u ld have been made, th e e q u a tio n co u ld have been s o lv e d .
Tbe on ly means of doing t h i s know n,to th e a u th o r i s by
c a lo r im e tr y .
-2 1 ”
Bb
R e s is ta n c e and.
Changes
The e q u iv a le n t r e s i s t a n c e o f th e c o i l i s composed
o f two p a r t s :
Rq w hich i s th e a» o . r e s i s t a n c e o f the. c o i l
w ith o u t th e s lu g and th e r e f l e c t e d r e s i s t a n c e w hich i s
g iv e n by
|% j ^ ^2
,
R sa + Xs
d is c u s s io n ,
>
As s t a t e d in th e r e a c ta n c e
Rg, a n d ■Zg v a ry w ith s lu g p o s i t i o n an d , as
o f th e tim e of w r i t i n g , no method o f d e te rm in in g th e v a r ­
i a b l e s h as been found u s in g th e equipm ent a v a i l a b l e .
The e x p e rim e n ta l d a ta c u rv e s o f R e s is ta n c e V ersus
S lu g P o s i t i o n , F ig u r e s 12, th ro u g h 1 7 , in d ic a t e t h a t th e
p o in t o f maximum r e s i s t a n c e v a r i e s xM t h C o il d ia m e te r,
•'\ ‘
s lu g d ia m e te r and s lu g le n g th . W ith, th e - .la r g e s t d ia m e te r
\
c o i l s and s lu g s , th e p o in t o f m a x im u m 'resistan c e o cc u rs
where th e slug, c e n te r i s a p p ro x im a te ly a t th e end o f th e
-
c o il.
’
As th e d ia m e te rs d e c re a s e , th e p o in t o f maximum
r e s i s t a n c e moves tow ard th e c o i l c e n te r .
As was to be e x p e c te d , i f th e c o i l d im en sio n s r e ­
mained c o n s ta n t, th e m agnitude of th e r e s i s t a n c e maximum
d e c re a se d w ith th e d ia m e te r of th e s lu g .
As th e e v id e n c e i s i n s u f f i c i e n t to form any r e ­
l i a b l e c o n c lu sio n s a s to th e v a r i a t i o n s of th e r e s is ta n c e .,
th e manner in w hich Q1 v a r ie s i s a l s o l e f t in d o u b t a s Q,
i s dependent on X and Rj
Q, — Xg/R .
.-2 2 -
The v a r i a t i o n o f Q i s n o t l i n e a r w ith s lu g p o s i­
t i o n 9 n o r does th e g e n e ra l shape of th e s e c u rv e s v a ry con­
s i s t e n t l y w ith v a rio u s
.
X/d r a t i o s .
\
X
"SS"
SUMMARY OF RESULTS
P re lim in a r y i n v e s t i g a t i o n r e v e a le d t h a t b r a s s
s lu g s w ith a p e rc e n ta g e o f copper ra n g in g from 62 to 72
p e r c e n t h ad , w ith in th e a c c u ra c y o f th e r e a c ta n c e b rid g e
u se d , alm o st i d e n t i c a l e f f e c t s on th e r e a c ta n c e and r e - .
s is ta n c e v a r i a t i o n s of th e non-m agnetic s lu g c o i l .
A f te r
t h i s was d is c o v e r e d , a l l f u r t h e r e x p e rim e n ta tio n was done
w ith b r a s s h av in g 65 p e r c e n t copper c o n te n t„
W ith th e d ep th of p e n e tr a tio n o f th e eddy c u r­
r e n t s a c tin g a s f lu x b o u n d a rie s , th e p e rc e n ta g e .of i n ­
d u ctan ce o r re a c ta n c e change was d i r e c t l y p r o p o r tio n a l
to th e m ag n etic i n t e n s i t y d i s t r i b u t i o n alo n g th e a x is of
th e c o i l .
The e q u a tio n f o r t h i s i s
AL =
H
. CUL-
■
w here K i s a p r o p o r t i o n a l i t y
c o n s ta n t.
From c o u p l e d - c ir c u it th e o r y , two e q u a tio n s ex p r e s s th e r e l a t i o n s h i p s of th e r e a c ta n c e and r e s i s t a n c e
w ith in th e s lu g - tu n e d c o i l
R% —
Rq 4-
'gr
Rgs +
Z1
Rg2
~I ; ?
and
: Xl.
”
+
Zg 2
R2
The te rm
-H
i s th e change in r e a c ta n c e due to th e s lu g arid i t 9 p o s i - ,
tio n .
I t i s t h i s te rm w hich i s p r o p o r tio n a l to
»
mF
•
The s o lu t io n o f th e above two e q u a tio n s r e q u ir e d
th e f in d i n g of one a d d i t i o n a l v a r ia b le w hich, a t p r e s e n t,
co u ld n o t be d eterm in ed due to equipm ent l i m i t a t i o n s ,
S u f f i c i e n t d a ta w ere p ro c u re d to show, by means
of c u r v e s , th e tr e n d of th e v a r i a t i o n s o f re a c ta n c e and
r e s i s t a n c e o f th e c o i l .
-2 5 -
CONGLUSIONS AND RECOMMENDATIONS
The non-m agnetIe s lu g tu n in g g iv e s a l i n e a r de­
c re a s e in in d u c ta n c e o v er most o f th e v a r ia b le s lu g p o s i­
tio n ra n g e o
The Q o f th e c o i l i s red u ced s u f f i c i e n t l y . s o
a s to allo w th e c o i l t o be re s o n a n t o ver a sm a ll ran g e of
f re q u e n c ie s w ith o u t r e - t u n i n g „
T hus, th e non-m agnetic
s lu g -tu n e d c o i l can be used t o ad v a n tag e in low-powered
r , f o a m p l i f i e r s , e s p e c i a l l y w ith p en to d e o r beam-power
tu b e s w hich r e q u ir e sm a ll e x c i t a t i o n pow er.
The r e s u l t s o f t h i s t h e s i s in d ic a te t h a t , in t h e .
o p in io n of th e a u th o r , a nomograph could be c o n s tru c te d to
f a c i l i t a t e th e d e s ig n of th e n o n -m ag n etic s lu g - tu n e d c o i l .
To a c h ie v e th e c o n s tr u c tio n of th e nomograph and to prove
i t m a th e m a tic a lly , more in fo rm a tio n on th e s lu g v a r ia b le s
m ust be p ro c u re d .
To o b ta in more in fo rm a tio n a b o u t s lu g v a r i a b l e s ,
th e equipm ent l i m i t a t i o n s m ust be overcom e.
S p e c ia l i n ­
stru m e n ts m ust be c o n s tr u c te d , such as an r . f . v o ltm e te r,
■capable o f m easu rin g 0 . 0 1 m i l l i v o l t s ;
a means o f m easur­
in g power o f th e o r d e r o f m i l l i w a t t s a t r a d io fre q u e n c y ;
a means o f d e te rm in in g th e a c tu a l f i e l d w ith in th e c o i l ;
and some means o f d e te rm in in g Zg, Rg o r
.
“ S6-=?
LITERATURE CITED AHD CONSULTED
C ream er, W- J- , 1948, ELEMENTS OF ELECTRICAL ENGINEERING,
pp„ 228-231, M cGraw-Hill Book' Company I n c . ,
New Y ork, T oronto and London.
H enney, K -, 1941, THE RADIO ENGINEERING HANDBOOK,, p p . 7099, M cGraw-Hill Book Company, I n c . , New
York and London,
Jo rd a n , E- C*, 1950, ELECTROMAGNETIC WAVES AND RADIATING
SYSTEMS, p p . 7 2 - 9 4 , 112-160, P r e n tic e - H a ll,
I n c „, New Y ork.
Reed, M- B - , C o p y rig h t 1948, ALTERNATING-CURRENT CIRCUIT
THEORY, pp- 85-101, 312-318, H arper &
B r o th e r s , New Y ork.
Tang, K- Y ., 1949, ALTERNATING-CURRENT CIRCUITS, p p .2 0 0 217, The I n t e r n a t i o n a l Textbook Company,
S c ra n to n , P e n n s y lv a n ia .
Term an, F . E - , 1937, RADIO ENGINEERING, p p . 14-23 and p .
77, M cGraw-Hill Book C o ., I n c . , New York
•and London.
T im b ie 5 W. H. and Bush, V -, 1947, PRINCIPLES OF ELECTRICAL
ENGINEERING, p p . 362-374, John W iley & S o n s,
I n c . , New Y ork.
U. S= D epartm ent of Commerce, N a tio n a l B ureau of S ta n d a rd s ,
1937, RADIO INSTRUMENTS AND MEASUREMENTS,
CIRCULAR 6 7 4 , p p . 242-285, U n ite d S t a t e s
Government P r i n t i n g O f f ic e , W ashington, D.C.
"27"
APPENDIX
Page
Fig,
Fig.
1 - .Inductance Change and H D i s t r i b u t i o n
v e rs u s S lu g P o s i t i o n f o r a Long C o il
2 - In d u c ta n c e Change v e rs u s L ength of
* * * * *
.Slug,
I
Ii
*
F ig ..
3 - In d u c ta n c e Change v e r s u s S lu g D iam eter
Fig.
4 =, In d u c tiv e R eactan ce v e rs u s S lu g
P o s itio n f o r S o lid and Hollow S lu g s .
F ig .
5
F ig .'
R eactan ce Change and H D i s t r i b u t i o n
v e rs u s S lu g P o s i t i o n . f o r S h o rt C o il .
.6 " R eactance.C hange and H D i s t r i b u t i o n
v e rs u s S l u g .P o s i t i o n : f o r S h o rt C b il .
iii
iv
v
vi
Figo
7 " . R e a c ta n c e . v e rs u s S lu g P o s itio n f o r
C o ils w ith j^/d = I
Fig.
8 - R eactan ce v e rs u s S lu g P o s itio n
Fig,
9 - R eactan ce v e r s u s S lu g P o s i t i o n
i%
F ig .
10 - R eactan ce v e rs u s S lu g P o s itio n
x
Fig.
11 - R eactan ce v e rs u s S lu g P o s i t i o n
xi
Fig.
12 - E f f e c tiv e R e s is ta n c e v e rs u s S lu g
P o s i t i o n f o r th e 750 Ohm, R eactan ce
C o ils o * o o * * e o
Fig,
l
l
S
o
.
.
.
,
.
.
.
*
o
o
o
o
o
14 - E f f e c t i v e R e s is ta n c e v e rs u s S lug
P o s itio n f o r th e C o ils 1 .2 5 " in
L ength <
e
Fig.
v iii
x ii
13 - E f f e c tiv e R e s is ta n c e v e rs u s S lu g
P o s itio n f o r th e 750 Ohm R eactan ce
C
O
Fig.
v ii
*
* • *
e
o
o
*
15 - E f f e c tiv e R e s is ta n c e v e r s u s S lug
P o s i t i o n f o r th e C o ils 1 .2 5 " in
L e n g th ,
o
e
e
e
-
o
e
o
o
e
e
o
x iii
o
* ' o
o
*
O
x iv
xv
«-28 ***
APPENDIX (G o n lld e)
Page
E i g e 16 - E f f e c t i v e R e sista n c e - V ersu s S lu g
P o s i t i o n f o r C o ils w ith I / d = 1» .
F ig . 17 - E f f e c tiv e R e s is ta n c e v e rs u s S lu g
P o s itio n f o r C o ils w ith ^ /d = I .
F i g 0 18 - P h o to g rap h of Equipm ent. ......................
„
xvi
x v ii
x v iii
'
CHANGE
-
PER
CENT
---------<----------
INDUCTANCE
DISTRIBUTION
-
r e l a t iv e
u n it s
------- --------- - ----------
9 -3 /4 "
LENGTH
COIL
3 /4 "
DIAMETER
COIL
5 /8 "
SLUG DIAMETER
□-
DISTRIBUTION
THE
O-
DISTANCE
FROM
COIL
CENTER
IN
%
COIL
OF
FIG. I
LENGTH
H
ALONG
AXIS
CHANGE OF INDUCTANCE
1/16
INDUCTANCE CHANGE AND H DISTRIBUTION VERSUS SLUG POSITION
FOR A LONG COIL
9
CENT
per
—
CHANGE
INDUCTANCE
H*
H*
I
DIAMETER
l"
LENGTH
O - 7 /8 "
O 5 /8 "
A — 3 /8 "
LENGTH
INDUCTANCE CHANGE
OF
SLUG
VERSUS
FIG. 2
IN
1/16
LENGTH
OF SLUG
COIL
COIL
DIAMETER
DIAMETER
DIAMETER
SLUG
SLUG
SLUG
I"
DIA METER
I"
LENGTH
COIL
COIL
LENGTH
SLUG
O - 1/2"
LENGTH
SLUG
A - 5/16"
LENGTH
SLUG
PER
CENT
0 -5 /8 ”
Z
CHANGE -
Vzy y
Z
7
—
,/
iii
/
INDUCTANCE
Z
-i
<
>
0 »——^
O
.
I
____
------- ------------------------ ------------------------------------------------------2
3
SLUG
INDUCTANCE
4
DIAMETER
IN
5
1/8
CHANGE VERSUS SLUG DIAMETER
FIG. 3
6
7
350
r
325
OHMS
300
REACTANCE
—
"
H-
4
250
225
1 -3 /1 6 " LENGTH COIL
3 /4 "
Dl A M.
C O IL
200
5 /8 "
S LU G
LEN G TH
0 - 5 / 8 " D l/ VM. SO LID SI.UG
D - HOLLOVH SLlJG ,
5 /8 " O D .,
I/'2 " I. C).
150
bLUG
POSITION—
INDUCTIVE REACTANCE
DISTANCE
FROM
SLUG
CENTER
TO
COIL
CENTER
IN
1/16"
VERSUS SLUG POSITION FOR SOLID AND HOLLOW SLUGS
FIG. 4
I"
l"
I"
O 3
LENGTH
COIL
Dl A M.
COIL
Z
DIAM
SLUGS
5 / 8 " LENGTH SLUG
□—
1/2"
LENGTH
SLUG
A
5/16" LENGTH
SLUG
Z
- V
REACTANCE —
PER CENT
CHANGE
Z
_
) ---------
z
Z
*
D --------
S
Z
Z
/
Z
/ /
Z
D ---------
n
15
IO
DISTANCE
REACTANCE
CHANGE
FROM
„5
COIL
CENTER
IN
1/16
AND H DISTRIBUTION VERSUS SLUG
FOR SHORT COIL
FIG.
5
POSITION
3 /4 "
LENGTH
3/4"
D IA M .
COIL
COIL
5/8 "
D IA M .
SLU GS
O - 5/8 "
LENGTH
SLUG
a -1 /2 "
LENGTH
SLU G
A - 5/16" LEN GTH
d
SLU G
* 20
<j
H-
cn uj
DISTANCE
FROM
COIL
CENTER
IN
1/16
REACTANCE CHANGE AND H DISTRIBUTION VERSUS SLUG POSITION
FOR SHORT COIL
FIG.
6
Dl AM.
LENGT
SLUG LENGTH
SLUG LENGTH
5 /1 6 "
SLUG LENGTH
7 / 8 " SLUG
5 / 8 " SLUG
DIAM.
DIAM.
3 /8 "
DIAM.
SLUG
DIAM.
200<>i
v ii
REACTANCE
—
ohms
5 /8 "
1/2 "
LENGl
DIAM.
LENGTH
SLUG
POSITION
DISTANCE
FROM
SLUG
CENTER
TO
COIL
REACTANCE VERSUS SLUG POSITION
FOR
COILS WITH L/D = I
FIG. 7
CENTER
IN
1/16
I" DIAM
LONG
COILS
DIAM
COIL
v iii
<
300
O - 5 / 8 . SLUG LENGTH
O —1/2 SLUG LENGTH
A 5 / 1 6 SLUG LENGTH
--------7/8 " SLU G DIAM.
-------- 5 / 8
SLUG DIAM
DIAM.
SLUG POSITION
—
DISTANCE FROM SLUG CENTER
TO
COIL
CENTER
REACTANCE VERSUS SLUG POSITION
FIG. 8
IN I/1 6
I"
DIAM. COIL
3750
1 i- i/e f COIL LENGT
V
5
N
\
350
\
. x ,
325
^
i
rX
.
N
\
300
L s
OHMS
X
\
' s
—
I
— — —O
<
X
\
---------e
\
275
\
< x
<
250
H*
K
X>
T
REACTANCE
__
f /
Xx X
U
X
>
X
X
N
X
225
200
C —
5 /8 "
SLUG
LENGTH
□ —
1 /2 "
SLUG
LENGTH
A — 5/16"
SLUG
LENGTH
---------------7 /8 "
SLUG
DIAM .
x \
X
X
\
X
"
X C
Lx
X
-------------- 5 / 8 "
SLUG DIAM.
-------------- 3 / 8 "
SLUG DIAM
X
------ X
150
SLUG
POSITION
—
DISTANCE
FROM
SLUG
CENTER
REACTANCE VERSUS SLUG
FIG. 9
TO
COIL
POSITION
CENTER
IN
1/16"
-
—n
DIAM.
3750'
1-3 /1 ;"
COIL
COIL
LE NGTH
Z 250
O -
5 /8 "
SLUG
C — 1/2"
SLUG
LENGTH
A — 1/16"
SLUG
LENGTH
------- 5 / 8 "
-------- 3 / 8 "
LENGTH
SLUG D I A V .
SLUG DIAM.
SLUG
POSITION
—
DISTANCE
FROM
SLUG
CENTER
TO
COIL
REACTANCE VERSUS SLUG POSITION
FIG. IO
CENTER
IN
1/16
i
d ia m .
DIAM. SLUG
" CCH L LE NGTH
ohms
375< »
M
REACTANCE
—-
H-
SLUG
LENGTH
SLUG
LENGTH
SLUG
LENGTH
SLUG POSITION
DISTANCE FROM
REACTANCE
SLUG
CEN TER
TO
COIL
CENTER
VERSUS SLUG POSITION
FIG. Il
IN
1/16
X ii
— OHMS
I" D IA M . COIL
V 8 " Dl A M • SLUGS
O — 5 / 8 " LENGTH SLUG
D — 1/2" LENGTH SLUG
A — 5/16" LENGTH SLUG
A
>—
r =
RESISTANCE
Y /
/ 7 /
y%A
320
15
1
IO
SLUG
POSITION
5
—
O
1/16"
RESISTANCE
-
OHMS
I'
DlAM
COIL
5 / 8 " D lAM. SLUGS
O — 5 /8 " LENGTH SLUG
0 — 1/2“ LENGTH SLUG
A - y is "
LENGTH SLUG
“ 1------ ^
'— <----- ■— <
4.5
POSITION —
1/16"
DIAW . COIL
I'
3 / 8 " D I A M . SLUGS
O - 5 / 8 LENGTH SLUG
Q - 1/2 LENGTH SLUG
A - 5/16" LENGTH SLUG
RESISTANCE
—
OHMS
SLUG
r —-t
-/
SLUG
t,
EFFECTIVE
r—
1—
----- L
1/16
POSITION
RESISTANCE VERSUS
FOR THE COILS HAVING
750
FIG. 12
SLUG POSITION
OHMS REACTANCE
h
3 / 4 " DIAM. COIL
5/8 "
DIAM
SLUGS
O - 5 / 8 " LENGTH SLUG
Q - 1/2" LENGTH SLUG
A ~ 5/16" LENGTH SLUG
SLUG
POSITION —
1/16
SLUG
POSITION —
1/16'
SLUG
POSITION -
1/16
3 / 4 " DIAM.
COIL
3 / 8 " DIAM.
SLUGS
O - 5 / 8 " LENGTH SLUG
O - 1/2" LENGTH SLUG
A - 5/16" LENGTH SLUG
R E S IS T A N C E -ohms
RESISTANCE
—
ohms
RESISTANCE
-
ohms
X iii
1 /2 " DIAM. COIL
3 / 8 " D IAM . SLUGS
0 - 5 / 8 " LENGTH SLUG
D — 1/2" LENGTH SLUG
A - 5/16" LENGTH SLUG
EFFECTIVE
FOR THE
RESISTANCE
COILS
VERSUS
HAVING 7 5 0
FIG .‘ 13
SLUG
OHMS
POSITION
REACTANCE
RESISTANCE—
OHMS
xiv
I" Dl A M . COIL
7/8" DIAM. SLUGS
O - 5 / 8 " LENGTH SLUG
O - 4 / 8 " LENGTH SLUG
A - 5/16" LENGTH SLUG
SLUG
POSITION -
1/16
DIAM.
C O IL
DIAM.
SLUGS
5 / 8 LENGTH SLUG
4 /8 " LENGTH SLUG
5/16" LENGTH SLUG
RESISTANCE —
OHMS
I"
5/8"
OO '
A -
SLUG
POSITION- 1/16
RESISTANCE—
OHMS
l" D IA M . COIL
3 / 8 " D IA M . SLUGS
O - 5/8 " LENGTH SLUG
D - 4 /8 " LENGTH SLUG
A - 5/16“ LENGTH SLUG
SLUG
EFFECTIVE
POSITION -
RESISTANCE
FOR THE COILS
FIG.
1/16
VERSUS
1.25"
14
IN
SLUG
LENGTH
POSITION
X V
COIL
D lA M .
° - 5/8" LENGTH SLUG
° ‘ t 8 " LENGTH SLUG
A ~
5/16" LENGTH SLUG
RESISTANCE
—
ohms
3 /4 "
IO
POSITION
SLUG
POSITION
SLUG
POSITION
3/4" Dl AM. COIL
3/8 ’ DIAM
SLUGS
O - 5 /8 " LENGTH SLUG
c _ 4 /8
LENGTH SLUG
A - 5/16" LENGTH SLUG
1/2
DiAM
COIL
3/9"
DiAM
SLUGS
° - 5 / 8 " LENGTH SLUG
4ZS" LENGTH SLUG
A - 5/16 LENGTH SLUG
RESISTANCE
—
ohms
RESISTANCE
-
ohms
SLUG
EFFECTIVE
RESISTANCE
FOR THE COILS
FIG
VERSUS SLUG
1.25"
15
IN
POSITION
LENGTH
I" DlAM
COIL
7/8" DlAM.
SLUGS
0 - 5 / 8 " LENGTH S l UG
O - 1/2" LENGTH SLUG
£• —5/16" LENGTH S l UG
_
RESI STANCE
— OHMS
xvi
POSITION -
1/16
l"
D I AM.
COIL
5/8"
Dl AM.
SLUGS
0 - 5 / 8 " LENGTH SLUG
Ti - 1/2 " LENGTH SLUG
A - 5/16" -ENGTH SLUG
r-d
Dl AM.
IO
SLUG
POSI TI ON -
SLUG
P O SI TI ON—
1/16
„
COIL
O - 5 / 8 " LENGTH SLUG
n - 1/ 2 " l e n g t h s l u g
A*
R E SISTAN C E-
OHMS
R E
S I S TA N C E —
OHMS
SLUG
EFFECTIVE
IO
1/16
RESISTANCE
VERSUS
FOR
WITH
COILS
FIG.
16
SLUG
L/D = I
POSITION
X V il
R E S I S T A N C E — OHMS
4 .0
3 / 4 " D l AM. COIL
5 / 8 " DIAM S L U G S
0 -5 /8 '
LENGTH SLUG
3.5 0 - 1 / 2 "
LENGTH SLUG
A - 5/16" LENGTH SLUG
J
K
I
t
T
2 .5
SLUG
P OSI TI ON —
1/16"
OHMS
4 .0
RESISTANCE—
3.5
3 / 4 " D I AM. COIL
3 /8
D IAM . SLU GS
0 - 5 / 8 " LENGTH SLUG
O - 1/2" LENGTH SLUG
A - 5 / 1 6 ’ LENGTH SLUG
3 .0
r*
2 . 5 (>
15
IO
POSITION
5
-
1/16"
1 /2 " D IA M . C O IL
3 / 8 " D IA M . SLUGS
0 - 5 / 8 " LENGTH SLUG
□ - 1/2" LENGTH SLUG
A - 5 / 1 6 " LENGTH SLUG
RESISTANCE
— OHMS
SLUG
/ (
/
J
SLUG
EFFECTIVE
POSITION —
RESISTANCE
FOR
COILS
FIG.
VERSUS
WITH
1/16"
SLUG
L/D = I
17
103047
POSITION
MONTANA STATE UNIVERSITY LIBRARIES
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