‘
T ING E FFI C I E NCY O F T H E R E S IS T ANC E
T O 6 000
M E T E RS
D I SS E RTAT I O N
OA RD O F UNI V E R S I TY S T UD I E S
JOH NS HO P K I NS U NI V E R S I T Y
C O NFO R MI T Y W I T H T H E RE ! U I R E ME NT S F O R T H E
D E GR E E O F D OC T O R O F P H I L OSO P H Y
T O TH E B
.
IN
.
U
BY
\N G
.
.
B R O M BA C H E R
BALTI MO R E
I
9
2 2
A
I
3
‘
C O UPLE D A M PLIFI E R
T O 6 00 0
M E T E RS
S T UD I E S
O F TH E
IN
JOH NS H O P K I NS
U NIV E R SI T Y
g.
.
CO NFO R MI T Y W I TH T H E R E ! U I REME NT S F O R
D E GRE E O F D O CT O R O F PH I L OSO P H Y
.
BY
W
.
G
.
B R O M B AC H E R
B A LT I M O R E
1
9
2 2
THE
rin t d fro m
[R e p
e
P H Y S I C AL
T HE
R EV IEW
No 5 No ve m b er
V o l XX
.
.
.
.
,
»
»
.
s
k
U 0
D E T E C T I NG E FF I C I E NC Y O F T H E R E S I STA NC E C A P A C I T Y
M E T E RS
C O UP LE D AM P L I F I E R T O
!
.
W
BY
.
G
B RO M B A C H E R
.
S Y NO P S I S
D etec ti ng
.
Cu rrent A mp l ific atio n
and
E fiic ien cy
.
th e R es is ta n ce
f
o
Co up l ed
c a p ac ity
!
,
t f H ul b urt for m ul a gi v ing a r l t ion b tw n d t t ing
ffi i n y d th on tan t of th t ub and ir u i t h b n xt nd d to
b /A
T h d t ting ffi i n y i d fi n d
wh r A n d b
th am pl i
m t r
r p t i v l y of t h e inp ut grid pot nt ia l and f t h r ti fi d om pon nt of
tud
o utp ut p l t u rr nt It w fo u nd t h t ( ) for ny wa v l ngt h t h r l at ion
th
b tw n b nd A i l in ar ; ( ) for on tant wa v l ng t h b /A vari d wi t h th
o up l ing p i ty in a ordan wi t h t h for m ul a wi thin a b o ut p
n t b ing
pr t i a l l y on t nt for apa iti gr t r t h n 0 up F ; (3) for on t nt p i t i
m t r in
to
and
to
b l A v ari d w i t h w v l ng t h for r ng
f ir gr m n t wi t h t h t h or t i l ur v T h u rr n t m p l i fi at ion n b /E g
wh r E g i th a m p l i t ud f t h pot n t ia l i m pr d u t h grid of t h
ond
m t r
t ub w fo und to b ind p nd n t of t h w v l ngt h t
fo und t b n itiv t th
P l t urr t f v um t b ( R d i t n UV
)w
t r
l t mp r t r
1
I NT R O DUCT O R Y
T w o tu b e A m [) l tfi er
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.
The detecting e fficien cy of t h e res is ta n c e capaci ty cou pled electro n
1
tube ampli fier has been discussed by E O H ul burt
H e derived a
formula which i ndicated the connection between i t and the constan ts Of
the electron tubes and the coupli ng ci rcu i ts
His experi ments showed
that the theoretical relation held i n the regio n fro m 4 0 0 to
meters
‘
!
.
.
.
.
.
.
The detecting e fficien cy
w as
3:
defi ned by the relation li m
A
A
i n which
and
are the ampl i tudes respectively Of the i npu t grid poten tial
and oi the recti fied componen t Of the Ou tpu t plate cu rren t
C onsider the high frequen cy ampli fier Of two tubes as S hown i n Fig I
A
,
,
.
.
1
PH Y S
F ig
.
R EV
.
,
1
8,
1
65 ,
1 921
.
.
1
.
.
W
.
G
.
B R O IWB A
CH E R
.
For this type O f amplifier H ul bu rt derived the following formu la
to the conditions that there be no rectification i n the fi rst tube and
grid fi lamen t curren t i n the second tube
,
(g 2g 3
(g 2g a
3
64
%
)
[x 4 (g 2
)
2
[x 4 (g 1
g2
g i g s)
x 4 x5
2
g3
l
x5 (g 1
x5 g 2
g 3)
.
no
2
g g )]
2
(I )
i n which A is the ampli tude Of the radio frequency potential impressed
0 n the grid of the fi rst tube b e is the recti fied component Of the resul ting
,
radio freq uency cu rren t i n the pl ate circui t Of the second tube ; k is the
ampl ification con stan t of the fi rst tube r1 is the i n ternal resistance O f
the first tube from filamen t to plate
C5 is the fil a m en t grid capaci ty O f
the second tube
Resistances r2 and r3 and capacity C 4 are as shown
i n Fig I
Le t w/ 2 1r be the frequency Of the impressed vol tage
.
!
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.
.
.
.
Le t
1
g1,
OJ
C4
X4
£ 2,
w cs
X5
,
71
1
.
1
£ 3:
O ne
term has not been defined which is
,
n
be
I
I
I
E0
2
where E , i s the ampli tude Of poten tial i mpressed 0 n the grid o f the
second tube n does not depend o n the frequency Of the impressed
vol tage
(See Fig
.
.
.
Le t
g 2g 3
x4
(g 2
g 3)
x 43
65
0
xsg z
I)
,
.
Then more accu rately the formula may be written
,
,
551 23)
x 4g 1
xsg i
)
(2 )
I t is to be noti ced that thi s formula gives the detecting e ffi cien cy in terms
figj
’
g
x
D E T EC T I NG
E
FFI C I E NC Y
OF
A MP L IF I E R
4 35
.
of the constan ts of the electron tubes and the cou pling circui ts Al so
Formul a ( 1 ) i s an approxi mation of
the us e of which i s j usti fied u nde r
obvious condi tions
The ob j ect o f this paper is to make the experi men tal measuremen ts
necessary i n order to test Formula ( I ) for l ong wave lengths and to this
end measuremen ts were made from
to
meters
.
.
!
,
.
2
APPA RA T U S
.
.
The a p paratus consisted O f a condenser poten tial d ivider the am plifier
a nd a D A rson v al galvanometer The arrangemen t is essential ly that
I The potential d ivide r con sisted of the coi l L the W eston
o f Fig
thermo galvanometer T and the conden sers C 1 C2 and C 3 . This appa
1
ratu s has been p reviously described by H ul bu rt and B rei t
The poten
tial impressed on the grid o f fi rst tube may be found from
,
’
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,
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,
,
.
.
A
w( C 1 C2
3
C 20 3)
C 1 C3
i n which I is the e ff ective cu rren t measu red by T
By coupli ng L to a
suitable electron tube generating se t u n modulated high frequency vol tage
O f a smal l known ampli tude and freq uen cy w as i mpressed o n the grid of
the fi rst tube The high resistance leak r0 was con nected across C2 to
insure a defi ni te val ue of the grid poten tial d uri ng the experi men t
The e ffect of r0 u pon the i mpedance o f C2 was negligibl e because C2 was
large (ei ther 0 5 1 o r 2 M P ) and the freq uen c ies used were of the
5
order of 1 0
The ampli fier was a two tube o n e wi th resistance capacity cou pling
The tubes were General E lectric C ompany tubes Rad iat ro n type UV 2 0 1
they were used wi th the filamen t cu rren t Of 9 4 ampere and had a
common plate vol tage su pply of
vol ts Separate storage cell s
supplied each filamen t The plate cu rren t was foun d to be sensi tive to
external temperatu re changes an e ffect explained perhaps by th e
fluctuatio n i n the amou n t of the absorbed gases in the glass wall s of th e
tubes
I t was therefore fou nd necessary to enclose the electron tubes i n
covered cardboard tubes i n order to keep thei r temperatures c o nstan t
The plate battery was sh un ted by a
M E condenser C6 The re
3
3
s is ta n c e r2 was
1 15 X 10
ohms and r3 was 360 X I O ohms
The
resistances r0 r2 and r3 were non i nductive bei ng of the type descri bed
2
by H ulburt
These were found to give satisfactory service The val ue
of the resistance for high frequency curren ts was assu med the same as
that measu red wi th di rect curren t
.
'
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,
,
,
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!
,
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!
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1
2
PH Y S
L oc
.
.
REv
c it
.
.
,
1
6.
2 74 , 1
9 20
.
4 36
W
.
G
.
E KO
M B A CH E R
S
[S
.
E C O ND
E R IE S
.
The change i n the valu e o f the rectified high frequen cy compo n en t o f
the plate cu rren t o f th e second tube of the amplifier designated by b e
w as measu red by a D A rso n va l galvanometer G Fig I
con nected
across a resistan ce r4 placed i n the plate ci rcui t n w as
oh ms
The galvanometer had a resistance o f
ohm s and a sen sibil ity of
am peres per mi lli meter de flection o n a scal e 1 2 5 cms distan t
X
P I and P 2 Fi g I were poten t ial dividers P I serving to keep th e plate
vol tage a t the desi red val ue and P 2 to compensate for the poten tial d rop
i n the resistance 7 4 so that the galvanometer rested approximately at
z ero
W hen the grid vol tage of the fi rst tube was changed a d e flection
of the galvanometer resu l ted which was proportional to the change i n th e
recti fied high frequency componen t o f the ou tpu t plate cu rren t
I t was i mpor tan t that the fi lamen t cu rren ts remain constan t Any
ch ange i n these cu rren ts resu l ted i n a shift of the operating poi n t Of the
tubes The electron tubes were seasoned before every series Of read ings
un ti l a reasonabl y constan t condi tion of fi lamen t cu rren t and electron
emission was reached
I n order to elimi nate the error due to the u sua l
slow d rift of the galvanometer the tw o z ero readings were averaged
It
was fou nd that th e grid leak r0 gave a constan t poten tial Of n early z ero
3
oh ms Thi s
o n the grid o f the fi rst tube when i ts val ue was 2 4 6 X 1 0
F o r large val ues of re the val ue of the grid
val u e was not cri tical
poten tial shi fted when i t was n ecessary to va ry the val ue o f C 3 A
Ko l s te r decremeter calibrated by the B ureau of Standards was used
to determine the wave lengths O f the high frequen cy cu rren t
!
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,
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,
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,
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,
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,
,
!
!
.
3
.
V A R I A T IO N
OF
C O UPL I NG C A P A C I T Y
.
The readi ng o f the cou pli ng condenser C ; was varied at each reading
a n u mber of i n pu t poten tials were impressed o n the grid of the fi rst tube
and the corresponding galvanometer de flection s were noted
From the
reading of T the thermo galvanometer an d a knowledge of the capaci ties
C 1 C 2 and C 3 the amplitud e of the change Of the i npu t grid vol tage A
was comp uted usi ng form ul a
Three sets of readi ngs were taken
at wave lengths 1 0 1 6 30 70 and 6 2 35 meters The resu l ting cu rves
2
wi th b e the ordi nates and A the abscissa are S hown in Figs 2 3 and 4
I t can be seen that for each val ue of C 4 for al l three wave lengths the
2
A cu rves are straigh t lines
This fact has been establ ished by a
be
l arge n u mber o f similar cu rves not shown here The cu rves fo r any one
wave length are plotted from data taken with the p oten tial divider
condensers C2 and C 3 held constan t A C hange i n the val ue of C 3 caused
the curve for any particular val ue o f C 4 to shift an d al so to C hange its
S lop e This i s shown i n Fig 3 by the cu rve marked
T h isY ac t
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A MP L IF I E R
Y OF
4 37
.
“
20 0 10
.
E
8
g
e
.
z
z
5
‘
A
.
d’
50
o
6 00
300
5 00
Fig 3
F ig 2
.
.
.
.
can be explai ned by a shift in the Operati ng poi n t of the fi rst tube because
of a shift i n the n o rmal val ue o f the grid poten tial r0 had the val ue
.
A 6 2 35
'
M
.
It
LU
a
z
’
.
d
O
O
50
’
V O LTS
A
IS O
z
Fig 4
.
3X
.
ohms d urin g these readings Another poin t of i n terest i n these
c urves is that the straigh t l ines do not pass through the origin al though
1
10
5
.
,
4 38
W
G
.
.
E KO
MB A CH E R
.
wi thi n the limi t of experi men tal error they pass th rough a common
2
poi n t o n the A axis This seems to i ndi cate a constan t error i n th e
2
determi nation o f A al tho ugh a check u p of the cal ibrations revealed n o
di ff erences large enough fo r compensation
I t is also of in terest to notice
that fo r each wave length there is practical ly the same cu rren t rang e
2
(b e) bu t that there i s a large range i n the val ue of A ; for 1 0 1 6 meters
0 0 0 6 to
0 0 2 to 0 0 5 and for 6 2 35 meters
0 0 6 to 0 1 5 ; for 30 70 meters
z
0 0 1 5 vol t
The mai n fact however remai ns that the straigh t l i nes were obtained
as is predicted by formu l a ( I )
In order to further test formula ( I ) the sl opes o f the cu rves corre
s p o n d in g to each val ue o f C 4 were determi ned and then p lotted agai n st
val ues of C4 fo r each of the three wave lengths as shown i n Fig 5 That
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0
'
'
6 235
30 70
4 00
Fig 5
.
M M
F
6 00
.
is experi mental val ues o f b o/A are plotted against val ues of C4 Then
from formul a ( I ) the theoretical val ue was computed V al ues of the
constan ts not before given r1 the di rect cu rren t fi lamen t to plate re
3
s is ta n c e o f the fi rst tube
was 60 X 1 0 ohms ; C5 th e fil am en t grid
capaci ty of the second tube was 1 8 M M F This was measured i n i ts
socket and i n cl uded the capaci ty o f i ts lead wi res which were S hort
however As n ei ther n or k were determi ned experi men tally the com
p uted cu rve w as made to coi ncide wi th the experi men tal cu rve at C 4
2
,
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,
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DE TE C T I NG E FF I CI E N C Y
A M PL I FI E R
OF
4 39
.
equa l to 6 2 8 M M F The compu ted cu rves are the broken lines W hi le
the agreemen t between the e xperi men tal and comp uted cu rve is n o t
exact i t is qu ite satisfactory reveal ing no marked di fferen ces i n behavior
for two of the wave lengths considered while for wave len gth
m
the agreemen t is good
No change i n the character o f the compu ted curve was fou nd whether
formula (2 ) or its approxi mation ( 1 ) was used
.
.
,
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4
.
V A R IA T I O N
WA V E LE NGT H
OF
!
.
The coupli ng capaci ty C 4 was kep t at i ts max i mu m val ue o f 62 8 M M F
3
3
r 2 rs and r4 remained at thei r former val ues o f 1 1 5 X 1 0
360 X 1 0 and
3
A S eries o f readings were taken s o that the variation
60 X 1 0 ohms
.
T he
o f detecti ng e fficiency wi th wave length could be d etermined
experimen tal resu l ts are given i n the ful l l ine cu rve of Fig 6
,
'
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!
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.
80
5
3
O
S
MET ER
20 0 0
O
Fig 6
.
6 00 0
4 0 00
.
AS
the curve con necting the sq uare of the in p u t grid poten tial and
the recti fied componen t of outpu t plate cu rren t does not pass through
the ori gin a seri es of readings was taken at each wave length a cu rve
2
d rawn and the slope determined This slope i s b o/A
The experi men tal
cu rves j ust men tioned were straight l ines wi thin experimen tal error
I n order to keep the gri d poten tial of the fi rst tu be constan t fo r the
en tire range of wave lengths used i t was found necessary to fix i ts val ue
3
n ear z ero wh i ch was do ne by maki ng r0 equal 2 4 6 X 1 0 oh ms This
w as tested by ob tain ing the de flection of the galvanometer when the
condenser C 2 w as short ci rcui ted there being no high frequ en cy curren t
i n the in pu t ci rcui ts This test was made when the condensers C 1 and
C 3 had val ues correspondi ng to the range o f wave lengths u sed
C2 was
M M F throughou t the ru n
The compu ted cu rve shown dotted i n Fig 6 was made to agree wi th
the experi mental curve i n the neighborhood o f 2 90 0 meters
I t was
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W
4 40
.
G
.
B R OM B A
CH E R
E
gg ;
.
c o mpu ted from formula
as th e approxi mate fo rmul a ( I ) di ffe red
wi th i t over the range o f wave lengths compu ted
T h e ag reem en t o f the two cu rves is substan ti al above
meters
and i t i s believed would be even better if the apparatus had been
used wi th bette r con trol over the grid potential s The poor agreemen t
at lower wave lengths is d ue to the d i ffi cul ty of keepin g condi tion s
constan t for the enti re range o f observations An u np ubli shed cu rve
detecting e fficien cy agai ns t wave length for the region between
meters gives a straigh t li ne o f abou t the same S lope as the theoretical
curve This is i n agreemen t wi th the straigh t li ne rel ation ob tai ned by
H ul bu r t between 6oo l 6oo meters
Thus the simpl e theory u nder
lying H ul burt s formula is i n agreemen t wi th experimen ts th us far made
I t is seen that the detecting e fficiency at higher wave len gths (lower
frequencies ) becomes i ndependen t of the wave length
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5
.
AMPL IFI CA T IO N
.
I t was necessary to test the i ndepend en ce of
length
By defi ni tion
n
wi th respect to wave
.
50
n
5
E0
2
!
where b e i s the recti fied compo nen t o f the ou tpu t plate curren t and E ,
is the ampl i tude o f the potential variation o n the grid of the second tube
I n order to measu re n the i n p u t vol tage was i mpressed di rectly o n the
second tube the fi rst tube bei ng disconnected and the ou tpu t plate
cu rren t was found for a series of wave lengths As before su fficien t
observations were made for each wave length so that a cu rve could be
Z
d rawn and the slope determi ned
The slope was b o/E O
The cu rves
It was found to be sensibly constan t
s o determined were straight li nes
for al l wave lengths as is shown i n C u rve 3 Fig 6
I f the ordinate of C u rve I be divided by the ordi nate of C u rve 3 at
the same wave length both o f Fig 6 the q uotien t i s the ampl i fication
o f th e cu rren t Obtained by the use o f the amplifyi ng electron tu be
That i s the quotien t gives the n u mber o f ti mes the rectified componen t
of the plate cu rren t b o is i ncreased by the use of two tubes i nstead of
The quotients or cu rren t ampli fications are the ordin ates on the
one
righ t margi n of Fig 6
I f telephones are used the s o u nd i n tensi ty
a mpli fication is proportional to the square of these n u mbers
Thi s problem was suggested to me by D r E O H u l burt now at the
State Universi ty of I owa who derived the form ul a u nderlyi ng the
i nvestigation
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JO H NS H O P K I NS
J une 1 9 2 2
,
.
U NI V E R S I T Y
,
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,
B I O G RA P H I C A L NO T E
W il lia m
.
B rombache r so n o f He nry and E li z abeth ( C ase )
B ro mbache r was bo r n in C leveland O h io Fe b ruary 2 3 1 8 9 1
He
received h is early edu catio n in C h icago H igh Schools I n 1 9 1 5 he re
c e ive d the degree Of B achelo r o f Arts fro m Lake Fo rest C ol lege with
Shield Ho nors and in 1 9 1 7 the degree o f M aste r o f Arts fro m the same
college Th e yea r 1 9 1 8 was S pent i n th e Uni te d S tates Army sta t io ned
a t the B ureau o f Sta ndards Upon le aving the a rmy j oined the B ureau
o f S ta ndards s ta fl
G eo rge
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I n the fall of 1 9 1 9 h e was en te red at th e Ip h n s Hopkin s Unive rsity
a s a grad uate stude nt and as a n instructor i n P h ysics
He fol lowed the
courses o f P rofessors Ames W ood and P fun d i n P hysics Professor
M urnagha n in mathematics an d P rofesso r Reid in G eo physics
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UNI V E RS I TY O F C A L IF O R NIA L IB R A RY ,
’ ‘
1
act
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to
a
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fine
in r
of
in
in
d u e.
c ea s
g
B o o ks n ot
i s m ad e b ef o r e
od
.
T7
75 m