Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 294 ~
299
DOI: 10.115
9
1
/ijeecs.v1.i2.pp29
4-2
9
9
294
Re
cei
v
ed O
c
t
ober 5, 20
15;
Revi
se
d Ja
n
uary 20, 201
6
;
Accepte
d
Ja
nuary 31, 20
1
6
Design and Simulation for UHF Oscillator using SAWR
with Different Schematics
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, Egy
p
t
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: motaz.ali@fe
ng.bu.e
du.e
g
A
b
st
r
a
ct
Vario
u
s sche
m
atics for col
p
itts
oscillator
w
i
th fixed ultra-hi
gh frequ
en
cy using eith
e
r
LC tank
circuits or o
n
e
port surface
acoustic w
a
ve
reson
a
tor
are
p
rese
nted. F
o
ur circuits us
e
d
to ach
i
eve
4
33.
9
MH
z
oscil
l
atin
g frequ
ency, T
w
o of them u
s
ing NP
N
Bip
o
lar j
uncti
on tr
ansistor, w
h
il
e
the others
us
in
g
oper
ation
a
l a
m
plifier w
i
th hi
gh
speed, ga
in a
nd accu
r
a
cy. A comp
ariso
n
b
e
tw
een usin
g passiv
e
ele
m
e
n
ts
as a sourc
e
of reson
ance fre
q
uency a
nd
usin
g SAW
resonat
or is intro
duce
d
.Another c
o
mparis
on b
e
tw
ee
n
usin
g an
eq
uiv
a
le
nt lu
mp
ed c
i
rcuit inste
ad
o
f
SAW
R pa
cka
ge i
n
osci
llator
desi
gn is
also
introd
uced. T
w
o
differentsoftw
aretools are us
ed
to achi
eve
the
re
quir
ed
simulati
on. Pro
t
eus an
d ADS
toolsar
e
us
ed
i
n
simulati
on
w
i
th AC, S-par
a
m
e
t
ers an
d hy
brid
si
mul
a
tio
n
. T
h
is pa
per
is co
n
s
ider
ed
a d
i
rec
t
appl
icati
on fo
r
SAW
resonator
s in w
i
deba
nd
w
i
dth ASKT
ransmitter / Recei
v
er.
Ke
y
w
ords
: os
cillator, R
e
son
a
tor and SAW
R
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
ts reser
ve
d
.
1. Introduc
tion
There i
s
n
o
doubt th
at su
rface
a
c
o
u
sti
c
wave
devices
are n
o
w
applie
d in
ba
sic an
d
importa
nt
ap
plicatio
ns
a
s
filters, sen
s
o
r
s, corr
elato
r
s and
resonat
o
rs.SA
W
re
sonator i
s
re
cently
prefe
r
abl
e th
an crystal
s
in
desi
gn of
oscillators
as a freque
ncy sel
e
ctive
comp
o
n
ent.
It
can b
e
use
d
to a
c
hi
e
v
e larg
e scal
e of freq
uen
cies from lo
w
range
up to
G
i
gahe
rtz [1
-2]
.
Variou
s typ
e
s
of oscillato
rs
are
presente
d
u
s
ing
different sch
e
ma
ti
c d
e
si
gn
as g
eneri
c
o
scillat
o
r,
clap,
Ha
rtl
e
y,
VCO, colpitts, and
crystal
oscillators [3]
.
In previou
s
studie
s
, L
C
t
ank
ci
rcuits
were
used d
u
e
to
its simpli
city for desi
gn, then crystal o
scill
ator
s we
re famously u
s
ed in orde
r to its stability
according to
temperature
cha
nge.
Now SAW co
m
p
onent a
c
hiev
e more stabi
lity than crystal
oscillator does.Many other features
of using SAW devices like its
mi
nimum inserti
on loss [4], low
co
st an
d fab
r
icatio
n n
o
t complicated. I
n
this
pap
er,
a p
r
eviou
s
ly
model
ed
of
one
port SA
W
resonato
r
i
s
use
d
in a fixed freq
uen
cy
oscilla
tor
circuit [5].A pre
v
ious
work o
f
using SA
W
resonato
r
in
VCO de
sig
n
i
s
p
r
esented [
6
]. The aim o
f
this pap
er i
s
to achi
eve 4
3
3.9 MHz
col
p
itts
oscillator u
s
i
ng SAW resonator
with h
i
gh q
uality fa
ctor.
W
e
also
intro
d
u
c
ed
a de
sig
n
fo
r
the
oscillator using primarily LC tank
circuit
s
. In both cases, oscillator
is built with negative feedback
stru
cture usi
n
g bipola
r
jun
c
tion transi
s
to
r or
ope
ration
al amplifier a
s
sh
own in Figure 1.
Figure 1: General Block
Di
agram of Col
p
itts oscillator usi
ng LC tank or SAWR
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Design and Sim
u
lation for UHF
Oscillat
o
r usi
ng SAWR with Different… (M. M. El
sherbini
)
295
2.
Oscillator Schematics and Simulation Results
In this se
ction, variou
s
schemati
c
fo
r
fixed frequ
ency o
scill
ator of 433.9
2
MHz
are
introdu
ce
d.Th
e main
criteri
a
of o
scill
ator is t
hat
a po
rt
ion of o
u
tput
being fe
edb
a
c
k to the i
npu
t.
The insertio
n loss is ba
si
ca
lly dependin
g
on the oscilla
ting freque
ncy.
2.1.
Ordinar
y
Oscillator Circuit Design
w
i
t
h
BJT
Ordinary
desi
gn of
colpitts
oscillator based on
simpl
e
LC tank
circuitshown i
n
Fi
gure 2,
that co
nne
cte
d
bet
wee
n
b
a
s
e
and
colle
ctor of B
J
T am
plifier
o
r
between output pi
n
an
d
in
put
pi
n
of operational
amplifier to
d
e
liver si
ne
wa
ve in
output.L
C tan
k
net
wo
rk fo
rm a
ca
p
a
citive voltag
e
divider that control
s
the oscillation frequency.
Figure 2. LC - Tank
Circuit of
ordinary colpitts oscillator
To a
c
hieve
o
scill
ator
at 4
33.9 M
H
z,
we u
s
e th
e fol
l
owin
g eq
uati
on for fre
que
ncy of
oscillation to
estimate valu
es for L
1
, C1
and C2.
1
2
os
c
eq
f
L
C
(
1
)
12
12
*
eq
CC
C
CC
(2)
With simpl
e
cal
c
ulatio
ns, we assu
med
equated val
ues for b
o
th twocapa
citors C1 and
C2 a
nd
equ
al 20pF,
so
at 4
33.92 M
H
z, the expe
ct
ed
value for th
e
coil i
s
1
3
.45n
H we
can
de
sign
a simple o
r
di
nary ci
rcuit for colpitt
s
oscil
l
ator usi
ng A
D
S is preced
ed in Figu
re 3
.
Figure 3. Sch
e
matic of ordi
nary 433.9 M
H
z
colpitts o
s
cillator
with BJT
C1
C2
L1
ou
t
R
R3
R=
1
k
O
h
m
p
b
_nec
_2S
C
4228_1
9921211
Q2
C
C3
C
=
10 p
F
C
C4
C
=
8.
0 pF
C
C5
C
=
2.
0 pF
Te
r
m
Te
r
m
1
Z=
5
0
O
h
m
Nu
m
=
1
R
R5
R=
5
0
O
h
m
C
C6
C
=
2.
0 pF
R
R4
R
=
160 O
h
m
V_
D
C
S
RC1
V
d
c
=
12 V
R
R2
R=
2
k
O
h
m
C
C1
C
=
1 nF
C
C2
C
=
1 nF
L
L1
R=
L=
0
.
269 nH
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ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 294 – 299
296
The AC Sweep response (Gain in dB
) of the
output waveform of
ordinary oscillator is
sho
w
n
in Fi
g
u
re
4 a
nd it i
s
p
r
o
c
ed
ure
usin
g
p
r
oteu
s tool. A ba
nd
of fre
quen
ci
es
between
420
MHz and 450 MHz i
s
selected to
ensure
the oscillation frequency.
Figure 5 indi
cate
s the im
peda
nc
e parameters (S
-p
ar
am
eters) fo
r refle
c
ted tra
n
smitted
signal of the
oscillator and
it is procedure for the sam
e
ci
rcui
t usi
n
g ADS tool. S
m
ith chart i
s
also
obtaine
d to indicate the ov
erall im
p
edan
ce of the oscil
l
ator ci
rcuit.
Figure 4. AC sweep respo
n
se of L
C
col
p
ittsoscillato
r (Using Proteu
s)
Figure 5. Smith chart and
S-par
ameters response of LC colp
itts oscillator
(Using ADS)
In order to sustain the osc
illations, operational am
plifier may al
so be used with high
freque
ncy a
n
d
negative a
nd po
sitive feedb
ack rath
er than B
J
T.
Another
co
nfiguratio
n with
OPAMP is bu
ilt using ADS
and proteu
sto
o
ls in the nex
t section.
2.2.
Ordinar
y
Oscillator Circuit Design
w
i
t
h
OPAMP
The previo
us tank ci
rcuit
is re-used
w
ith High
spee
d,
Low noi
se
op
eration
a
l a
m
p
lifier a
n
d
negative fee
dba
ck to a
c
h
i
eve gain.Th
e positive fe
e
dba
ck (Ta
n
k
ci
rcuit) is
adde
d
to su
stain
oscillation. Fi
gure
6 indi
ca
tes 433.9
2
M
H
z o
s
cillato
rwith the sam
e
tank
circuit
param
eters
bu
t
with repla
c
in
g
the NP
N bipola
r
ju
ncti
on
tran
si
sto
r
with high
pre
c
isi
on OP
AMP.
Another
para
m
eter va
lues sugg
esti
on fo
r
C1,
C2 an
d L
1
i
s
cho
s
e
n
to
achieve the
sa
me fre
q
ue
ncy of
oscillation.
We appli
ed S-Para
meter
si
mulation u
s
in
g ADS tool and Figure 7 reco
rdin
g S11
for th
e
expecte
d out
put and i
ndicate the maxi
mum val
ue at
approximate freque
ncy
o 4
33.92
M
H
z (4
34
MHz).Smith chart
that re
cord
s
imp
eda
nce ci
rcl
e
is also monito
re
d
within
the same
figure.The
maximum of S11 is do
wn
wards d
ue to negative feed
back of ope
ra
tional amplifie
r that inverts the
expecte
d cu
rves.
f
r
eq
(
4
20
.
0
M
H
z
t
o
45
0.
0M
H
z
)
S(
1
,
1
)
In
p
u
t R
e
f
l
e
c
t
i
o
n
C
o
e
ffi
c
i
e
n
t
42
5
4
30
4
3
5
4
4
0
44
5
42
0
4
50
-2
0
-1
5
-1
0
-5
-2
5
0
fM
H
d
B
(S
(1
,
1
)
)
R
e
v
e
r
s
e
T
r
an
s
m
i
s
s
i
on
,
d
B
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Design and Sim
u
lation for UHF
Oscillat
o
r usi
ng SAWR with Different… (M. M. El
sherbini
)
297
Figure 6. Sch
e
matic of ordi
nary 433.9 M
H
z
colpitts o
s
cillator
with O
PAMP
Figure 7. Smith chart and
S-parameters of Oscillator
2.3.
SAW Localoscillator Ci
rcuit using ECM and BJT
No
w, the LC tank ci
rcuit is repl
aced
with
equival
e
nt circuit mo
del of one p
o
rt SAW
resonato
r
th
a
t
estimate
d i
n
[5]. To
ach
i
eve ap
pr
oxi
m
ately 12
62
4 Qu
ality fact
or,
so th
e
se
ries
parall
e
l re
so
nan
ce with p
a
ram
e
ters estimated as
shown in Figu
re 8. Applyin
g
the AC sweep
simulatio
n
, we obtain si
nu
soid
al wavefo
rm sh
own
in Figure 9. Sna
p
sh
ot for the output sig
nal
is
captu
r
ed
for a
small
fre
quen
cy rang
e in
pr
oof t
he m
a
x/min
gain
occu
rs
at the d
e
si
g
ned
freque
ncy 43
3.9 MHz. Proteus u
s
ed t
o
obtain the result. The value
s
of C1, C3 and R1 are
cal
c
ulate
d
to achieve the
same de
sire
d osc
illating
freque
ncy. S11 value for
usin
g SAWR is
better than
simulated in Fi
gure 5 u
s
in
g tank
circuit.
Figure 8. Usi
ng ECM for S
A
W re
son
a
tor in local o
scill
ator de
sign a
nd BJT
S-
Pa
r
a
m
e
t
e
r
Si
m
u
l
a
t
i
o
n
Li
near
F
r
equenc
y
S
w
eep
L
L1
R=
L=
0.
269 n
H
C
C2
C
=
1 nF
C
C1
C
=
1 nF
R
R1
1
R
=
50 O
h
m
D
i
s
p
l
a
y
T
em
pl
at
e
di
s
p
t
e
m
p
1
"
S
_P
ar
am
s
_
Q
uad_dB
_S
m
i
t
h
"
Te
m
p
Di
s
p
S_
Pa
r
a
m
SP1
S
t
ep=
S
t
op=
450 M
H
z
S
t
ar
t
=
420 M
H
z
S-
PAR
AM
ET
ER
S
R
R8
R
=
2 k
O
hm
Te
r
m
Te
r
m
1
Z
=
50 O
h
m
Nu
m
=
1
Op
A
m
p
AM
P2
V
C
C
=
15 V
VEE=
-
1
5
V
Z
e
r
o1=
P
o
l
e1=
BW
=
1
M
H
z
VO
S=
0
V
IOS
=
0
A
S
l
ew
R
a
t
e
=
1e+
6
CCo
m
=
0
F
R
C
o
m
=
1 M
O
hm
CDif
f
=
0
F
R
D
i
f
f
=
1 M
O
hm
R
out
=
100 O
h
m
CM
R=
G
a
i
n
=
100 dB
R
R1
0
R=
1
k
O
h
m
fr
e
q
(
4
2
0
.0
M
H
z
to
4
5
0
.
0
M
H
z
)
S(
1
,
1
)
I
n
p
u
t R
e
fl
e
c
ti
o
n
C
o
e
f
fi
c
i
e
n
t
4
2
5
4
30
43
5
4
4
0
44
5
42
0
4
5
0
-1
3
.
5
-1
3
.
0
-1
2
.
5
-1
2
.
0
-1
1
.
5
-1
4
.
0
-1
1
.
0
fr
e
q
, M
H
z
d
B
(S
(1
,
1
)
)
m1
R
e
v
e
r
s
e T
r
a
n
s
m
i
s
s
i
on
,
d
B
m1
fr
e
q
=
d
B
(S
(1
,
1
))
=
-
1
1
.
1
4
3
Ma
x
43
3.
9M
H
z
Q1
2
S
C
1
162
C2
2pF
R1
16
0
L2
9
6
.
5
29u
C?
0.
00
1
3
9
4
p
C6
2.
11
2
p
F
R4
22
.
1
C2
(
2
)
R2
2K
C4
1u
F
R5
(2
)
R5
2k
C1
10
p
F
C3
8p
F
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 294 – 299
298
Figure 9. AC sweep respo
n
se of ECM
-
SAW oscillat
o
r
2.4.
SAW Oscillator Based on
OPAMP using SAW
Resonator
In this se
ctio
n, another
co
nfiguratio
n of
SAW oscill
ator u
s
ing on
e port SAW re
son
a
to
r
instea
d LC ta
nk ci
rcuit and
based o
n
op
eration
a
l am
p
lifier with hig
h
gain. Figure 10 is for using
the eq
uivalen
t
circuit m
ode
l for
one
po
rt
SAW resonat
or,
while
Figu
re
11 i
n
trod
u
c
e
s
e
m
bed
de
d
packa
ge
co
mpone
nt in
ADS for SAW
re
son
a
tor.
The
de
sig
n
is procedu
re Referring
to
(SARCC4
3
3
M
92BXM0) S
A
WR
with eq
uivalent circui
t model of (L
1 = 96.52
9 u
H
, C2
= 0.001
394
pF, R4
=22.1
ohm and
C1
= 2.112 p
F
)
withqu
ality fa
ctorcal
c
ulate
d
as 11
908 a
c
cordi
ng to value
s
of
equivale
nt passive para
m
eters
of
SA
W resonato
r
[
7
]. The
clo
s
e
d
loop
gai
n
i
s
de
signe
d
to
be
(2). Using
ADS
with s-para
m
eter simul
a
tion we
g
o
t Fi
gure
12
-13.
5
0
ohm
termi
n
al impe
dan
c
e
is
adde
d for sim
u
lation. Th
e o
u
tput obtain
e
d
from
usi
ng
SAW re
so
nat
oris relatively better tha
n
th
at
obtaine
d fro
m
passive L
C
tan
ks
circu
i
t of Figure
5. Figure 14, i
s
a com
p
a
r
ati
v
e study of u
s
ing
LC tan
k
circui
t and SAW re
son
a
tor on th
e S11 param
eter of the sa
me oscillato
r.
Figure 10. Using ECM for
SAW re
sonat
or in OPAMP oscillator d
e
si
gn
Figure 11. 43
3.9MHz oscill
ator usi
ng fixed frequ
e
n
c
y SAWR
S-
P
a
r
a
m
e
t
e
r
Si
m
u
l
a
t
i
o
n
Li
ne
ar
F
r
equenc
y
S
w
e
e
p
D
i
s
p
l
a
y
T
em
p
l
at
e
di
s
p
t
e
m
p
1
"
S
_
P
ar
am
s
_
Qu
ad
_dB
_Sm
i
t
h
"
Te
m
p
Di
sp
S_P
a
r
a
m
SP1
St
ep=
St
op=
450
M
H
z
St
ar
t
=
420
M
H
z
S
-
P
A
RA
M
E
T
E
RS
Po
r
t
P2
Nu
m
=
2
Op
Am
p
AM
P
1
R
C
om
=
1
M
O
hm
CD
i
f
f
=
0
F
R
D
i
f
f
=
1 M
O
hm
R
o
ut
=
1
00 Oh
m
CM
R=
Ga
i
n
=
1
00 d
B
Te
r
m
Te
r
m
1
Z
=
50 Oh
m
Nu
m
=
1
c
R
es
SAW
SA
W
r
es
1
C
p
=
2
e-
12 F
rs
=
1
O
h
m
f
o
=
433
.
9
2 M
H
z
Q=
11
909
.
6
7
R
R2
R=
2
kO
h
m
R
R1
R=
1
kO
h
m
R
R3
R=
5
0
O
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Design and Sim
u
lation for UHF
Oscillat
o
r usi
ng SAWR with Different… (M. M. El
sherbini
)
299
Figure 12. S11 for OPAMP oscill
ator u
s
i
ng
ECM of SAWR
Figure 13. S11 of 433.9MHz oscillato
r using
fixed frequen
cy SAWR
Figure 14. S11 para
m
eter
while u
s
ing L
C
tank circuit versu
s
SAW
reso
nator
3. Conclu
sion
Some differe
nt schemati
c
s for d
e
si
gn
of 433.
92 M
H
z
colpitt
s
oscillatorare prese
n
ted in
this pa
pe
r.Both BJT a
nd
O
PAMP are
used in th
e de
si
gn u
s
ing
eith
er SAW re
so
nator
or
ordi
n
a
ry
passive el
em
ents
(L
C tan
k
circuit). A
D
S and
pr
ote
u
s
a
r
e
CAD tools used i
n
pro
c
e
dure t
h
e
desi
gn sch
e
m
atics
and
si
mulation for
AC swee
p an
d S-pa
ramete
rs.
U
sin
g
SAW re
so
nato
r
lead
s
for a
high
a
c
cura
cy o
scill
ator
with mi
nim
insertion
lo
ss a
nd
be
st ga
in. SAW
reso
nator i
n
the
b
e
st
choi
se for o
s
cillator d
e
si
gn
beca
u
se its stabilit
y, high speed a
nd fixed freque
ncy o
f
oscillatio
n
.
Referen
ces
[1]
GSM Galanda
nci, KO E
w
a
n
s
i
ha. Des
i
gn An
d Simul
a
tion O
f
A 20 Khz
T
o
50 Khz Vari
abl
e F
r
eque
n
c
y
Oscillator (VFO).
Internation
a
l Journ
a
l of R
e
searc
h
and
R
e
view
s in App
l
i
ed Scie
nces (IJRRAS)
. 201
3;
16(1): 24-
38.
[2]
S T
homas, Z
Rácz, M Cole, JW Gardner.
High-fre
q
u
e
n
cy One-p
o
rt
Colp
itts SAW Oscillator fo
r
Che
m
ic
al S
e
n
s
ing.
Proc. of the Si
xth Inter
n
ation
a
l C
onfer
ence
on Adv
a
nces in
Circu
its, Electronic
s
and Micr
o-el
ec
tronics (CENIC
S). 2013; 13-
1
7
.
[3]
AT Kabir. Voltage C
ontrol
l
ed
O
scillators Tune
d
w
i
th BS
T Ferroelectric
Capacit
ors. Univers
i
t
y
of
Color
a
d
o
at Co
lora
do Spri
ngs.
2012.
[4]
MM Elsherbini, MF Elkordy
,
A
M
Gomaa. Ins
e
rtion
Loss Pre
d
ictio
n
an
d Mo
nitori
ng for SA
W
Dela
y-l
i
n
e
.
Internatio
na
l J
ourn
a
l for
Res
earch
in E
m
er
gin
g
Sci
ence
and T
e
chn
o
l
o
gy (IJREST
)
. 201
5; 2(9): 1
6
-
18.
[5]
MM Elsher
bini, MF Elkordy
,
AM
Gomaa. S
c
attering P
a
ra
meters pre
d
icti
on for 4
33M
H
z
SAW
R
w
i
t
h
Minimum Ins
e
rtion loss.
T
E
LK
OMNIKA Indon
esia
n Journ
a
l o
f
Electrical Engin
eeri
n
g
. 20
1
6
; 17(1).
[6]
T
Yasuda, K Uchin
o
, S Izumi
y
a, T
Adach
i
, SS Senana
yaka. 433 MHz
w
i
de-tu
nab
le
hig
h
Q SAW
oscill
ator.
Eur
ope
an F
r
eq
ue
ncy and T
i
me
F
o
rum & Internati
ona
l F
r
eque
ncy Contr
o
l Symp
osi
u
m
(EFTF/
IFC).
IE
EE
. 2013: 74
4-
746.
[7]
SAW
Resonat
ors, SARCC4
3
3
M92B
XM
0, http://
w
w
w
.
di
gch
i
4
2
5
4
30
4
3
5
440
44
5
42
0
4
50
-1
2
.
5
-1
2
.
0
-1
1
.
5
-1
1
.
0
-1
0
.
5
-1
0
.
0
-1
3
.
0
-9
.5
fre
q
,
MH
z
d
B
(S
(1
,
1
))
m1
R
e
v
e
r
s
e T
r
an
sm
i
ssi
o
n
,
d
B
m1
f
r
eq=
d
B
(S
(1
,
1
))=
-1
2
.
9
1
9
Mi
n
4
33.
9M
H
z
4
2
5
4
30
43
5
4
4
0
44
5
42
0
4
50
-1
4
.
0
-1
3
.
5
-1
3
.
0
-1
2
.
5
-1
2
.
0
-1
1
.
5
-1
1
.
0
-1
0
.
5
-1
0
.
0
-1
4
.
5
-9
.
5
f
r
eq,
M
H
z
d
B
(
S
(1
,
1
))
m1
R
e
v
e
r
s
e
Tr
an
s
m
i
s
s
i
on
,
dB
m1
fr
e
q
=
d
B
(
S
(1
,1
))
=
-
1
4
.0
3
1
Mi
n
4
33.
9
M
H
z
42
5
4
3
0
43
5
4
4
0
44
5
4
2
0
450
11
.
5
12
.
0
12
.
5
13
.
0
13
.
5
11
.
0
14
.
0
-14
-13
-12
-11
-10
-15
-9
fre
q
, M
H
z
LC
t
an
k
(R
e
d)
SAW
R
(B
l
ue
)
Evaluation Warning : The document was created with Spire.PDF for Python.