a o cha ac e is ic,
a
ol age linea wi h equency o e
a
na ow band.
The
ne wo k
can be
designed
o
ha e
an
ou pu
cha ac e is ic which
has a
ela i ely
low
de ia ion om linea -
i y
and a
s eep g adien o e
he
disc imina o bandwid h.
The ci cui
was
analysed using
he
elec ical equi alen
ci -
cui
o he m.c. .
(Fig. 2).
To
ob ain
he
heo e ical disc imina-
o cha ac e is ic,
i was
necessa y
o
sub ac
he
absolu e
magni udes
o he wo
ou pu ol ages, which could only
be
achie ed
by
nume ical echniques. We de ine i s
a
mode spac-
ing,
Aco,
which
is he
di e ence be ween
he
an isymme ic-
mode
and
symme ic-mode equencies
o
one
m.c. .
F om
he
equi alen ci cui
o Fig. 2, he
mode spacing
is
Aco
=
l/co0 LCC.
Fo a
gi en alue
o
maximum de ia ion om
linea i y
and
mode spacing
o
each
m.c. ., he
maximum disc i-
mina o bandwid h
can be
achie ed
by
op imising
he
il e
design pa ame e s.
1737721
Fig.
2
Elec ical equi alen ci cui
o
one
m.c. .
su ace-acous ic-wa e-coupled esona o il e s4 which ha e
he same equi alen ci cui .
Acknowledgmen s:
The
au ho s hank Ca hodeon C ys als
o
p o iding
he
monoli hic c ys al il e s;
S. J.
Fos e acknow-
ledges
a
Science Resea ch Council s uden ship.
S.
J.
FOSTER
N h
Decembe
1979
M. REDWOOD
Depa men
o
Elec ical & Elec onic Enginee ing
Queen Ma y College,
London
El 4NS,
England
Re e ences
1
KEE-SIANG LU,
s.: 'The
applica ion
o
qua z c ys als
o
disc imina-
o s,
il e s
and
monoli hic il e s', Aus alian Elec onics
Eng.,
1971,
pp. 21-24
2
SMITH,
w. L.: 'The
monoli hic
FM
disc imina o :
a new
piezo-
elec ic de ice', IEEE T ans., 1968, CT-16-3,
pp.
460-463
3
TRAVIS,
c:
'Au oma ic equency con ol', P oc.
IRE,
1935, 23,
pp.
1125-1141
4
REDWOOD,
M.,
TOPOLEVSKY,
R. B.,
MITCHELL,
R. F., and
PALFREEMAN,
J.
s.:
'Coupled- esona o acous ic-su ace-wa e il e ', Elec on.
Le .,
1975, 11, pp.
253-254
0013-5194/80/030104-02 $1.50/0
As
an
example,
a
disc imina o
was
designed
o
ha e
a 6%
maximum de ia ion om linea i y o e
a 22 kHz
bandwid h
cen ed
a
10-7 MHz.
The
heo e ical
and
expe imen al ou pu
cha ac e is ics
a e
compa ed
in Fig. 3. The
m.c. .s
had a
mode
spacing
o 11-8 kHz and a
esonan equency sepa a ion
o
29-6
kHz. No
spu ious modes we e obse ed
a
equencies
ei he abo e
o
below
he
ange shown;
as he
ec i ied ou pu
ol ages
a e
sub ac ed, il e s wi h
a
poo s opband
can be
ole a ed.
1-0
-25
-20 -15 -10 -5 0 5 10 15 20 25
equency de ia ion. kHz I737/3I
Fig.
3
Disc imina o ou pu cha ac e is ic
— heo e ical;
+
expe imen al. Cen e equency
10-7 MHz,
inpu
signal
1 V
.m.s.
Wi h disc imina o s designed
in
his way, smalle de ia ions
om linea i y
may be
achie ed o e
a
na owe band, wi h
he
same
m.c. .
mode spacing,
by
educing
he
esonan equency
sepa a ion. La ge bandwid hs
may be
ob ained
by
uning
ou
he s a ic capaci ance
(Co in Fig. 2) o
bo h m.c. .s. Wi hou
uning,
he
disc imina o bandwid h
is
ypically
1-3
imes
he
mode spacing
o a 2%
maximum de ia ion
and 2-2
imes
he
mode spacing
o a 10%
de ia ion. Wi h uning,
he
band-
wid hs
a e 1-7 and 2-6
imes
he
mode spacing
o
de ia ions
o
2%
and
10%.
The
maximum bandwid h,
o a
pa icula alue
o de ia ion,
is
limi ed
by he
maximum mode spacing
o he
m.c. .
ha
can be
achie ed ( ypically 30
kHz a
10-7 MHz).
The
disc imina o bandwid h
and he
mode spacing
can
bo h
be
equency scaled,
i.e.
inc easing
he
mode spacing
by 10%
inc eases
he
disc imina o bandwid h
by 10%.
A simila design echnique
can be
used
o
p oduce disc im-
ina o s
o
highe equencies, using o e one mode m.c. .s
o
DESIGN
OF
BANDSTOP FILTERS
BY
REACTANCE TRANSFORMATION
Indexing e ms: Fil e s, Reac ance
The usual me hod
o
designing bands op il e s
is he
eac-
ance ans o ma ion om
a
lowpass p o o ype. When
he
il e speci ica ions
do no
sa is y geome ical symme y,
he
choice
o
s opband cen al equency cons i u es
an
in e -
es ing p oblem. This le e shows ha
he
mean squa e
o
he s opband edges
is he
s opband cen al equency ha
leads
o he
lowes selec i i y pa ame e
o he
p o o ype.
The speci ica ions
o a
bands op cha ac e is ic
a e
shown
symbolically
in Fig. la.
This implies ha
o (co|
<<opl
o
|
co |
> op2,
he
passband loss should
be
less han
ap. Fo
o)al
<
| co |
<
coa2,
he
s opband loss should
be
g ea e han
aa.
The lowpass-bands op eac ance ans o ma ion
is1
whe e
<<Oa
COp2
(1)
I s applica ion
o he
speci ica ion
in Fig. la
de ines
he
p o o-
ype shown
in Fig. b,
whe e
ip
=
max
(Clp , ilp2)
i0
=
min (QBl, Qa2)
wi h
o -
P
(0ol
Wp2 -
co£>
0)a2
(2a)
(2b)
(3a)
(3b)
being
he
ans o med equencies
o
iopX,
cop2, coal
and
coa2,
espec i ely.
The p oblem ha a ises
is he
choice
o coo,, he
cen e
ELECTRONICS
LETTERS
31s
Janua y
1980 Vol. 16 No. 3
105
equency
o he
ans o ma ion.
I is
e iden ha
he
mos
con enien alue
o
co^
is
ha which equi es
he
lowes -o de
p o o ype. Conside ing ha
he
o de
is an
in ege , he e will
be
in
gene al
a
ange
o
alues
o
co^,
which p o ides such
a
minimum. This ange depends
on he
bands op il e
speci ica ions
and he
app oxima ion used
o he
p o o ype.
The e o e
i s
gene al cha ac e isa ion
is
di icul ,
i no
impossible.
a
77777777777777777,
Theo em
2: I
col,
—
<*>ai
u>a2,
he
selec i i y pa ame e
o he
p o o ype ake
he
lowes possible alue.
P oo :
Le us
assume ha
coaXcoa2
<
coPicop2
Acco ding
o
heo em
1, he
alue
o co^
ha p o ides
he
lowes
K
sa is ies
0)aiCOa2
<
CO o
<
COpiCOp2
In his case,
i is
easy
o
p o e ha
lpl > lp2 l2
> O.1
which, ollowing eqns.
2 and 3,
leads
o
(6)
[6907i]
n
Fig.
1
a Bands op il e speci ica ions
b Lowpass p o o ype speci ica ions
I
is
possible, hough,
as is
shown
in
his le e ,
o
iden i y
he
alue
o
Woo
ha equi es om
he
selec i i y pa ame e 1
o
he
p o o ype
(4)
he lowes possible alue. This in o ma ion
is
e y con enien ,
because
i
allows
us o
de e mine
he
lowes o de necessa y
o
he p o o ype
and
p o ides
a
e e ence
o he
ange
o
alues
o
a),*,
ha such
a
minimum equi es.
Theo em
1: The
alue
o
co^
ha p o ides
he
lowes selec i i y
pa ame e
o he
p o o ype sa is ies
min {coplcop2, coal(oa2)
<
col,
< max
(copicop2, (oalo)a2)
P oo :
Le us
assume ha
col,
< min
{copicop2, (oaicoa2)
I
is
easy
o
check
in eqn. 3
ha
The e o e, ollowing eqns.
2, 3 and 4, we ge
(5)
K
=
0>a2
Fo
co^
sa is ying eqns.
1 and 5, K
will ake
he
lowes alue
when
col, is
maximum, ha
is
col,
= min
{copicop2, coalcoa2)
To comple e
he
p oo
we
ha e
o
p oceed
in a
simila
way
wi h
he
uppe limi .
Co olla y:
I
<opicop2
=
coalcoa2 (geome ical symme y),
col,
=
copi
coP2
=
coai
coa2
p o ides
he
lowes selec i i y pa a-
me e
o he
p o o ype.
Excep
o
col,
=
<Wpi,
we
ha e ha
dK
dcol >0
The e o e,
o col,
sa is ying
eqn. 6, K is
minimum
o
col,
=
coaicoa2.
By
a
simila p ocedu e,
we can
show ha ,
i
wai
wa2 > wpi wp2, an
iden ical esul holds. This comple es
he
p oo .
I
is
in e es ing
o
men ion ha
a
simila esul
can be ob-
ained
in he
bandpass case. When iden ical minimum losses
a e speci ied
o
bo h s opbands,
he
mean squa e
o
he pass-
band edges
is he
cen al equency
o he
passband ha
p o-
ides
he
lowes alue
o he
selec i i y pa ame e
o he
lowpass p o o ype.
23 d No embe
1979
J.
B.
MARl O-ACEBAL
C. NADEU-CAMPRUBI
E. MASGRAU-GOMEZ
ETSI
Telecomunicacion
Ap do.
2549,
Ba celona,
Spain
Re e ence
1
TEMES,
G. c, and
MITRA,
S.
K.:
'Mode n il e heo y
and
design'
(Wiley,
1973)
0013-5194/80/030105-02$!.50/0
OPTICAL DEMULTIPLEXER USING
CONCAVE GRATING
IN 0 7-0 9 u n
WAVELENGTH REGION
Indexing
e m:
Communica ions,
In eg a ed op ics
Expe imen al esul s
o a
demul iplexe using
an
abe a ion
co ec ed conca e g a ing
o
an op ical sys em a e desc ibed.
The demul iplexe
has
10
channels
and a
wa eleng h spacing
o
20
mm om
0-7 o
0-9
nm
wa eleng hs. Inse ion losses
and c oss alk we e less han 2-5 dB and
—
30 dB,
espec i ely,
o
all
channels.
In oduc ion: Op ical- ib e ansmission echnology
has
de eloped apidly owing
o
imp o emen s
in
op ical ib es,
ligh sou ces
and
passi e de ices. Among hem, wa eleng h-
di ision-mul iplexing (w.d.m.) ansmission
is
conside ed
a
p omising app oach
o
u u e sys ems—especially
o sub-
sc ibe loops
and
la ge-capaci y ansmission sys ems.
The wa eleng h-di ision-mul iplexing (w.d.m) echnology,
106ELECTRONICS LETTERS
31s
Janua y
1980 Vol. 16 No. 3