Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
58
3
~
59
5
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.8
809
5
83
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Comparative Assessment on
Linearity Test based V2
π
and V
π
/2
Voltage Variations of Closed Loop IFOG
T. Sireesha
1
, K.
Kris
hn
a Murth
y
2
1
Department of
ECE, Potti Sriramulu Chalav
adi
Malli
kharjuna R
a
o College of
En
gineer
ing and
Technolog
y
,
Vijay
a
wad
a
, Krishna (Dt), Andhra Pradesh
,
India
2
Department of Electronics,
P.
G
.
Center, P.B. Sid
dhartha Arts & Scien
c
e College,
Vijay
a
wad
a
, Krishna (Dt), Andhra
P
r
ades
h, Ind
i
a.
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 14, 2015
Rev
i
sed
No
v
30
, 20
15
Accepted Dec 22, 2015
Interferometric
Fiber Optic G
y
r
o
scope (IF
OG)
has to operate in
closed loop
condition
to a
c
h
i
eve
inert
i
al
gra
d
e perform
anc
e
.
The c
l
osed loo
p
s
y
stem
is
m
a
inl
y
d
e
pends upon the am
plitu
de of the ram
p
signal (V2
π
of IOC) and bias
(square wave) signal frequ
ency (f
bias
). The digital phase ramp function is
given as feedb
a
ck to the optical s
y
st
em and makes g
y
ro
to null condition
.
The peak-to-p
e
ak amplitude (V
π
/2) of biasing
signal is one-fo
urth of th
e
ramp amplitude (V2
π
). If there
are an
y
v
a
ri
ati
ons
in the am
plitude of the
ramp and bias
ing signals, th
en it
introdu
ces variations in
the g
y
ro
perform
ance
. In this
paper, a
com
p
arativ
e dis
c
us
s
i
on m
a
de in the g
y
r
o
parameters for
three
cases: (
i
) V
2
π
(var
y
)
& V
π
/2 (constant), (
ii)
V
π
/2 (va
r
y)
& V2
π
(constan
t
) and (iii) both
V2
π
and V
π
/2
are var
y
ing simultan
e
ously
.
The eff
ects on g
y
roscop
e are d
e
scribed with th
e derived v
a
lues
in terms of
line
a
rit
y
.
From
t
h
e exp
e
rim
e
nta
l
results, i
t
was o
b
served th
at th
e
g
y
ro ou
tput
is ver
y
sensit
ive
with respe
c
t
to
V2
π
variations and obtain
e
d th
e
percen
tag
e
error of 10% in g
y
ro output, but ver
y
less effect due to V
π
/2 variations
. So,
the proper r
e
setting of ramp voltage (V2
π
) is r
e
q
u
ired to
avoid n
online
a
rit
i
es
and inst
abil
iti
es
in g
y
ro ou
tput
.
Keyword:
B
i
asi
ng s
q
uare
wa
ve si
gnal
Vo
ltag
e
(V
π
/2)
C
l
osed l
o
o
p
a
p
pr
oac
h
Inter
f
er
om
etric fibe
r
optic
Gy
ro
sco
p
e (I
F
O
G
)
Linearity
Ra
m
p
vo
ltag
e
(V2
π
)
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
T. Siree
s
ha
,
Assistant Profe
ssor, Depa
rtm
e
nt
of
ECE
,
Po
tti Sriram
u
l
u Ch
alav
ad
i Mallik
h
a
rj
un
a Rao
C
o
lleg
e
o
f
En
g
i
n
eeri
n
g
and
Techno
log
y
,
Vi
jay
a
wa
da,
K
r
i
s
h
n
a (Dt
)
, An
dh
ra Pra
d
es
h, I
ndi
a.
Em
a
il: sirish
ata
m
m
a
n
a
@ red
i
ffm
ail.co
m
1.
INTRODUCTION
A fi
be
r o
p
t
i
c
gy
r
o
sco
p
e (
F
O
G
) se
nses cha
nge
s i
n
ori
e
nt
at
i
on, t
h
us pe
r
f
o
r
m
i
ng t
h
e fu
nct
i
on
of a
m
echani
cal
gy
rosc
o
p
e.
FO
G
i
s
an i
m
port
a
nt
de
vel
o
pm
ent
in t
h
e
fi
el
d
of
fi
bre
o
p
t
i
c
sens
o
r
s,
whi
c
h
have
been
st
udi
e
d
a
n
d
de
vel
o
ped
m
o
re t
h
an
t
w
o
deca
d
e
s. F
O
Gs a
r
e
u
s
ed i
n
Ine
r
t
i
a
l
Navi
gat
i
o
n
Sy
st
em
(IN
S),
gu
i
d
ance
,
cont
rol systems in airc
raft
and s
p
acecra
f
t et
c.
FOGs are
designe
d to m
easure the rotation induces
pa
th
differe
n
ce as m
e
a
s
ure
of
pha
se or fre
quency
di
ffe
re
nce bet
w
een t
h
e c
o
u
n
t
er pr
o
p
agat
i
n
g wa
ves
.
Tw
o
di
ffe
re
nt confi
g
urations exist
:
Interferom
etr
i
c Fiber
Opt
i
c
Gy
r
o
sc
o
p
e (
I
FO
G
)
an
d
R
e
sona
nt
Fi
be
r O
p
t
i
c
Gy
ros
c
ope
s (R
F
O
G
)
.
The i
n
duce
d
o
p
t
i
cal
pat
h
di
f
f
e
rence
can be m
easured in two
ways (i) by m
easu
r
ing a fre
que
nc
y in
a laser reso
nato
r
o
r
in
a reson
a
tor fibre o
p
tic
gy
r
o
sco
p
e (i
i
)
by
m
easuri
ng
a phase
of t
w
o
i
n
t
e
rfe
ri
n
g
be
am
s i
n
an Int
e
r
f
er
om
et
ri
c fi
ber o
p
t
i
c
gy
r
o
sco
p
e [
1
]
.
The RFOG is
use
d
in
researc
h
stages
and
perform
a
nce of
th
e g
y
ro
sco
p
e
is li
mited
b
y
back
scattering
no
ise of
fre
que
ncy
[
2
]
.
A bet
t
e
r al
t
e
r
n
at
i
v
e t
o
t
r
a
d
i
t
i
onal
spi
n
ni
n
g
m
a
ss gy
rosc
ope
s p
r
o
v
e
n
b
y
IFO
G
s,
hav
e
hi
g
h
reliab
ility, wide d
y
n
a
m
i
c rang
e, l
o
w power
co
nsu
m
p
tio
n
,
lig
h
t
weigh
t
, and
low co
st
[3
].
The si
g
n
al
p
r
o
cessi
ng s
c
hem
e
of a
IF
OG i
s
br
oadl
y
cl
assi
fi
ed i
n
t
o
t
w
o
m
a
jor cat
e
g
o
r
i
e
s nam
e
l
y
an
o
p
e
n
l
o
op
ap
pro
ach and
a cl
osed
loop
ap
pr
oach
,
bu
t r
e
str
i
cts it p
r
esen
tly in
Av
i
o
n
i
cs and I
n
er
tial N
a
v
i
gatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
58
3 – 5
9
5
58
4
Grad
e app
licatio
n
s
[4
] du
e t
o
its co
m
p
lex
ity o
f
t
h
e
former.
In op
en
loo
p
IFOG syst
e
m
th
e ro
tatio
n
rate
sen
s
ing
is ob
tain
ed
thro
ugh
a
d
i
rect m
easu
r
emen
t [5
], bu
t th
is system
is n
o
t
pe
rfectly stable beca
use the
r
e is a
vari
at
i
o
n i
n
t
h
e
ret
u
r
n
i
n
g
opt
i
cal
po
wer
,
cha
nge
s i
n
t
h
e am
pl
i
t
ude
o
f
t
h
e
p
h
as
e m
odul
at
i
o
n
i
n
t
h
e
dem
odulated biased signals
whic
h
will
cause errors i
n
detector
output an
d the
re
sponse
is nonlinear, l
i
m
i
ted
d
y
n
a
m
i
c ran
g
e
, low accu
r
acy
an
d less sen
s
itiv
ity.
In o
r
der t
o
el
i
m
i
n
at
e t
h
e depende
ncy
of t
h
e
l
i
ght
i
n
t
e
nsi
t
y
a cl
osed l
o
o
p
schem
e
i
s
used. I
n
cl
os
e
d
lo
op
IFOG syste
m
th
e
ro
tati
o
n
rate
sen
s
i
n
g
is o
b
t
ai
n
e
d th
ro
ugh
a feed
b
a
ck
(ram
p
) sig
n
a
l
t
o
n
u
llify
th
e
r
o
tation
-
indu
ced
Sagn
ac
p
h
a
se er
ror
.
Th
e an
alog
so
lu
tion
o
f
clo
s
ed
loop con
f
i
g
ur
ation
,
b
a
sed
on
an
an
alog
pha
se ram
p
wi
th a biasing
(sine wa
ve
) m
odulation,
does
not re
prese
n
t a
very
efficient solution because
the
o
u
t
p
u
t
is
v
e
ry
sen
s
itiv
e to the env
i
ro
n
m
en
t. A
g
r
eat im
p
r
o
v
e
m
e
n
t
is ach
i
ev
ed
with
the d
i
g
ital clo
s
ed
-l
o
op
con
f
i
g
urat
i
o
n
of
bi
asi
n
g (s
q
u
are
wave
) m
o
d
u
l
a
t
i
on a
n
d
feed
bac
k
p
h
as
e ram
p
i
s
adopt
ed t
o
s
u
pp
re
ss t
h
e
closed loop error ne
ar the zero poin
t and to im
prove the linear characte
r
is
tic and stabilize the scale factor and
its in
sen
s
itiv
eness ag
ai
n
s
t environ
m
en
t, esp
e
cially ag
ain
s
t v
i
bratio
n. Howev
e
r, th
e
cl
o
s
ed
loop
IFOG syste
m
is stable and
ha
s good
accurac
y
[6].
2.
DESRIPTIO
N O
F
FIBE
R
OPTIC G
Y
ROSCOPE
Fi
ber
opt
i
c
gy
rosc
o
p
e i
s
a r
o
t
a
t
i
on sens
o
r
,
wo
rki
n
g on the principle of
sagnac effect.
Sagnac first
dem
onst
r
at
ed
t
h
e opt
i
cal
gy
r
o
sc
ope
p
r
i
n
ci
p
l
e
i
n
19
1
3
. Im
pl
em
ent
a
t
i
on
o
f
opt
i
cal
gy
ro
s
c
ope
s was d
o
n
e
by
usi
n
g
Sag
n
ac
e
ffect
,
so
fa
r,
w
h
i
c
h
st
at
es t
h
at
i
n
duce
d
o
p
t
i
cal
pat
h
di
ffe
renc
e by
c
o
unt
e
r
pr
opa
gat
i
n
g
bea
m
s i
n
a ro
tatin
g
referen
ce fram
e
is
p
r
op
ortio
n
a
l to th
e ab
so
lu
te ro
tatio
n
[7
], [8
]
.
Th
e op
eration
p
r
i
n
cip
l
e of Sagn
ac
in
terfero
m
e
ter is as shown in
Fig
u
re
1
.
Figu
re
1.
Sa
gn
ac I
n
terfe
rom
e
ter
Wo
rki
n
g
P
r
inciple
Wh
en
system
h
a
s
n
o
ro
tation
(i.e., at
rest) th
e ligh
t
propag
a
tin
g in
cl
ock
w
ise
(C
W)
an
d coun
ter
clockwise (CC
W
)
directions t
r
ave
r
se ide
n
tical paths, t
h
e
n
there is
no phas
e diff
ere
n
ce
be
tween t
h
em
.
Whe
n
th
e syste
m
ro
tates at an
angu
lar ro
tatio
n
rate
Ω
, th
en
t
h
e b
eam
o
f
lig
ht ro
tatin
g
with ring
h
a
s
op
tical p
a
th
lo
ng
er th
en
the co
un
ter
p
r
o
p
a
gat
i
ng
beam
by
a di
st
ance
C
LR
[5
]. Th
e resu
l
t
an
t ro
tation
in
du
ced
sagn
ac
p
h
a
se sh
ift is,
C
LD
s
2
(1
)
Whe
r
e,
D i
s
di
am
et
er of t
h
e sens
or coi
l
,
L i
s
l
e
ngt
h
of t
h
e
opt
i
cal
fi
ber
,
λ
i
s
l
i
ght
wave
l
e
ngt
h
,
Ω
is rotatio
n
rate and
C is sp
eed of ligh
t
in v
a
cu
u
m
[1
],
[9
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Com
p
arative Assessm
ent on
L
i
nearity Test based
V2
π
and
V
π
/2
Vo
ltag
e
V
a
riation
s
o
f
…
(
T
.
Si
rees
ha
)
58
5
Fi
gu
re
2.
B
a
si
c C
o
nfi
g
u
r
at
i
o
n
of
FO
G
A ba
si
c FO
G
con
f
i
g
urat
i
o
n i
s
sh
ow
n i
n
Fi
g
u
re
2.
In
t
w
o-
wave i
n
t
e
r
f
er
o
m
et
er, t
h
e i
n
t
e
nsi
t
y
on t
h
e
p
h
o
t
o
d
e
tector
represen
ts w
ith a co
m
b
in
atio
n o
f
t
h
e two
light waves
,
va
ries
as cosi
ne of
Sagnac phase with
its
maxim
u
m
value at zero.
Th
is in
ten
s
ity (I
o
r
I
d
) is expr
essed
as,
(2
)
Whe
r
e,
I
0
is th
e m
ean
v
a
lu
e
o
f
th
e in
ten
s
ity.
Th
e
ro
tation
rate
is calcu
lated w
ith
t
h
e
d
e
tected
in
ten
s
ity [6
].
Th
e li
m
ita
tio
ns in
th
e b
a
sic co
nfigu
r
ation
are [7
], [10
]
: Poo
r
sen
s
itiv
ity fo
r sm
all
rotatio
n
rates,
di
rect
i
o
n am
bigui
t
y
, rest
ri
ct
e
d
dy
nam
i
c range d
u
e t
o
t
h
e 2
π
p
e
riod
icity o
f
th
e resp
on
se
cu
rv
e and
ou
tpu
t
is a
n
o
n
lin
ear fu
n
c
tio
n
of th
e ro
tatio
n
rate. Th
e
p
r
ob
lem
s
o
f
p
o
o
r sensitiv
ity
an
d
d
i
rection
am
b
i
g
u
ity are u
s
u
a
lly
ove
rc
om
e by
t
h
e a
ppl
i
cat
i
o
n
of
t
h
e
di
f
f
ere
n
t
i
al
phase
m
odu
l
a
t
i
on.
2.
1. T
h
e O
p
en
L
o
op
Co
nfi
g
ura
t
i
o
n
A phase m
o
dulator is use
d
for t
h
is purpose and
it is placed in asymmetric position i
n
the se
nsi
ng
fi
ber l
o
o
p
, s
o
t
h
at
t
w
o c
o
u
n
t
e
r pr
o
p
a
g
at
i
ng
wave
s pass t
h
ro
ugh
th
e m
o
d
u
lato
r at d
i
fferen
t
ti
m
e
in
stan
ts b
e
fo
re
that interfere
with each
ot
her t
h
an di
ffe
rent
phase
delay
is obtained by c
ounter
prop
agati
n
g
wave
s [11], [12].
In open
l
o
op approach,
a
lock
in
am
p
lifier is u
s
ed
t
o
measu
r
e th
e
p
h
o
t
o
d
e
tecto
r
ou
tpu
t
at the
fund
am
en
tal
m
o
d
e
frequ
ency an
d
th
e ro
t
a
te rate is d
i
rectly co
m
p
u
t
ed
fro
m
th
is
measurem
ent [13], [14].
Ad
di
t
i
onal
l
y
, t
h
e am
pl
i
t
ude o
f
t
h
e sec
o
n
d
a
n
d hi
ghe
r ha
rm
oni
cs m
a
y
al
so be m
easured t
o
com
p
ensat
e
f
o
r t
h
e
vari
at
i
o
ns i
n
t
h
e ret
u
rni
n
g o
p
t
i
cal
po
wer a
nd c
h
an
ges
i
n
t
h
e
am
pl
it
ude
of di
ffe
rent
ph
ase
m
odul
at
i
o
n
[
15]
.
Th
e
b
l
o
c
k
d
i
agr
a
m
o
f
an op
en lo
op
FOG
is
as show
n in
Figu
r
e
3 [1
3
]
.
Fig
u
re
3
.
Op
en Loop
Configuratio
n Fib
e
r
Op
tic G
y
ro
sco
p
e
w
ith
Ph
ase M
o
du
lator.
Thi
s
creat
es p
h
ase di
f
f
ere
n
c
e
bet
w
een t
w
o
cou
n
t
e
r p
r
o
p
a
g
at
i
ng
beam
s.
Whe
n
a p
h
ase
m
odul
at
or i
s
use
d
, t
h
e e
x
p
r
e
ssi
on
f
o
r
t
h
e i
n
t
e
nsi
t
y
on
t
h
e
p
hot
o
det
ect
or
i
s
,
(3
)
))
cos(
1
(
0
s
d
I
I
))
)
cos((
1
(
0
m
s
d
I
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
58
3 – 5
9
5
58
6
Ev
en
th
oug
h, th
ere is a d
r
awb
ack
ex
ists in
o
p
e
n
loo
p
ap
pro
a
ch
du
e to
variatio
n
s
in
the retu
rn
ing
optical
power
and c
h
anges
in the am
plitude
of the
phas
e
m
odulation which will
cause errors
in
output
[7],
[10
]
and
t
h
e
resp
on
se is
n
o
n
lin
ear, limited
dyn
amic rang
e,
lo
w
accuracy an
d less sen
s
itivity.
2.
2. T
h
e
Cl
ose
d
L
o
op
C
o
n
f
i
g
ur
ati
o
n
Fi
gu
re
4.
Sc
he
m
a
t
i
c
di
agram
of
cl
ose
d
l
o
o
p
fi
ber
o
p
t
i
c
gy
r
o
sc
ope
wi
t
h
di
gi
t
a
l
pha
se r
a
m
p
fu
nct
i
o
n
In cl
ose
d
l
o
op
app
r
oach
, t
h
e
ph
ot
o
det
ect
o
r
out
put
dem
odu
l
a
t
e
d at
t
h
e p
h
a
se m
odul
at
i
on f
r
eq
ue
nc
y
i
s
used as a
n
err
o
r si
gnal
.
T
h
i
s
l
o
op i
n
t
r
o
duce
s
a co
nt
r
o
l
l
e
d am
ount
of
no
n
reci
p
r
o
cal
phase
di
f
f
e
rence
bet
w
ee
n t
h
e t
w
o co
unt
er
pr
op
agat
i
ng
opt
i
cal
waves t
o
co
un
t
e
ract
t
h
e rot
a
t
i
on i
n
d
u
ced si
g
n
al
phase s
h
i
f
t
[1
5]
,
[1
6]
. T
h
e
bl
oc
k
di
ag
ram
of cl
ose
d
l
o
o
p
F
O
G
i
s
sh
o
w
n
i
n
Fi
gu
re
4.
Thus the net phase differe
n
ce
betw
een
th
e t
w
o
in
terfering
w
a
v
e
s is
m
a
in
t
a
in
ed
at zero
reg
a
rd
less of
t
h
e r
o
t
a
t
e
rat
e
.
It
i
n
t
r
o
d
u
ces
t
h
e am
ount
o
f
no
nr
eci
pr
ocal
phas
e
shi
f
t
i
s
t
h
e o
u
t
p
ut
o
f
t
h
e gy
r
o
sc
ope
and i
s
lin
early w
ith
resp
ect to
ro
tat
e
rate [7
], [10
]
, [16
]
i.e., it i
s
fed
b
a
ck
in
to th
e syste
m
to
g
e
n
e
rate an
feed
b
a
ck
p
h
a
se
d
i
fferen
c
e
t
h
at is m
a
in
tain
ed
opposi
t
e to the
Sa
gna
c phase s
h
ift
.
There
f
ore,
(4
)
The a
dva
nt
a
g
e
s
of
t
h
e cl
osed
l
o
o
p
sy
st
em
[17]
are:
N
o
m
o
v
i
ng
part
s
,
Hi
gh
Li
neari
t
y
,
W
i
de
dy
nam
i
c
rang
e, V
e
ry rug
g
e
d
,
Go
od
Accu
racy
an
d
Hig
h
sen
s
ib
ility
, Bias stab
ility,
Scale Facto
r
l
i
n
earity an
d
stab
ility,
lo
ng
an
d reliable lifeti
m
e an
d
Low
co
st
[18
]
.
3.
HA
RD
WA
RE
A
N
D
SOFT
WA
RE I
N
TERFA
CE
Th
e pr
opo
sed
ap
pro
ach
is to g
e
n
e
rate the feedbac
k
signal for
com
p
ensating the pha
s
e error
of
C
L
FO
G as s
h
o
w
n i
n
t
h
e Fi
gu
re 5
.
He
re, t
h
e
feed
bac
k
l
o
op
i
s
m
a
de by
di
ffe
rent
c
o
m
ponent
s s
u
c
h
as
Si
gna
l
co
nd
itio
n
i
ng
Am
p
l
ifier (SCA), A
D
C
, FPG
A
, D
A
C
, tem
p
er
atu
r
e sensor
and o
u
t
pu
t d
i
ff
eren
tial d
r
iv
er
CLFOG
is b
i
ased
w
ith
sq
uare w
a
v
e
sig
n
a
l of p
e
riod eq
u
a
l to
tran
sit t
i
m
e
(
τ
) of the fibe
r-c
oil. Here
, a squa
re
wav
e
m
odulation is use
d
to m
odulate the light, there
b
y to in
crease the sensitivity and to de
tect the rotation rate
p
o
l
ar
ity. Th
e
PI
NFET conver
t
s op
tical pow
er,
w
h
ich
is
o
u
t
p
u
t
of
FOG
to electr
i
cal sign
al. Th
is
ou
tpu
t
is
square wa
ve
m
odulated co-sinus
oida
l signal. The syste
m
accepts
m
o
dulat
ed Sa
gna
c
Phase error data is
receive
d through PINFET
out
put of CLFOG. On-board
16-bit ADC
will receive the data from
PINFET and
will be proces
sed
by usi
n
g F
P
GA.
It is de
m
odulated to
e
x
tract the
Sagnac
phase
error and
use
d
to
gene
rat
e
t
h
e fee
d
back
s
i
gnal
fo
r t
h
e
p
h
ase m
o
d
u
l
a
t
o
r i
s
gi
ve
n t
h
r
o
ug
h
1
6
-
b
i
t
D
A
C
. Thi
s
fee
d
b
a
ck si
gnal
re
pre
s
ent
s
p
h
a
se-erro
r
-com
p
e
n
s
atio
n
sign
al to
ach
i
ev
e
clo
s
ed
loo
p
fun
c
tio
n
a
lity of t
h
e system
[1
9
]
, [2
0
]
.
m
Biasin
g
Si
g
na
l
Lock in
Am
plifi
e
r
ADC
DAC
Controller
Error
Signal
Digital Output
Ω
(Rota
tio
n Ra
te
)
Phase Modu
la
tor
m
Sour
ce
Directional
Coupler
Polarizer
Directional
Coupler
Photo
Detecto
r
CW
CCW
Fiber Coil
Ω
fb
s
s
fb
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Com
p
arative Assessm
ent on
L
i
nearity Test based
V2
π
and
V
π
/2
Vo
ltag
e
Variation
s
o
f
…
(
T
.
Si
rees
ha
)
58
7
Fig
u
r
e
5
.
Propo
sed
Design
Ap
pro
ach of
CLFOG
Th
e feed
b
a
ck
p
h
a
se n
u
llifying
sig
n
a
l (ram
p
sig
n
a
l v
o
ltag
e
is V2
π
and i
t
s
freq
u
e
n
cy
20
0 KH
z) an
d
the biasing signal (squa
r
e wa
ve signal volta
ge is V
π
/
2
an
d i
t
s
freq
u
e
n
c
y
of 1
00
KHz
) are use
d
as
cont
rol
si
gnal
s
fo
r C
L
FO
G. S
o
t
h
e
r
a
m
p
an
d t
h
e s
qua
re
wave
bi
asi
ng si
gn
al
fo
r t
h
e
pha
se m
o
d
u
l
a
t
o
r (
I
OC
)
of t
h
e
FO
G are
gi
ve
n t
h
ro
u
g
h
1
6
-
bi
t
D
A
C
.
T
h
e
DPEC
b
o
ar
d t
r
ans
f
er
s t
h
e
p
h
a
se i
n
t
e
g
r
at
o
r
out
put
t
o
t
h
e
host
by
com
p
ensat
i
ng
t
h
e t
e
m
p
erat
ur
e i
nduc
ed
bi
as erro
rs,
up
o
n
t
h
e re
quest
of
sy
nch
r
o
n
i
zat
i
o
n p
u
l
s
es [
21]
.
In t
h
e
current
desi
gn, with a
selected tim
e
of eve
r
y
2m
s the ave
r
a
g
ed step-size
data is sen
t
v
i
a
UART to
t
h
e PC.
3.
1. Har
d
w
a
re
Inter
f
ace
The ha
rd
wa
re im
pl
em
ent
a
t
i
o
n of C
L
F
O
G sy
st
em
(as shown i
n
Fi
gu
re 5
)
, som
e
of t
h
e com
pone
nt
s
are discusse
d below:
1)
FPG
A
FPG
A i
s
use
d
i
n
i
n
t
e
r
f
aci
ng
wi
t
h
va
ri
o
u
s c
o
m
pone
nt
s, pe
rf
o
r
m
i
ng di
gi
t
a
l
si
g
n
a
l
pr
ocessi
n
g
functions a
n
d c
o
mm
unicating
with
user interface.
2)
ADC Interfac
e
It is a 16-bit parallel interfac
e
use
d
to
receive da
ta
from
ADC t
o
FPGA. T
h
is
data represe
n
ts the
m
odul
at
ed gy
r
o
p
h
ase e
r
r
o
r
.
C
l
ock a
nd
rese
t
t
o
ADC
i
s
dri
v
en
by
FP
G
A
.
Dat
a
rea
d
sy
nc
hr
o
n
i
zat
i
on c
o
nt
r
o
l
i
s
dri
v
en
by
FP
G
A
. M
a
xi
m
u
m
sam
p
l
i
ng
rat
e
o
f
A
D
C
i
s
4M
Hz
.
3)
DA
C1
a
n
d DA
C2
Int
e
rf
ace
It is also a
16-bit pa
rallel interface
used to
provide
data
from
FPGA t
o
DAC
1 a
n
d DAC2. This
DAC
1
dat
a
re
prese
n
t
s
t
h
e s
q
uare
wa
ve
bi
a
s
si
g
n
al
use
d
f
o
r i
n
t
e
nsi
t
y
m
o
d
u
l
a
t
i
o
n
,
whe
r
eas t
h
e
D
A
C
2
dat
a
represe
n
ts the
pha
se error com
p
ensati
ng si
g
n
al
an
d t
h
e
nat
u
re
of t
h
i
s
co
m
p
ensating signal is stair cas
e ram
p
.
C
l
ock si
gnal
t
o
D
A
C
i
s
dri
v
en
by
F
P
G
A
.
M
a
xi
m
u
m
sam
p
l
i
ng
rat
e
of
D
A
C
i
s
2
0
M
H
z
.
PI
NF
E
T
Ou
tp
u
t
fr
o
m
G
y
r
o
Ph
a
s
e
Mo
d
u
l
a
t
o
r
(I
O
C
) o
f
G
y
r
o
Sou
r
c
e
Dire
c
t
i
o
n
a
l
C
o
u
p
le
r
Pol
a
r
i
z
e
r
D
ire
c
t
io
n
a
l
Co
u
p
l
e
r
P
h
ot
o
De
t
e
c
t
o
r
Ph
a
s
e
Mo
du
la
t
o
r
CW
CCW
Fi
b
e
r
C
o
i
l
Ω
Si
g
n
al
Co
ndi
t
i
o
n
i
n
g
Am
p
l
if
ie
r
Ou
tp
u
t
Dif
f
er
e
n
ti
a
l
Dr
iv
e
r
Dem
o
d
u
latio
n
M
u
l
tip
l
i
er
T
e
m
p
era
t
u
r
e
S
e
ns
or
UAR
T
DP
E
C
Bo
a
r
d
FP
G
A
AD
C
AD
C
Da
t
a
Sam
p
ler
Filt
er
Ga
i
n
M
u
lt
ip
l
i
e
r
In
t
e
g
r
a
l
C
ont
r
o
l
l
e
r
Ra
m
p
G
e
n
e
rat
o
r
Bi
a
s
Ge
n
e
r
a
t
o
r
Ref
e
r
e
n
c
e
Si
g
n
al
Ge
n
e
r
a
t
o
r
Dead
B
a
n
d
Co
mpe
n
s
a
t
o
r
DAC
1
DAC
2
Ho
s
t
A
dde
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
58
3 – 5
9
5
58
8
4)
RS
2
32/
RS
42
2
Inter
f
ace
This interface is use
d
for Communicating with PC
application softwa
re,
whic
h was implem
ented
on
UAR
T
.
F
P
G
A
act
i
ng as
M
a
st
er o
f
c
o
m
m
uni
cat
i
on t
r
a
n
s
f
er
s t
h
e
desi
re
d
d
a
t
a
t
o
PC
.
C
o
n
f
i
g
urat
i
o
n
para
m
e
t
e
rs
from
PC are re
ceived
on the s
e
rial line.
5)
Temperature
Sens
or
(AD7415) Interface
AD
7
4
1
5
i
s
an
I2C
base
d 1
0
-
b
i
t
t
e
m
p
erat
ure se
ns
or
is u
s
ed
to
co
llect te
m
p
eratu
r
e d
a
ta o
n
th
i
s
i
n
t
e
rface
(
bot
h
On
-b
oa
rd
se
ns
or
an
d
ot
he
r c
o
nnect
ors
)
.
3.
2. So
ftw
are Inter
f
ace
In s
o
ft
ware Im
plem
entation of CLFO
G sy
stem
,
to
m
easu
r
e th
e ro
tation
rat
e
in
fib
e
r
op
tic g
y
ro
scop
e,
we re
q
u
ire s
o
m
e
softwa
re’s
as follo
ws: P
r
o
A
X
E
SE
5.
5.
0, R
eal
t
e
rm
seri
al
capt
u
re
pr
og
ram
,
Dev C
++,
Matlab progra
m
,
XILINX
ISE 10.1.
Ho
we
ver, the
ProAXE SE s
o
ftwa
re is
a GUI Int
e
rface use
d
to cont
rol
t
h
e rat
e
t
a
bl
e o
p
erat
i
o
n
of
gy
r
o
. It
i
s
us
ed
fo
r
t
e
st
i
ng p
r
oces
s gi
ve
n t
o
ou
r
expe
ri
m
e
nt
al
set
up
ope
rat
e
d i
n
t
w
o
m
odes (i
.e., m
a
nual
a
nd a
u
t
o
m
a
t
i
c
m
odes) whe
r
eas, t
h
e R
eal
ter
m
serial
captu
re p
r
o
g
r
a
m
software is
use
d
to
capt
u
re t
h
e
dat
a
(
h
ex
val
u
es)
fr
om
FOG a
n
d
i
t
i
s
gi
v
e
n
to ho
st thr
oug
h a
MO
XA
U
por
t
ser
i
al ad
ap
ter
.
4.
TEST PROCEDURE
Th
e FOG is sub
j
ected
to v
a
ri
o
u
s
k
i
n
d
s
o
f
tests to
certai
n
its p
e
rfo
r
m
a
n
ce
in
term
s o
f
linearity. Th
e
gyro
has e
x
ternally available
term
in
als
for te
m
p
erature
se
nsor rea
d
out fo
r each test and it is
noted t
h
at all
tests requ
ire st
ab
le te
m
p
eratures to
p
e
rform
at th
er
m
a
l eq
u
ilib
riu
m
. Th
e gyro
op
eratin
g
t
e
m
p
eratu
r
e is tak
e
n
fr
om
25°C
t
o
4
0
°C
.
Before go
ing
t
o
th
e testing
pro
c
edu
r
e and
afte
r s
w
i
t
c
h O
N
t
h
e
po
we
r s
u
p
p
l
y
, che
c
k
whet
her t
h
e
Gyro o
u
t
p
u
t
(PINFET), b
i
asing
(squ
are wav
e
)
an
d
ram
p
sign
als
o
u
t
p
u
t
s in
th
e eq
u
i
p
m
en
t are
g
e
ttin
g prop
erl
y
or
n
o
t
.
The p
r
o
p
e
r
fi
ne t
uni
ng
of
t
h
e cl
osed l
o
o
p
ap
p
r
oac
h
was o
b
ser
v
e
d
by
d
o
i
n
g t
h
e p
r
oces
s
i
m
p
l
e
m
en
tatio
n
as
show
n in Figu
r
e
6. The g
y
ro
r
e
qu
ir
es m
o
r
e
th
an on
e inpu
t vo
ltag
e
.
For
each
cir
c
u
i
t
,
ope
rat
i
n
g
vol
t
a
ge a
n
d c
u
r
r
ent
sh
o
u
l
d
be
spe
c
i
f
i
e
d i
n
or
der
t
o
m
easure a
n
d
reco
r
d
t
h
e
i
n
put
p
o
we
r
re
q
u
i
r
e
d
from
each source.
B
e
fo
re st
art
i
n
g
u
p
t
h
e t
e
st
pr
ocess,
m
ount
t
h
e
gy
ro
(C
LF
OG
) i
n
t
h
e
fi
xt
ure
o
n
t
h
e
rat
e
t
a
bl
e so t
h
at
th
e inpu
t referen
ce ax
is
(z-ax
i
s) is p
a
rallel to
t
h
e tab
l
e ro
tatio
n
a
l ax
is,
as shown in the Figu
re 7 test setup.
C
o
n
n
ect
t
h
e g
y
r
o t
o
t
h
e o
u
t
put
m
easuri
n
g
and rec
o
rdi
n
g
equi
pm
ent
(s
oft
w
are i
n
PC
)
.
Ap
pl
y
p
o
we
r
t
o
t
h
e
g
y
ro
and
record
th
e g
y
ro
ou
t
p
u
t
with
resp
ect to
ti
me. Here, th
e g
y
ro
ou
tpu
t
co
nsists o
f
raw d
a
ta and
th
e
avera
g
e data for
c
o
rrespondi
ng rate
agai
nst
t
e
m
p
erature
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Com
p
arative Assessm
ent on
L
i
nearity Test based
V2
π
and
V
π
/2
Vo
ltag
e
V
a
riation
s
o
f
…
(
T
.
Si
rees
ha
)
58
9
Fi
gu
re
6.
Pr
oce
ss Im
pl
em
ent
a
ti
on
f
o
r
Fi
ne
Tu
ni
n
g
of
t
h
e C
l
o
s
ed L
o
op
A
p
pr
oach
Fi
gu
re 7.
Test
Set
u
p
5.
R
E
SU
LTS AN
D COMPAR
ISON
S
In th
e testing
resu
lts,
first
o
p
e
n
-
l
o
op
and
closed
-l
o
o
p c
o
nfi
g
u
r
at
i
o
ns a
r
e
d
e
m
onst
r
at
ed
wi
t
h
r
o
t
a
t
i
ons
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
58
3 – 5
9
5
59
0
5.
1. T
h
e O
p
en
L
o
op
Co
nfi
g
ura
t
i
o
n
Th
e ou
tpu
t
o
f
th
e o
p
e
n
loo
p
co
nfigu
r
ation
w
ith
ro
tation
w
a
s ob
serv
ed
in
th
e o
s
cillo
sco
p
e
as sh
own
in the
Fig
u
r
e
8
.
I
n
t
h
is
fig
u
re
the
first
wa
ve
fo
rm
repr
esen
t
s
th
e
g
y
ro
ou
tp
u
t
, th
e seco
nd
represen
ts the ram
p
si
gnal
an
d t
h
e
t
h
i
r
d
rep
r
ese
n
t
s
t
h
e sq
uare
-
w
ave bi
asi
ng si
gnal
.
In t
h
e o
p
e
n-l
o
o
p
, t
h
e am
pli
t
ude o
f
t
h
e gy
r
o
out
put
c
h
a
nges
wi
t
h
t
h
e
rot
a
t
i
on acc
o
r
di
ng t
o
t
h
e s
q
uare
-w
ave bi
asi
ng
si
g
n
al
b
u
t
i
n
cl
u
d
e
d
wi
t
h
t
h
e e
r
r
o
r. T
h
e
ram
p
rem
a
in
s co
nstan
t
ev
en
w
ith
th
e ro
tation
.
Fi
gu
re
8.
O
u
t
p
ut
o
f
t
h
e
ope
n l
o
o
p
c
o
nfi
g
u
r
at
i
o
n
wi
t
h
r
o
t
a
t
i
o
n
5.
2. T
h
e
Cl
ose
d
L
o
op
C
o
n
f
i
g
ur
ati
o
n
Th
e
ou
tpu
t
of t
h
e closed loo
p
co
nfigu
r
ation
w
ith
ro
tation
w
a
s
ob
serv
ed
i
n
th
e
o
s
cillo
sco
p
e
as sho
w
n
i
n
t
h
e
Fi
g
u
re
9
(a).
The
fee
d
ba
ck l
o
o
p
i
s
not
c
l
osed
p
r
o
p
erl
y
,
so t
h
e
out
put
i
s
cha
nge
d at
re
set
of t
h
e
ram
p
. To
rem
o
v
e
th
is erro
r, th
e am
p
litu
d
e
o
f
th
e ram
p
vo
ltag
e
is adju
sted to
8
.
75
V w
ith a
f
r
e
q
u
e
n
c
y of
20
0
K
H
z. The
g
a
in
is adj
u
sted
to
co
m
p
en
sate th
e error in th
e am
p
litu
d
e
o
f
th
e
g
y
ro
ou
tpu
t
. Th
e
b
i
asin
g
sign
al is
also
chan
ge
d acc
or
di
n
g
t
o
t
h
e
ra
m
p
vol
t
a
ge.
A
f
t
e
r a
d
j
u
st
i
n
g
t
h
e am
pl
i
t
ude of t
h
e r
a
m
p
vol
t
a
ge, t
h
e
out
put
o
f
clo
s
ed
l
o
o
p
con
f
i
g
uratio
n of
p
r
op
er
fin
e
t
u
nin
g
w
ith
ro
tati
o
n
w
a
s ob
served
in th
e
o
s
cillo
sco
p
e
as sh
ow
n i
n
the Figure
9 (b).
(a
)
(b)
Fi
gu
re
9.
O
u
t
p
ut
o
f
cl
osed
l
o
op
co
n
f
i
g
urat
i
o
n
(a)
wi
t
h
out
fi
ne t
u
ni
n
g
(
b
)
w
i
t
h
fi
ne
t
u
ni
n
g
Aft
e
r
fi
ne t
u
ni
ng
, t
h
e
Gy
ro
o
u
t
p
ut
(P
IN
FET
)
, bi
asi
ng
(s
qu
are wa
ve) a
n
d
ram
p
si
gnal
s
o
u
t
p
ut
s i
n
t
h
e
D
P
EC
bo
ard
are ob
serv
ed
in th
e
o
s
cillo
scop
e is as sh
own
i
n
Fig
u
re’s
1
0
,
1
1
&
1
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Com
p
arative Assessm
ent on
L
i
nearity Test based
V2
π
and
V
π
/2
Vo
ltag
e
V
a
riation
s
o
f
…
(
T
.
Si
rees
ha
)
59
1
(a
)
(b)
Fig
u
r
e
10
. (
a
) PI
NFET ou
tput
an
d
(b
)
D
i
f
f
e
ren
tia
l
PI
NFET
out
put
o
f
a
SC
A am
pl
i
f
i
e
r be
fo
re
ADC
(a)
(b)
Fi
gu
re 1
1
. (a)
R
a
m
p
Si
g
n
al
o
u
t
p
ut
at
D
A
C
1
an
d (b
) Di
ffe
r
e
nt
i
a
l
R
a
m
p
Si
gnal
o
u
t
p
ut
at
dri
v
er 1
(a)
(b)
Fi
gu
re
1
2
.
(a)
B
i
as Si
gnal
(s
q
u
are
wa
ve)
o
u
t
put
at
D
A
C
2 a
n
d
(
b
)
Di
ffe
ren
t
i
a
l
B
i
as Si
gnal
o
u
t
p
ut
at
d
r
i
v
e
r
2
5.
3. T
e
s
t
Resu
l
t
s
Th
e lin
earity
test w
a
s
p
e
rform
e
d
an
d its
resu
lt
(pro
p
e
r fin
e
tun
i
ng
of closed loo
p
g
y
ro
wh
en
V2
π
=
8
.
7
5V
) i
n
M
A
TLAB
a
s
sh
ow
n i
n
Fi
g
u
re
1
3
a
nd t
h
e
t
e
st
resul
t
s
de
scri
be t
h
e l
i
n
e
a
ri
t
y
resp
on
se
of
o
u
r
pr
o
pose
d
cl
ose
d
l
o
o
p
gy
ro sy
st
em
[22]
, [
23]
. The ram
p
vol
t
a
ge (o
r bi
as
v
o
l
t
a
ge) i
s
i
n
c
r
e
a
sed f
r
om
1% t
o
1
0
%
an
d d
e
cr
eased
to
1% to 10
%
an
d p
e
r
f
or
m
e
d
the va
rious test
s in t
h
e
below t
h
ree
cases:
Case
1
:
V2
π
(ra
m
p
sign
al vo
l
t
ag
e)
is va
ried and
V
π
/
2
(s
q
u
a
r
e
wave
bi
asi
n
g si
gnal
v
o
l
t
a
g
e
) i
s
fi
xe
d.
Case
2
:
V
π
/
2
(
s
qu
are
wa
ve
bi
asi
n
g
si
g
n
al
v
o
l
t
a
ge) i
s
vari
e
d
an
d t
h
e
fi
ne t
u
ned
v
o
l
t
a
ge
V
2
π
i
s
fi
xe
d.
Case 3
:
Bo
th V2
π
(ram
p
si
gnal
vol
t
a
ge
) an
d V
π
/
2
(
s
qu
are
wave
bi
asi
n
g si
g
n
al
vol
t
a
ge
) are
var
i
e
d
sim
u
l
t
a
neousl
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
58
3 – 5
9
5
59
2
Figure
13. Li
nearity Test of t
h
e
Gyro Out
p
ut against
t
e
m
p
erat
ure
f
o
r
cl
ose
d
l
o
o
p
wi
t
h
pr
o
p
er
fi
ne
t
u
ni
n
g
The linearity test wave
form
s
for each test a
n
d their
ta
bulation a
r
e as s
h
own bel
o
w. The li
nearity test
is perform
e
d for
42 m
i
nutes
for each case
within a
dyna
mi
c range of -
400
deg/sec to
+ 400
deg/sec. In thre
e
cases, co
m
p
ariso
n
is m
a
d
e
in
ter
m
s o
f
its li
n
earity an
d
it is tab
u
l
ated
as
sh
own
in
th
e t
a
b
l
e-1
(a,
b
&
c) and
recorde
d
t
h
e c
o
rres
ponding
m
a
xim
u
m
a
nd
m
i
nim
u
m
nonl
inearities for three cases
.
Table
1. C
o
m
p
arison
of linearity for t
h
ree
ca
ses
(a)
(b)
(c)
Th
en
th
e actu
a
l o
u
t
pu
t ro
tation
rate w
a
s ob
serv
ed
fo
r a g
i
ven
in
pu
t ro
tatio
n
rate for th
ree cases as
sho
w
n i
n
t
h
e
F
i
gu
re
14
(a,
b
& c)
.
%
Max.
Non-Linearity
Min.
Non-Linearity
-6
%
8095
400.
0
0
-
24191
00.
00
-5
%
3423
00.
00
-
24460
00.
00
-4
%
3712
6.
00
-
48338.
0
0
-3
%
1930
9.
00
-
35850.
0
0
-2
%
1755.
5
0
-
5697.
40
-1
%
2653.
2
0
-
3393.
00
⁻⁻
1313.
6
0
-
1290.
10
1%
928.
99
-
1653.
80
2%
887.
67
-
3833.
20
3%
1706.
2
0
-
4748.
40
4%
4316.
7
0
-
3456.
70
5%
1658
3.
00
-
4109.
80
6%
1177
2.
00
-
1767.
20
7%
1064
90.
00
-
4268.
10
8%
1141
6.
00
-
4554.
10
9%
1779
2.
00
-
5367.
50
10%
3766
2.
00
-
13060.
0
0
%
Max.
Non-Linearity
Min.
Non-Linearit
y
-
10%
2688.
5
0
-
3126.
10
-9
%
684.
21
-
2050.
50
-8
%
596.
31
-
2587.
10
-7
%
1136.
0
0
-
1970.
60
-6
%
2700.
0
0
-
3482.
00
-5
%
892.
66
-
2517.
70
-4
%
956.
70
-
2371.
20
-3
%
1134.
4
0
-
1916.
20
-2
%
1640.
8
0
-
1978.
40
-1
%
1325.
5
0
-
1638.
50
⁻⁻
1313.
6
0
-
1290.
10
1%
905.
97
-
927.
39
2%
1835.
2
0
-
852.
05
3%
1112.
1
0
-
618.
84
4%
2028.
3
0
-
1052.
50
5%
715.
85
-
320.
57
6%
2345.
5
0
-
947.
60
7%
1313.
7
0
-
565.
32
8%
1298.
8
0
-
917.
00
9%
3696.
7
0
-
1287.
50
10%
1837.
4
0
-
397.
62
%
Max.
Non-Linearity
Min.
Non-Linearit
y
-
10%
7440
1.
82
-
54742.
3
6
-9
%
7921
5.
30
-
44836.
5
6
-8
%
3431
2.
72
-
29535.
0
0
-7
%
1830
4.
01
-
22702.
4
7
-6
%
5854.
4
0
-
18803.
0
0
-5
%
1317.
0
0
-
7440.
80
-4
%
1537.
9
0
-
1986.
40
-3
%
2331.
9
0
-
989.
33
-2
%
4277.
8
0
-
4844.
30
-1
%
1570.
4
0
-
2457.
30
⁻⁻
1313.
6
0
-
1290.
10
1%
7949.
7
0
-
12441.
0
0
2%
7673.
1
6
-
2007.
70
3%
6355.
0
0
-
6229.
60
4%
7695.
3
0
-
1595.
00
5%
1283
4.
00
-
1802.
90
6%
1653
2.
00
-
8478.
10
7%
1637
4.
00
-
23949.
0
0
8%
2040
0.
00
-
14813.
0
0
9%
2508
4.
00
-
12932.
0
0
10%
3636
6.
00
-
15803.
0
0
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