1956
IEEE
TRANSACTIONS
ON
APPLIED SUPERCONDUCTIVITY, VOL.
9,
NO.
2,
JUNE
1999
Nume ical Op imiza ion o Hyb id Dielec ic/HTS Resona o s o Su ace
Impedance E alua ion
o
HTS Films
C. Collado,
D.
Gonzalo, E. Rozan,
J.M.
O’Callaghan.
Uni e si a Poli ecnica de Ca alunya. Campus No d UPC-D3. Ba celona
08034,
Spain.
C.
Sans
Uni e si a de Vic. C/ Mi ama ges
4.
Vic
08500,
Spain
Abs ac -
This wo k desc ibes an al e na i e o he
adi ional dielec ic esona o opology used o
measu ing su ace impedance in High Tempe a u e
Supe conduc ing (HTS) ilms.
A
gap is in oduced abo e
he dielec ic
so
ha only he lowe ilm is in di ec
con ac wi h i . This a angemen has been used
ex ensi ely o mechanical uning o dielec ic esona o s
and, when used o su ace impedance measu emen , i
can be designed o make he losses in he uppe ilm small
ela i e
o
he o e all esona o losses. Then, measu ed
esul s a e mos ly due o one o he ilms and no he
a e age o wo. The speci ics o a esona o design o
measu ing 2-inch wa e s a e p esen ed. An analysis and
op imiza ion o he esona o is done using a nume ically
e icien mode-ma ching algo i hm.
I.
INTRODUCTION
Commonly used echniques o e alua ing su ace
impedance in HTS hin ilms a e based on measu emen s o
esona o s on ei he pa e ned, plana s uc u es
o
in a
dielec ic esona o ca i y in which he uppe and lowe walls
a e made o
HTS
ilms and a e in con ac wi h he dielec ic
[l].
Only he la e app oach is non-des uc i e, bu i yields
he a e age su ace esis ance o wo ilms. Thus, o measu e
a sample wi h unknown p ope ies, i has o be pai ed wi h a
e e ence sample o de e mine i s su ace impedance. The
deg ee o accu acy o which he su ace esis ance o he
e e ence is known can be a signi ican sou ce o e o in
hese measu emen s. The e o e, o he non-des uc i e
me hods need o be explo ed u he .
11.
HYBRID
DIELECTRICIHTS
RESONATOR
The dielec ic esona o opology unde s udy is a
modi ica ion o he adi ional dielec ic-HTS one
[
11, whe e
a gap is in oduced be ween he uppe endpla e and he
dielec ic cylinde (Fig.
1).
The pu pose o in oducing his
gap is o lowe he
RF
losses in he uppe ilm and
Manusc ip ecei ed Sep embe
15,
1998
This
wo k
has been unded by he Spanish Minis y o Educa ion and
Cul u e h ough CICYT g an MAT95-1038-C02-02 and by he Ca alan
ClRlT
h ough g an SGROOO43.
Coupling
p Dba1
Sapphi e/
c ys ol
.G-
I
,
U‘
U
Fig.
1.
Dielec ic esona o s uc u e. De ini ions o dielec ic
heigh
(hd),
dielec ic adius
( d)
and gap size
(h,)
concen a e hem in he lowe one,
so
ha i s
R,
is he la ges
con ibu ing ac o o he o al losses o he ca i y.
Expe imen al use o his ype o ca i y o measu emen o
R,
is men ioned in [2], bu no design de ails a e gi en.
Am
analy ical s udy o his opology, based on an a.xia1 mode-
ma ching me hod wi h a single mode is p esen ed in [3]. No
desc ip ion is gi en in any o hese wo ks o he p ocedu e o
op imize he ca i y o
R,
de e mina ion pu poses.
In
[3] i is
poin ed ou ha , as he uppe gap
is
inc eased, he
elec omagne ic ields on he no mal me al side walls also
inc ease,
so
he con ibu ion o he RF losses
o
he uppe
ilm a e educed a he expense o inc easing hose o he side
walls. Fo
R,
de e mina ion, an op imal heigh exis s o
.a
gi en esona o size and a gi en diame e o he
supe conduc ing endpla es, o which he a io o he
RI3
losses in he lowe pla e o he o e all losses in he ca i y is
maximum. This op imum may be ound using an e icien.
mode-ma ching code
[4],
which calcula es he
elec omagne ic ield dis ibu ion in s uc u es wi h azimu all
symme y. The algo i hm is no es ic ed o small gap sizes
and can be used
o
op imize he whole s uc u e (gap size:,
dielec ic heigh and dielec ic diame e ) o a gi en diame e
o he supeconduc ing wa e s o be measu ed.
Re e ence [2] p oposes a su ace esis ance de e mina ion
p ocedu e based in wo consecu i e measu emen s o quali y
ac o s in which he op and bo om samples a e ‘exchangecl.
The op imiza ion p oposed he e migh make his unnecessa y,
so
ha a single measu emen and a ough es ima e o he
su ace esis ance o he op ilm and side walls migh lead o
an accu a e de e mina ion o he su ace esis ance o he
lowe ilm.
1051-8223/99$10.00
0
1999
IEEE
1957
Fig. 2. Radial egions (A,B,C) and axial laye s (1,2,3)
conside ed by he mode-ma ching algo i hm. Dielec ic
pe mi i i y can be de ined independen ly
o
each
o
he
9
cells
(AI..C3).
A.
Full-wa e adial mode-ma ching me hod
The so wa e de eloped
[4]
can analyze up o h ee
di e en adial egions, each one di ided in o h ee di e en
laye s (Fig.2). The dielec ic cons an in each egion and laye
can be se independen ly, and he whole olume analyzed is
assumed o be enclosed by conduc ing walls. Fields in e e y
adial egion a e exp essed as an in ini e se ies o pa icula
solu ions
o
he wa e equa ion in cylind ical coo dina es.
Azimu al and axial eigen unc ions a e ha monic unc ions
while adial eigen unc ions a e Bessel unc ions, which mus
be chosen app op ia ely o a oid singula i y in he axis
( egion A), ul ill bounda y condi ions on he ex e nal walls
( egion
C),
o p o ide con inui y be ween adjacen egions
( egion
B).
The eigen alues o each adial egion a e ound
by sol ing a pai o anscenden al equa ions ela ed o he
h ee-laye p oblem.
A
sys em o equa ions is hen ound
by
o cing con inui y condi ions
o
he angen ial ields be ween
adial egions
A
and B, and
B
and
C,
om which he
coe icien s
o
he mode expansion a e ound. In ou case
12
modes a e su icien . Fig.
3
illus a es he ield and cu en
dis ibu ions o a sapphi e dielec ic wi h a 12
mm
diame e
and a
6
mm
heigh .
B.
Op imiza ion. Basics and al e na i es
Fo
R,
de e mina ion, he op imal dimensions
o
he ca i y
in Fig.
1
a e hose ha make he losses o he lowe pla e
dominan wi h espec o he o he ype
o
losses. This
is
equi alen o maximizing
Qo/Qlc,w,
whe e:
U
is he o al s o ed ene gy in he ca i y,
Pd
he o al
dissipa ed powe ,
Pd-/ow
he powe dissipa ed in he lowe
wall, and
Qo
he unloaded quali y ac o . Bo h he o al ene gy
U
and he dissipa ed powe s
Pd
and
P l-lOw
can be calcula ed
om he ield dis ibu ion inside he ca i y wi h p ope ly
de ined su ace and olume in eg als o he elec omagne ic
ields
[5].
De ini ions analogous o ha
o
Qlclw
in (1) can be
used o
Qu/,,
Q.,d
and
Qd
which accoun o he losses in he
uppe wall, side wall, and dielec ic espec i ely. Thus, he
unloaded quali y ac o can be w i en as:
...._..........
....
,
I,,................
I#,,.-.........
.
...
Il .
.............
I ,.-
]I!..-::::::::'
::::
'id,
........
..
-),,,..........
/j/i
,,,........
.
$:j:::::;:;;:;;:
hzj:::
:
::
:
:
:
:
:
:
:
I
-.%.-A
"
..
.
.
.
.
. .
.
.
.
. .
.
-+c+
4-
-
.
.
. . . .
.
.
.
.
.
Fig. 3. Field and cu en dis ibu ions in he ca i y wi h
a
TEOI
mode and
a
sapphi e dielec ic. Bo om pla e diame e is 48mm, dielec ic diame e is
12mm and dielec ic heigh
is
6mm. The dashed line ep esen s he sapphi e
ou line.
(Top)
Radial cu
o
he esona o showing magne ic ield lines.
(Bo om)
Cu en s a he su ace
o
he lowe HTS ilm.
The ele ance o maximizing
Q0/Qluw
is due o he ac ha
his de ines he sensi i i y o he sys em:
(3)
which can. be p o en om
(1)
and
(2),
and om he
p opo ionali y be ween and
R,.
Also,
as
Qo/Qlc,w
is
inc eased, he accu acy in es ima ing
Q,,,
QSd
and
Qd
has a
lesse e ec on he
R,y
p edic ed om he measu ed
Qo
and
(2).
A
so wa e code has been de eloped, which includes he
elec omagne ic mode-ma ching algo i hm desc ibed
p e iously, and is capable o calcula ing
Q clw
,
Q,,
QSd
and
Qd
as a unc ion o dielec ic heigh
(hJ,
dielec ic adius
( d)
and gap size
(h,)
(Fig.
1).
To
es i , he ca i y dimensions
gi en in
[2]
we e used, and he code esul s we e compa ed
wi h hose in Table
I
in ha e e ence. The ag eemen is
excellen , as shown in Table I o his wo k.
The so wa e de eloped can use se e al s a egies o a y
hd,
d
and
h,
in he sea ch o a maximum o
Qo/QlcIw
:
1)
a ia ion o he gap size o a gi en ( ixed) dimension o he
dielec ic;
2)
exhaus i e sea ch a ying
hd,
d
and
h,
o e a
speci ied ange, wi h a speci ied inc emen al s ep size; and
3)
1958
-D-
Q-Side
wall
(Qsd)
~
"i
j_
+
....
4
-
Q-Uppe wall (Qup)
'
.i..
....
~.
I.
:.
i..
........
:
-
.
Q-Dielec ic (Qd)
~
-
..
.
--+-.Q~/QIow~
.
,.
F
,<
j
.TABLE
I
COMPARISONS
BETWEEN
121
AND
THIS
WORK
Glow
is de ined
as
he p oduc
o
he su ace esis ance
o
he lowe
pla e and
Plow;
Cup
and
Gsd
a e
de ined simila ly.
(GHz) Glow GUP Gsd
PI
9.5 546 4.90e3 1.15e6
This wo k 9.510 541 4.81e3 l.lle6
E o
%
0.8%
1.7%
3.3%
,.
,.
-'
I
..
-.
.......
+
.....;
...........................................
I
+,
L.-
--
...............
&
..................................
.>
+-I---
__
x-
-.
1
*.
- -&--*----+-;
;A'
I
-
/I
y;
..
,,
.
,-
~,
.
I-
;
:
.......
~
................................
g adien sea ch using
Ma lab [6].
In his p ocess i is assumed
ha he uppe and lowe walls a e made o YBa2Cu3O7.8
(YBCO), and he side walls o a no mal me al (usually OFHC
coppe , bu i can be changed by he use ). Thei
R,T
is scaled
as he calcula ed esonan equency
o
he ca i y changes due
o a ia ions in
hd, d
and
h,.
The scaling law is aken as
*
o YBCO and
o he me al, and he alues o
R,y
a
lOGHz
and
77K
a e aken as
300@
(YBCO) and
9mQ
(Cu)
[7] espec i ely. The equency dependence o he loss
angen o sapphi e is neglec ed, aking ank4
[8]
h oughou he op imiza ion.
C.
Op imum gap o ixed dielec ic and wa e sizes
10
i
;
[1
*i-
xi.-
A
-/
Y
U.
11'1,,,,111,,,,,111,1,,
Fig.
4
shows he esul s o he gap heigh op imiza, ion o a
dielec ic wi h
hp6mm, p6mm
and a 2 inch wa e whe e
only an a ea o 48mm in diame e is exposed
o
he
elec omagne ic ields in he ca i y. This igu e indica es
ha , while he losses in he side walls a e s ongly dependen
on
h,,
his dependence is mode a e in he uppe wall, and
weak in he dielec ic and lowe wall. The e o e, he
op imum heigh ep esen s a ade-o be ween he losses in
he uppe wall and hose in he side wall. This esul s in an
op imum gap o
h,=6mm
and
Qo/Q1,,,,=O.85,
which essen ially
coincides wi h he esul s epo ed in
[2].
As
shown la e ,
subs an ial imp o emen s can be made by adjus ing
h,l,
d
and
h,
join ly.
Finally, Fig.
5
shows ha hese esul s deg ade !s ongly
i
he diame e o me al side wall is educed.
D.
Subs i u ion o he uppe HTSpla e by a coope
one
Unsuccess ul a emp s ha e been made a ep lacing he
YBCO in he uppe wall by coppe . E en when he gap
heigh op imiza ion p ocess was pe o med aking in o
accoun he new
R,,
o he uppe pla e, he sensi i i y
(Qo/Ql(,,,)
alues we e oo low o allow an (accep able
accu acy in he de e mina ion o he
R,,
o he bo oin pla e.
Inl
o he wo ds, he gap can ne e be high enough o eplace he:
uppe ilm by a no mal me al wi hou making i
a
dominani.
sou ce o loss in he ca i y and ende ing i useless €o su ace:
esis ance de e mina ion. Fig.
6
shows he e ec s o his
subs i u ion in he sensi i i y
(Qo/Q,,J.
When dimensions o he wa e and he dielec ic a e
known and ixed, only
h,
needs o be a ied o ind a
maximum o
Qo/Q o,,,.
This is done o wo easons: o
explo e a possible imp o ed design o he ca i y in [2] (while
main aining he sapphi e used); and
o
ind a good ini ial se
o alues o
hd, d
and
h,
om which a second op imiza ion
can be done using a g adien sea ch in which all h ee
a iables a e allowed o change.
E.
Join op imiza ion o hd, d
and
h,
The alues
o
hd, d
and
h,
ha e been op imized using wo
pa allel app oaches: a g adien op imiza ion and an
IO"
1
O'O
1
0'
1
o6
1
0.8
1
o8
0.6
Q
.
gi
4
0.4
0.2
0
Fig. 4. Dependence
o
Qw,
elow,
Qsd
wi h gap heigh
(h,).
The
op imum heigh
(max.
QO
/Q&
ep esen s
a
ade-o be ween he
losses in he uppe and side walls
(elq,
Qsd),
whose dependence on h,
is much s onge han ha
o
he
lowe wall
(elow)
and dielec ic
(Qd).
The maximum
o
Qo/QlOw
is a h,=6mm.
0.8
0.6
8
.
0.4
0.2
Ca i y adius
( n n)
Fig. 5. Dependence
o
Qw,
elow,
Q,Td
wi h ca i y adius.
As
he adius
is
dec eased, losses in he side walls inc ease, become dominan , and
deg ade
QO
/el(,,,,.
Gap heigh is hg=6mm.
As
in Fig.
4.
dielec ic
heigh is h~6mm
1959
Fig.
6.
De e io a ion
o
he sensi i i y
(Qo/QlOw)
as
he alue
o
R,
o
he
uppe sample is inc eased. A s ong deg ada ion occu s o he ange o
R,T
alues co esponding o coope a 77K a he esonan equencies o
he ca i y (abou
10
mn).
Fo hese alues o
Rs
in he uppe wall, he
Qo/Qim
is oo low
o
de e mina ion o he
R,y
o he lowe HTS ilm.
exhaus i e sea ch o e a b oad ange o hd,
d
and h, o ensu e
ha he g adien op imiza ion did no s op a a local
maximum o Qo/Qbw.
The exhaus i e sea ch was done om 2mm< hdlOmm,
3mm< 614mm and 1mm<hg<15mm.
A
maximum was ound
a hd=2mm, ~5mm and h,=6mm wi h Qo/Ql,,,~0.94. The
sea ch showed ha his op imum alue would deg ade sha ply
when hd was dec eased beyond i s op imum alue. Howe e ,
he dependence wi h hd and
d
was much weake ,
G adien op imiza ions we e un s a ing om se e al
alues, including
he
ones
om
Sec .
11-C.
They
all
eached
simila alues
o
Qo/Q o,,,. The bes one was he one s a ed
om hs2mm, d=5mm and h,=6mm ( he op imum o he
exhaus i e sea ch), which was used o ine- une he p e ious
sea ch esul ing in hd=l.7mm, &.Omm and hg=4.6mm wi h
Qo/Qlow
=0.95. In o he wo ds, i
no
o he losses a e
conside ed in a ca i y wi h hese dimensions, only a
5%
o e es ima ion o he su ace esis ance o he lowe sample
will be made, and his may be g ea ly wi h es ima es o he
su ace esis ance o he side walls, uppe
ilm
and dielec ic
loss
angen .
111.
CONCLUSION
An op imiza ion o he image dielec ic esona o ca i y
has been done by nume ical echniques. The so wa e
de eloped o he op imiza ion has been c oss-checked wi h
p e iously published esul s. The op imized ca i y should be
allow he de e mina ion o su ace esis ance o
YBCO
wi h
an e o lowe , han
5%
i no o he sou ces o
RF
loss
in
he
ca i y a e aken in o accoun .
REFERENCES
Z-Y Shen, C. Wilke , P. Pang, W.
L.
Hols ein, D. Face, D.J. Konu z.
“High Tc Supe conduc o -Sapphi e Mic owa e Resona o wi h
Ex emely High Q-Values up o 90K.
IEEE T ans. Mic owa e
Theo y Tech.,
ol. 40 no. 12, pp 2424-2432. Dec. 1992.
C.
Zucca o, N. Klein, A.
G.
Zai se , R. Wo denwebe , Y. Lemai e,
and J.C. Mage. “Nonlinea mic owa e losses o la ge
a ea
YBCO hin
ilms.
Applied Supe conduc i i y
1997,
Ins . Phys. Con . Se . no 158,
pp 295-298 [P oceedings EUCAS 19971.
N.
Tellman, N. Klein,
U.
Dihnem, H. Schulz, and H. Chaloupka.
“High Q
LaALO3
dielec ic esona o shielded
by
YBCO ilms”.
IEEE
T ans. Appl. Supe conduc .,
ol4, no. 3, pp143-148, Sep . 1994.
Sans, J.M. O’Callaghan, D. Sancho, R.
Pous,
J.
Fon cube a, J.-F.
Liang and G.C. Liang. “Full-wa e analysis o he image hyb id
dielec ic/HTS esona o ”.
IEEE T ans. Appl. Supe conduc .,
ol4, no.
7, pp3840-3844, Dec. 1997.
R.F. Ha ing on.
Time-Ha monic Elec omagne ic Fields.
McG aw-
Hill, 1961.
The Ma hwo ks, Inc.
Ma lab use ’s guide.
G.W.C. Kaye and T.H. Laby.
Table
o
physical and Chemical
cons an s.
Longmans G een London, 1966.
2.-Y. Shen.
High Tempe a u e Supe conduc ing Mic owa e Ci cui s.
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