TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 3, Dece
mbe
r
2
015, pp. 495
~ 501
DOI: 10.115
9
1
/telkomni
ka.
v
16i3.901
4
495
Re
cei
v
ed Se
ptem
ber 13, 2015; Revi
se
d Octob
e
r 17,
2015; Accept
ed No
vem
b
e
r
2, 2015
Analytical Modeling and Simulation of SAW Filter Using
Concave
M. M. Elsherbini
1
*, M. F.
Elkord
y
2
, A.
M. Gomaa
1
1
Dept. of Electrical En
gin
eeri
n
g, Shoubr
a F
a
cult
y
of Engin
e
e
rin
g
, Benh
a U
n
iversit
y
,
Cairo, Eg
ypt
2
Dept. of Communic
a
tions, F
a
cult
y of Electr
onic En
gin
eer
i
ng, Meno
ufia U
n
iversit
y
,
Menouf, Eg
ypt
*Corres
p
o
ndi
n
g
author, em
ail
:
motaz.ali@fe
ng.bu.e
du.e
g
A
b
st
r
a
ct
A Si
mp
le
nov
el to
ol
has
b
een
dev
el
ope
d to
mod
e
l
a
nd s
i
mul
a
te S
A
W
filter d
e
vi
ces. GN
U
Conc
ave;
F
r
ee
w
a
re
tool
w
i
th ope
n s
ource
c
odi
ng
has
b
e
e
n
us
ed
to s
pec
ify a
bas
ic
mo
del
for SAW
d
e
la
y
lines
and filt
e
r
s. T
h
is paper
presents a
w
a
y for obt
ainin
g
the esse
ntial p
a
ra
met
e
rs of design
an
d
deve
l
op
ment o
f
SAW
device
s
as inserti
o
n
loss. Other
para
m
eters w
e
r
e
also
pred
icted by w
i
thin t
h
e
reseac
h w
o
rk
l
i
ke th
e r
adi
ati
on c
o
n
ductanc
e, su
sce
ptanc
e, Imped
anc
e, Ad
meta
nce
a
nd th
e F
r
e
que
nc
y
Resp
onse. T
h
ey all ca
lcu
l
ate
d
and
plotte
d usin
g Math
mat
i
cal e
q
u
a
tions
drive
d
from
an
equiv
a
l
ent mo
de
l
used t
o
sim
u
late our tar
get.
A co
m
par
ision between
th
e sim
u
lated device and an
experim
e
ntal
puplis
hed
one h
a
s be
en
achi
eved.
Ke
y
w
ords
: SAW
, model, si
mulati
on a
nd filte
r
s
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Surfac
e
Aco
u
s
tic Wav
e
(SAW) we
re
di
c
o
v
e
rd
a
nd di
scu
s
sed the
surface a
c
ou
st
ic mod
e
of prop
agatio
n, also
pre
d
i
c
t
ed its
pro
p
e
rties i
n
18
8
5
, by
Lord Ra
y
l
eigh
.
White
an
d
Voltmer
prop
osed tha
t
surfa
c
e wave can b
e
exci
ted and
dete
c
ted easily by
depo
siting el
ectro
d
e
s
on t
he
surfa
c
e
of a
piezoele
c
tri
c
material [1].
Re
cenly, SAW devi
c
e
s
were d
e
si
gne
d
and d
e
velop
ed to
be u
s
ed in
g
eneration, de
tection, an
d amplifying th
e wave
s. De
lay lines, sto
r
es, o
s
cillato
rs,
filters, reson
a
tors a
nd
se
nso
r
s a
r
e
ba
sic an
d famil
i
ar type
s fo
r
SAW devi
c
e
s
. Mo
st p
opu
lar
appli
c
ation
s
for usi
ng S
A
W devices found in
T
V
s, rada
r, sonar,
satellit
es, and M
o
bile
comm
uni
cati
on sy
stem
s.
They can
be
use
d
withi
n
t
he fre
que
ncy
rang
e 1
0
MHz to multiple
G
H
z.
In the last de
cad
e
most re
sea
r
ch ha
s d
e
velope
d in
the are
a
of su
rface a
c
o
u
sti
c
wave filters and
sen
s
o
r
s [2]. The o
peratio
n of the SA
W device
is
ba
sed on acou
stic
wave
prop
agation nea
r the
surfa
c
e
of a
piezo
e
le
ctri
c solid mate
ri
al like ST-Quart
z
, lithiu
m
tantalate
(
LiTaO
3
), lithium
niobate (
LiNbO
3
) an
d
Ga
As Z
; etc. T
h
ey have different pie
z
o
e
le
ct
ri
c co
uplin
g
coef
f
i
ci
ent
s
(
K
2
)
and tempe
r
at
ure
sen
s
itivities.
ST quar
t
z
is ou
r choi
ce in the mod
e
ling an
d sim
u
lation work for
the rea
s
on th
at it is used for mo
st temp
eratu
r
e st
a
b
l
e
device
s
. Th
is indi
cate
s that the wave
can
be reformed
while
p
r
opa
g
a
ting.
Th
e su
rface
wave
can b
e
excite
d ele
c
tri
c
ally
by mea
n
s of
an
interdigital transdu
cer
(IDT). A basi
c
SAW devic
e
con
s
i
s
ts of couple IDTs o
n
a pie
z
oele
c
tri
c
sub
s
trate
as
indicated in
Figure 1. Th
e input
IDT
gene
rate
s an
d the outp
u
t IDT re
ceive
s
the
wave
s. Th
e
IDT h
a
s ma
ny identi
c
al
electrode
s
conne
ct con
s
ecutively
to cou
p
le of
m
e
tal
busbars,
Wh
en an
ele
c
tri
c
al
sign
al is
applie
d to
th
e input I
D
T, i
t
is converte
d to SAW
which
cau
s
e
a volta
ge to b
e
mo
n
i
tored
at the
output
after a
delay d
e
termined
by the
sp
ace bet
we
en
the tran
sdu
c
ers
and al
so
by surfa
c
e
wave velocity. The inp
u
t an
d output tran
sdu
c
e
r
s m
a
y be
equal o
r
different. It depends u
pon the
function whi
c
h the SAW
device h
a
s t
o
perfo
rm. The
magnitud
e
of the output voltage de
cay
s
as the fr
eq
uen
cy shifts from the ce
ntral frequ
en
cy. It
mean
s th
at
SAW devi
c
e
is like b
and
pass filte
r
[3]
.
The
area
b
e
twee
n the
i
nput a
n
d
out
put
transdu
ce
rs
may be a se
nsin
g elem
en
t to detect si
gnal
s and
co
nvert the dev
ice into
sen
s
or
type.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 495 – 501
496
Figure 1. Surface Acou
stic
W
a
ve Devic
e
Str
u
c
t
ure
The re
sea
r
ch
wo
rk
b
a
sed
upon mo
del a
nd simul
a
tion
for the basic
config
uratio
n of SAW
delay line an
d filters usi
n
g first orde
r
modelin
g kn
o
w
n a
s
impul
se re
sp
on
se
model. Impul
s
e
respon
se
mo
deling
is the
simpl
e
st
m
e
thod to
cal
c
ulate
an
s
p
l
ot ba
sic pa
rameters
of the
equivalent
circuit for SA
W sen
s
o
r
represented by
cr
o
s
s field mo
del,
sho
w
n i
n
Fig
u
re 2. In
se
rtion
loss is the m
a
in goal to b
e
expecte
d from the mo
d
e
l
, it is calcul
a
t
ed as the lo
garithmi
c
ratio of
the po
we
r d
e
livered to
the
load i
m
pe
da
nce
befo
r
e t
he SAW devi
c
e i
s
in
se
rte
d
to the
po
wer
delivere
d
to the load imp
edan
ce after it is
inserte
d
. Some pre
v
ious studi
es have studie
d
freque
ncy d
o
m
ain an
alysi
s
of SAW d
e
vice
s [4-7
]
and time do
main an
alysi
s
[8]. Many other
recent re
se
arche
s
in SAW device
s
from
1985
up to
2013 int
r
odu
ced a
nd com
pare
d
by haresh
pandya [9]. A prop
sed
solution for
si
mply obtaini
n
g
the ba
sic
para
m
eters o
f
SAW device is
pre
s
ente
d
via this re
sea
r
ch
work
with a novel s
i
mulation tool.
Figure 2. Cro
ss field mo
del
for SAW device
s
[9]
2. SAW
Dev
i
ce
Modeling
The
obje
c
tive of SAW devi
c
e
s
m
odelin
g
is to
reali
z
e
spread,
gen
e
r
ation
and
re
cog
n
ition
of aco
u
sti
c
waves u
pon
pi
ezo
e
le
ctric m
a
terial
s
an
d t
o
de
sign
geo
mertry
su
ch
as IDTs, d
e
l
a
y
lines, amplifie
rs, filters, correlators and
re
son
a
to
rs to achieve the fre
quen
cy doma
i
n respon
se
s.
Variou
s m
o
d
e
ling te
chni
q
ues are u
s
e
d
with
S
A
W
d
e
v
i
ce
s su
ch as
I
m
p
u
ls
e R
e
sp
on
se
Model, equiv
a
lent circuit
model, co
upli
ng of mode
s model an
d tra
n
smi
ssi
on ma
trix model.
Usi
ng both i
m
pulse re
sp
onse modeli
n
g and eq
uiva
lent circuit m
odelin
g are t
he main
contri
bution
that introdu
ce
d by th
i
s
re
search
wo
rk t
o
introdu
ce
a
first
ord
e
r a
nalytical m
o
d
e
ling
techni
que for
SAW sen
s
o
r
device a
nd p
e
rform th
e si
mulation by u
s
ing
Con
c
ave
tool ver. (4).
The mod
e
l base
d
on two
con
d
ition
s
, the first one tha
t
one or both
IDTs mu
st be
uniform
apodi
ze
d whi
l
e the oth
e
r
criteria i
s
to
m
a
ke
the fing
e
r
wi
dth
con
s
t
ant and
eq
ua
l to ea
ch
oth
e
r
.
To represent
su
rface a
c
o
u
stic
waves,
the SAW fre
quen
cy f
o
is related to t
he
perio
dicity of
the
IDTs
(
λ
) and t
o
the aco
u
sti
c
velocity V
s
.
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analytical Mo
deling a
nd Sim
u
lation of SAW
Filter Usi
ng Co
ncave (M. M. Elsherbini)
497
With aid of Maso
n equival
ent circuit of an ID
T, sho
w
n in figure (2
), the model compo
s
ed
of three com
pone
nts: the total cap
a
cita
nce
C
T
, the a
c
ou
stic
su
sce
p
tance B
a
(f) and the radia
t
ion
c
o
nd
uc
ta
nc
e
G
a
(f).
Starting with the time respo
n
se of SAW ID
T to obtain the req
u
ire
d
compon
ents
where f
o
is the syn
c
h
r
onou
s fre
que
ncy, K
2
is the
piezoele
c
tri
c
cou
p
ling
coef
ficient, D is th
e delay bet
ween
two IDT
s
(i
n
wavele
ngth
s
), Cs i
s
the
ca
pacita
n
ce for
a finger
pair
p
e
r unit le
ngth,
W
is the fing
er
overlap, Ri
n =Rg is the in
put or matche
d
impeda
nce and Np is the
numbe
r of finger pai
rs.
4
/
2
(
2
)
The Fou
r
ie
r transfo
rm of the impulse re
spon
se:
4
(
3
)
(4)
The num
be
r of fingers
(Np) m
a
y be
calculated
as a fun
c
tio
n
of desig
ne
d cente
r
freque
ncy an
d Null Band
wi
dth. Wa is al
so obtaine
d using the followi
ng relatio
n
:
(
5
)
The
radi
ation
co
ndu
ctan
ce
G
a
(f) is the
real p
a
rt of th
e inp
u
t admitt
ance a
nd i
s
e
qual to
the twice the
magnitud
e
of the freque
ncy
resp
on
se.
2
|
|
8
(
6
)
The
acousti
c su
scepta
n
ce
is th
e im
agi
nary
part
of
the inp
u
t ad
mittance
and
de
rived
from takin
g
the Hibe
rt tran
sform of the ra
diation cond
u
c
tan
c
e.
′
′
∞
∞
′
(
7
)
After integrati
on, the expre
ssi
on be
com
e
in the following form:
(8)
The norm
a
lization of
and
have been in
clud
ed in the software too
l
as th
e
ratio of
divid
ed by its maximum value and
divided by the maximum value for
r
e
spec
tively.
The last com
pone
nt of the model is C
T
and it is cal
c
ulated by mul
t
iplying the numbe
r of
fingers (Np), t
he finger ove
r
lap (W
a
) and t
he ca
pa
citan
c
e for a finge
r pair pe
r unit length Cs.
(
9
)
The
previo
us pa
ramete
rs
use
d
to
driv
e the tot
a
l a
d
mittance
a
n
d
imp
edan
ce
of IDT
r
e
spec
tively.
2
(
1
0
)
(
1
1
)
Finally, the inse
rtion lo
ss that is the
most important param
eter to measu
r
e the
perfo
rman
ce
of the SAW filter is written as:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 495 – 501
498
10
(
1
2
)
The total re
sp
onse of the SAW filter is al
so
ea
sy to be
driven by mu
ltiplying the absol
ute
value of frequ
ency re
sp
on
se for the first IDT by
the ab
solute valu
e of conju
gate
of the second
IDT frequency res
p
onse.
3.
S/W Tool Implementa
tio
n
Software tool
is requi
re
d to perfo
rm an
d pro
c
ed
ure the mathmati
cal equatio
ns
and plot
the
re
sults. A
code wa
s written with GNU
O
c
ta
ve
softwa
r
e, Fi
gure
3 which
like Matla
b
but
without
graph
ical
user inte
rface.
O
c
tave
is a
hi
gh
-lev
el inte
rpreted
lang
uag
e
which
is ba
si
cally
use
d
for
nu
meri
cal
com
putation
s
. Th
e nume
r
i
c
al
solutio
n
of li
near and
no
nlinea
r p
r
obl
ems,
perfo
rming
ot
her
nume
r
ica
l
experim
ents and p
r
ovid
i
n
g extensive
g
r
aphi
cs
capa
bilities fo
r dat
a
visuali
z
ation
and ma
nipul
ation is ea
sy
to be
pro
c
e
eded
with o
c
tave. A portable so
urce
of
softwa
r
e
tool
is u
s
e
d
h
e
re
and li
nked
wi
th matlab
to
gene
rate
a G
U
I interf
ace
f
o
r the
Softwa
r
e
cod
e
, Figure 4.
The
cod
e
i
s
devided
int
o
segme
n
ts,
a pa
rt of
definition the
paramete
r
s of the
piezoele
c
tri
c
material
u
s
e
d
(ST
-
Q
uart
z
), an
other
se
gment i
s
fo
r
the ge
ometry
de
sign
an
d
the
third for the p
r
eviou
s
math
ematical e
q
u
a
tions (1
-12) that
calculate
d
the requi
re
d para
m
eters.
C++ is u
s
ed
to compile the written code and G
U
I interface a
nd gene
rate
a self-
executa
b
le to
ol to be use
d
anwhere.
We can sum
m
ari
z
e the st
eps fo
r writin
g the co
d
e
to mode an
d si
mulate the SAW filter
in the following simple
steps:
1)
Con
g
igu
r
atio
n for the input
param
eters f
o
, Vs, Cs, Np, Rg, Wa, Del
a
y and K
2
.
2)
Building the e
quation
s
(1
-1
2)
in the form
of Concave tool.
3)
Cal
c
ulating a
nd Plotting the requi
re
d Parame
te
rs, G
a
(f), Ba (f), H (f
) and IL (f).
4)
Building a G
U
I interfa
c
e u
s
ing Matla
b
.
Figure 3. GNU Octave inte
rface
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analytical Mo
deling a
nd Sim
u
lation of SAW
Filter Usi
ng Co
ncave (M. M. Elsherbini)
499
Figure 4. GUI
Matlab interf
ace for th
e de
sign
ed tool
4. Simulation
Results
The respon
se compa
r
iso
n
of
SAW
devic
e, ope
ra
ting at 70
MHz a
nd nu
mber of
fingers of 33 has be
en do
ne, The sub
s
trate is ST cu
t Quartz. The
Null Band
widt
h (NB
W) is 4.
3
MHz. the d
e
l
a
y is 5
λ
a
nd
both input a
n
d
match
ed re
sista
n
ces i
s
50
Ω
. The Co
upling
Coefficen
t
for ST-Qu
a
rt
z is 0.04
and
the capa
cita
nce p
e
r u
n
it length for a p
a
ir of fingers
is Cs=0.503
3
85
pf/cm. the acousti
c velocit
y
,
ν
= 3158 m/s and the fing
er overl
ap is
1831.9
9
um. From the mo
del,
the IDT Re
si
stance at fo is
780.51
1
Ω
.
The co
mpa
r
i
s
on bet
wee
n
the radiatio
n cond
ucta
n
c
e and
su
scepta
n
ce ha
s been
visuali
z
ed at Figure 5. Figure 6 and 7 i
n
trodu
ce
the
admittance a
nd imped
an
ce of equivale
n
t
circuit mo
del.
Figure 8 sho
w
the
comp
arison th
e fr
eq
u
ency respon
se of i/p or o/p
IDT co
mpa
r
e
d
with the total
freque
ncy re
spo
n
se due t
o
both of the
m
. Figure
9 indicates the i
n
se
rtion lo
ss
of
the device; its max value is approximatel
y -20dB.
Figure 5. The
radiation
con
ducta
nce and
su
sceptan
ce
of SAW device
Figure 6. Admittance (Y
) of equivalent
circuit
model
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 495 – 501
500
Figure 7. Total Impedan
ce
(Z) of equival
ent
cir
c
uit
mod
e
l
Figure 8. Fre
quen
cy re
spo
n
se of si
ngle
IDT
comp
ared wit
h
the total frequen
cy re
spo
n
se of
the SAW device
Figure 9. Inse
rtion loss of the SAW devi
c
e
Comp
ari
ng o
b
tained
data
f
r
om ou
r simul
a
tion
with
co
mmercial
SAW filter (820
-IF70.0M
-
F), sh
own in
Figure 10 fro
m
Oscilent
Corpo
r
atio
n
Co
mpany, we
n
o
ticed th
at at -1dB the typi
cal
value of inse
rtion loss for the comme
rcial devi
c
e is -22.5dB, wh
ile the simul
a
ted re
sult is -
20.5dB. This
result sup
p
o
r
ts the de
sign
e
d
tool effectivene
ss.
Figure 10. 82
0-IF70.0
M
-F
comm
ercial
devic
e
with IL=22.5dB [11]
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Analytical Mo
deling a
nd Sim
u
lation of SAW
Filter Usi
ng Co
ncave (M. M. Elsherbini)
501
5. Conclu
sion
A simple tool
for modeli
n
g
and sim
u
lati
on
SAW filter device h
a
s b
een devel
ope
d usin
g
Con
c
ave
soft
ware. The
m
odel
can
be
use
d
for oth
e
r SAW del
a
y
line ba
se
d
appli
c
ation
s
.
All
requi
re
d parameters like
cond
uc
ta
nce, susce
p
ta
nce, impe
da
nce, admitta
nce, freq
uen
cy
respon
se a
n
d
insertio
n loss have been m
odelle
d and p
r
edi
cted.
A compa
r
i
s
o
n
betwe
en the sim
u
lated
In
sertio
n lo
ss a
nd the
measured h
a
s be
en
demon
strated
.
The sim
u
lati
on an
d expe
ri
ment re
su
lt
s
are
relatively
the sa
me an
d
the differen
c
e
error is quite
small. T
he
re
sults a
r
e
useful to
re
cog
n
ize pa
ram
e
ters e
ffec
t. Ins
e
rtion loss
, f
o
, Np
and sub
s
trate
material which are imp
o
rta
n
t param
eters in SAW dev
ice
s
de
sign.
Referen
ces
[1]
Marija Hr
ibs
e
k
.
Surface Acoustic W
a
ve D
e
vices i
n
Com
m
unic
a
tions.
S
c
ientific Tech
n
i
cal R
e
view
.
200
8; 58(2): 44
-47.
[2]
E Benes, M Grochl, F
Seifert. Comp
ariso
n
be
t
w
e
en BAW
a
n
d
SAW
Sensor
Princip
l
es.
IEEE Trans. Of
Ultraso
nic F
e
rroel
ectric and F
r
equ
ency co
ntrol
. 199
8; 45: 1
314-
133
0.
[3]
P Schio
pu, I Cristea, N Gros
u, A Craciu
n.
Devel
o
p
m
ent
of SAW
filters base
d
on GaP
O
4.
IEEE 17
th
Internatio
na
l S
y
mp
osi
u
m for
Desig
n
and
T
e
chn
o
lo
g
y
i
n
Electron
ic Pac
k
agi
ng (SIIT
ME). T
i
misoara
,
201
1: 169-
172.
[4]
JC Mend
es, DM SANT
O
S. Simulatio
n
of acoustic
w
a
v
e
dev
ic
es usin
g Ma
tlab.
Pr
z
e
gl
ad
Elektrotech
n
ic
zny
. 2012; 8
8
(1)
:
155-15
8.
[5]
MM Elsherbi
ni,
MF
Elkord
y
,
AM Gomaa.
T
o
w
a
r
d
s a Sim
p
le Mo
del for
SAW
Dela
yli
n
e Usin
g CAD.
Amer
ica
n
Jour
nal of Circ
u
its,
Systems a
nd S
i
gn
al Process
i
n
g
. 2015; 1(
3): 86-92.
[6]
Hares
h
M Pan
d
y
a, KB Raj
e
s
h
, AT
Nimal, MU Sharma. Imp
u
lse Mo
del
le
d Resp
onse
of a 300 MHz ST
-
Quartz SAW
Device for Se
nsor Spec
ific Appl
icatio
ns.
Jo
u
r
na
l
o
f
En
vi
ro
nm
en
ta
l
N
ano
te
ch
. 201
3; 2
:
15-2
1
.
[7]
W
C
W
ilson, GM Atkinson.
Ra
pid SAW
Sens
or Devel
o
p
m
en
t T
ools.
Confer
ence o
n
F
l
y
-
b
y
-W
ireless for
Aerosp
ace Ve
hicles. Grap
evi
ne Un
ited Stat
e. 2007.
[8]
MM Elsherbi
ni
, MF Elkord
y
,
AM Gomaa.
A
T
r
ansient Stud
y
for SA
W
Propagati
o
n upo
n GaAs
Substrate.
Inte
rnatio
nal Jo
urn
a
l of Materia
l
s Che
m
istry a
nd
Physics
. 201
5; 1(2): 182-
18
8.
[9]
Banu
Pri
y
a
R,
Venkates
an T
,
Pan
d
i
y
ar
aja
n
G, Haresh M
Pand
ya.
SAW
Devices
–A
Co
mpreh
ensiv
e
Revie
w
.
J. Env
i
ron. Na
notec
h
nol.
20
13; 3(3):
106-1
15.
[10]
GNU Ocave. http://
w
w
w
.
g
nu.o
r
g/soft
w
a
r
e
/oct
ave/
[11]
Oscilent
Corporati
o
n
IF SAW
F
i
l
t
er. 820-IF
70.0M-F
.
http://
w
w
w
.
osc
i
lent.com/spec
_
pag
es/if_sa
w
f
i
l
t
er/if_820
_if7
0
_0f.htm
Evaluation Warning : The document was created with Spire.PDF for Python.