PROCEEDIKGS OF THE IEEE
302
FEBRUARY
in effect , u"ed
The state-of-the-art for both ce,;ium beams and hydrogen m,!'ers
tram;former of Fig.
has undergone signiticant improvement . c\bsolute accuracy in the
impedance transforming lilters
vicinity of a few parts ill
10" for frequency
measurements is thus
1 was,
[4], [s J.
by "'\; orton in his work 011
ratio
In the tigure, the turns
is x and the a dmit tance }' is arb itrary. In '\ orton's til ter application,
x> 1, the two negative admittances are absorbed b y po"itive
when
confirmed.
R. BEEHLER
HALFORD
R. HARRACH
D.
admittances in the tilter in which the ideal transformer is imbedded
Y be the admittance of an inductor. On the other hand, if
}' i" a real number in Fig. 1, then one obtains a realization of a com­
by letting
D ..-\LLA:-'­
mon ground ideal transformer with two positive and two negative
D. GLAZE
resistors. '\]';0, if }'= l/jwLo, the network elemen\,; can be obtained
C. S:-;lDER
at a single frequency using two positive inductors and two positive
]. BAR�ES
capacitors .
Radio Standards Lab.
In order to re alize a general multiport ideal tran"fonn er , it is
'\"tional Bureau of Standards
necessary and suffi cient to realize the terminal behavior of a four­
Boulder, C olo .
terminal one with an arbitrary turns-ratio. General multiports can
R. VESSOT
H. PETERS
then be constructed by interconnecting many two ports, some of
]. \'A�IEl'
Q uantum
Electronic Devices
\'aria n Associates
Beverly, f.lass.
L. CTJTLER
L. BODILY
Ilewlett-Packard Co.
Palo Alto, Calif.
All appropriate fuur­
and Y
whose coil, are put in parallel or in series
[6].
terminal network is shown in Fig. 2 where
x is the turns-ratio
i s an a rbitrary admittance. This network has the isolatio n property
of the two port in addition to the proper transforming ratio. If
Y is
a
positive real number, the network represents a realization with three
nega tive resistors and four positi ve resistors for any positive turns­
ratio. "-\Iso, if
Y = l/jwLo, then the network elements can be obtained
at a si ngle frequency with four positi ve inductors and three positive
capacitors.
REFEREKCES
III
[1)
131
[41
15]
[6]
liJ
W. Markowitz. R. G. Ibll. II. F. Hastings. R. R. Stone. R. F. C. Vessot. and
H. E. Peters, >lRepurt OIl the freUliellcy of hydrogen, 11 j'requellcy, \'oL 1, nu. 5.
p. 46, July-Aul-:"ust 11)63. The freLluency of 1420405751.734=U.U2 q uu ted ill
this reference was not <.::orr ec tt" d fvf secolld�order UUfJpler shift nor for wall shift.
These corrections are given by]. Vauier, H. E. Peters, and R. F. C. Ve:;:::;ut,
"Exchange collisioJl::), \\ all interactions, and resettability of the hydrogell
maser," IFEI� 1 rallS. on Inslrumentatioll and Aleasuremelli, yul. I�I-13. Pl). 185I�X. December 19M.
S. B. Crampton. D. K. Klemmer. and �, F, Ramsey. "Hyperfllle sel)arathm
uf �ro und state atumic hydrogen," Phys. Re:I• Letters, vol. 11, no. 7, PI>. 338-34U,
Uctuber 1. 1903.
H. E. P eters . J. Hollowa y . A. S. Ha�ley. and L. S. Cutler, ·lIydro�en maser and
cesium beam tube fre4uenCy stand<.uds comparison," AppJ. Phys, LeUas, \'01. 6.
no, 1., pp, 34 ,)5. January 1�65.
H. F. Peter� and P. K�rtascll()ff. "Hydrogen maser frequelH':y comparisun with
Swiss Le�ill.1l atulillC bedJ:! staliddrd," Appl. l-'hys. Lctien. \'OLb, Bu. 2, IJp. 35 '36,
January 1905.
R. E. Beehler. R. C. �1 ockl er. alld .1, �L Richard�on. "Cesiulll beam atomic
timeancl f l eQ u ency �tatJclards." AIetru/oKia, \'01. I. no. 3. Pl'. 114---131. July ]<)65.
L. S. Cu tle r alld C. S. Searle. "SOllie aSIJccts of the theory and l1leasurementof
frequency fiuctuutiullS in frequency standards. If this DSUt\ }Jage 130.
E. H. JullIbon dud 1. E. 1-1cGulli:.;al. "Hydrugen maser freQuen<.:y cornpari::,ull
with Hewlett-Packard S()()UA I..-cSillill bea m :-5tandard," );:\SA Technical :\ute
1':--1 IJ·3292 (August. 1965).
__
--,
l(: 1
z
l'
2'
Fig. l.
:\ COllltllOIl gftllllld t\HJ-jlUIt ideal transformer
with turns-ratio x (Y arbitrd.ry).
2
JC
Fig. 2.
Ideal Transformer Realizations with
2'
:\ two-port id eal trallsfunner induding: isolation
pruperty with turns-ratio x (Y arbitrary).
Negative Resistors
The purpo"e uf this leUt:r is to point out that an ,' I U lI lti port
ideal transformer can be reaJi/.cd at all frequenc ies with p""itive
resi,tor" unly; or, at a "ingle frequenc y, with po,iti\'t:
capacitors and pu,itive inductur" onl y. Thlh, the range of pos sible
aud negative
terminal ur port behaviur of trau"formerle,;s networks with positive
,1I1d other elements i" identical \\ ith that of the
cia"s of networks which nJilLtin ide,Li tralbformers in addition. For
example, the nece",ary ,1IIe1 ,utticient conditiolh on an open-circuit
and negative resistors
impedance matrix in urdt:r that it corre'plJlld to an II-port of
and ideal transformer" ,Ire k no wn
[1 j;
± R,
C's,
with the present result it fol­
low, that th ese conditiolh arc "bu appropriate to networks uf = R.
C's oniy . The r e alization of ideal transformer" with pu,itive and
illten:�t ill c(Jlltlccti()II with receIlt rea]i/.­
ability conditions involvillg ideal t ra l hfortn er , with time-varying
llegative re:-,istor:-- is also of
turtls-raticb
[2 J. [.l j;
such elemenh can, ill fact, be realized by re­
si"tive network, with time-varying resi,tor,.
The equivalent Ilt:twork for a cummon ground two-por t ideal
Manllsc ript r eceh'ed January 5, 1966. This \\'ork was suppurted by the National
Science Foundation under Grant :--lSI' GP·63U.
I t can be shown that if positive and negative resistors are used, a
cummon ground two-port ideal transformer can be realized with no
fewer than two negative re"istors for a t l lfns-ratio different
from + 1.
.\iso, a four-terminal ideal tran"furmer realization which ha,; the
isolatiun property nece,;sarily req uires th ree negative resi"tors, even
for unity turns-rcttin.
The netwurks of Fig.
1
and Fig.
2 have been obtained by llsing a
general synthesis method which will realize any prescribed behavior
pos,;ible for networb of po,itive and negat ive resistors, capa citors,
and inductors on any pos,;ible port structure. This synthe si" tech­
nique
along with a comple te description of the possible port or ter­
minal behavior for this cia,s of networks will appear ebewhere.
Csing the general methods, one can realize a l-tertninal ideal trans­
t -1 negative re"istors, where the counting
that k coi b in "erie" acconnt for k + 1 terminab, not 2k. Thu s,
fortner with no more than
is such
fe wer negative re,i,tors are used t han when 1l1ultiports are con­
"tructed by interconnecting two-purh of three negative re,istol's
each. Abo, at a "ingle frequen cy, a I-terminal ideal tr,lnsformer ca n
be realized with positive inductors (capacitors) a n d
capacitor� (inductors).
/-1 po"itive
PROCEEDINGS LETTERS
1966
The
ACK)';OWLEDGME:\T
The author wi,he,; to thank Prof.
II. E. :\leadows of Columbia
C. ))£:\:\15 \\"EI5S
Columbia lSniversity
\:ew York, \:. Y.
error represents uncertainty in the determination of
the Loran
C frequency.
The following corrections were made
l'niversity for stimulating di,;cussiol1s and helpful suggestions.
Dept . of Elec. Engrg.
303
1) :Vlagnetic Field�The magnetic field was monitored by ob­
serving the Zeeman transition frequency v: (F= I, Inp = ± I->F= I,
11lP=0).
The result was v, = 1070 ± 10 c/s corresponding to a correction
lilI= - 1.4 1 6XlO-9v; c/s= -0.00 16 cis.
The
uncertainty
IS
neg­
ligible.
REFERE),;CES
[1] B. K. Kinarh',ala, "�ece!'.sar:.T and sufficient conditions for the existence of
± R. C n etwork s. " Proc. .",'ymp. Oil Act£z'e XeLu'orks and Ft:'fdb�ck Systems.
Brooklyn, ::':ew York; Polytechnic Press of the P ol ::,r tec hn i c Inst. of Brooklyn,
1960, pp. 189-200.
[2] H. D. Anderson, D. A. Spalliding, and R. \V. ),fewcornb, "The time-variable
trandorrner," Proc. [I'�EfC (Currespondence), \"01. 53, p. 634, June 1965,
[3J B. D. D .:\nderson and R. \Y. :\'ewcomb. ".\ capacitor-transformer gyrator
realization," Pl'r)c. JFj�F (CotrcsjJol!ticncr), \'01. 53, p. 1640, October t965.
[41 E. L. :r\orton, "Transforlt1er hand tilters," LT. S. Patent 1 681 544, August 21,
1928.
[S] T. E. Shea. Tra�15missi(m XetU'orhs a;u!H'a;:·eFiltfY,�'. :'\ew Y or k : Van :-': ost rand,
1929. PP. 325-334.
[61 \iVilhelrn Ca u e r, Synlhes;s of l.inear ConUlZUllicalioH .Ye!worl.'s, \,015. I and II.
)jew York: �lcGraw-llill, 1958. pp. 16;-170.
.
2)
Temperatllre�The
maser
was
operated
at
40°C , so that
.1 ],=0.0 ,
3) \\ ' a ll Shift- The maser has a S.7-inch diameter bulb so that
.1 , =0. 0 .
-I) Cavity Tuning---The cavity which was under thermal control
Wii' tUlled a t the beginning of the run. Du ri ng the run the maser's
frequency W;h monitored by compari,;on to a ,eco n d maser. The es­
timated limit to the etTen of mistuning i s
::'::0.00 13
cis
so that
De= ±0.00 1 3 c/s.
The corrected frequency is
Vll(H) = 1420405772.9918
±
0.0013 c/s.
HARVARD UNIVERSITY
:\ crystal oscillator was phase locked to the maser and a 100 kc/s
reference signal was transmitted by coaxial cable to the Cruft Lab­
oratory where it was compared continllously with the Loran C sign al
A Direct Frequency Comparison of Hydrogen Masers
The result was
in Separate Laboratories by Concurrent Monitoring
V/l(Il)
of Loran C Signals
of the absolute freq Ul' llcy rep rod ucibi lit y of the :'Homic
Maser, a comparison has beell made of twu m asers operat­
As a test
Hydrogen
ing in different
labor atories under dillerent conditiolls. The masers
also differed in many respect>, sllch as technique uf wall coating,
,; t orag e bulb
s ize,
and vacuum ,;ystem de,;ign and were operated at
\'arian :\,sociaties, Beverly, :\L"s., <llld the Lyman La boratory of
Physics, Il a r vard 1 r lliver,ity, Cam bridge , :\Ia". The in ter com pari­
son was ma d e by
\:antllcket
,imultaneuusly m onitori n g the Loran C
siglla l from
Island, :\Ia"., during the 2-1-hollr period from 0000 EST,
:'\ ovember II, 1 96-1 to 2-100 EST, \: ov cmber 11, 19()-l.
Both groups made a determination uf the apparelll fre quenc y of
th e hydrogen
masers in term, of the Loran C 100 kc/s , ign a l.
Corrections were made to the measured ma,;er frequencie,;
the operation to the f�l o w ing
to refer
conditions.
The fo11owing corrections were made:
:\ Iag neti c Field�The Zeeman frequency was 3500 ± 10 c/s
s o that O/l -0.01732 c/s with negligib le u ncertainty.
2) Temperat ure�The maser was operated at .)-l°C. Correction
to -10°C for the second order IJoppler shift i,; OT = - 1 . 96 X 1o-'t.. l'
1)
=
= -0.0012 c/s.
.3) \\ ' all Shift----The measurement was made during
varying conditions
[1]. The wa11 shift fur the bulb llsed during the run was measured
again,;t a second m ,,,er which served as it standard thron gh out the
series of m ea surem ent,; . The wa11 shift for the 6 . 17 -inch diameter
bulb llsed in this experim en t was -0.035 8 c/s. This was l arger than
normal, t he J i gu re for a properly coate d bulb of thi,; size being
-0'(LB4 c/s. It was felt that the evidence was ,;ufli cie ntly clear to
estimated ullcertainty of
± 0.0015 c/s.
The temperature coellicient of the wa11 shift in the range of in­
terest was measured and fuund to be 2 X 10-4 c/ s ; OC . \\'hen this cor­
rection, 0.0012 c/s, is combi ned with a correction of -0.0029 c/s to
this correction is
3) \\'a11 Shift: F.E.P. Tet10n in a 5.7-inch diameter bulb
ze ro .
These corrections are designated b) Q/J, Ilt', Ii", and Q" respectively,
s o that the corrected frequency
/( Jl) is rel ated
to
the ob,erved f re­
aCCollllt for the bulb diameter and the correction of 0.002-l c is in­
dicated in the above paragraph, the result is
quency, y(ll) by
Du' = 0.0007
4)
\lea,;urements made by each
group
will be dis cu s ,ed in tum.
Cavity Tun ing--The cavity tuning was checked hourly using
the line broadening techn i q ue
ual pulling of
to the maser and provided a
ti ming pulse which wa,; compared to the zero cro,;sing of a g ive n cycle
of the Lo ran C p ulse train. The comparis on wa,; IIlade on an oscil­
loscope at intervals of 30 mi nutes . The tiI lle rbolution "f each mea­
the 2-1-hollr
11-';.
The freq uency "f the maser when aver­
obs erva t i on period
the
[2]. Correction
for the estima t ed resid­
maser due t o lllistuning is oe= -0.0003
± O.OOOl
The corrected value for the Harvard determination is
A crystal os c illat or was phase-locked
surement was about 0.02
± 0.0015 cis.
c/s.
VARIA)'; :\SSOCIATES
aged over
a series of
determinations of the wall shift of Tetlon u n der
correct for the discrepancy. To aCCoullt for this, the observed fre­
1) :Vlagnetic Field: zero
m istuning:
142040577 3.0 1 1 2 ± 0.001 4 c/s.
quency must be raised by 0.002-1 c/s. Th e
2) Temperature: 40°C
-I) Cavity
=
was f un d to be
o
Pil(Il) = 1420405772.YY34 ± 0.0004 cis.
V/l(li) = 1420405772.9 931
J t sh ould be empha,;ized that the mea sured hydrogen maser
frequencies are given in terms of Loran C which is based on lIT-2
of 196-l. Furthermore they include the wall shif t corrections for si ze
and temperature and second order Doppler shift at -10°C, the COIl­
ditions of compa ri s on in this corrbpondence. 1!owever, the results of
the measurements made at the two laboratories ditfer by 0.00 13 c is
or one part in 1012.
.Manuscript received l'\ovember 15, 1965: revb;ed January.5. 1966. The work at
Harvard Was supported by a grant irom the National Sciellce Foundation. T he
work at Varian was supported by r\ASA's Marshall Space Flight Center.
± 0.002 c/s.
and that
I t is believed that thi,; represents good agreement
within the rbolution of the experiment there is no signiJicant
difference between the maser,.