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lim trE[V(Ii)V’(li)] =
I\-+-
where S is the number of data symbols that the filter spans and W
is the width of the time window used. SW < L provided W < TB.
where T Bis the data bit period. The fourth-order moments can be
approximated by second-order moments [3], and hence we study
the interference components in the second-order statistics. Neglecting the crossterms involving Gaussian noise, ELf ( y ) ]can he written after simplification as
E [ ~ ( Y ( I ~ ) ) ~ ( Y=~E( {I w~ ;) I)I ]( I ~ ) [ s-(sI(~A) - I)]’}
+ E{Wiiz(Ii)[N(Ii)-N(Ii-
l)]’}
-10
-15
-5
0
Fig. 1 BER performance improwmenr of TE-LMS o
IO
5
signal to interferenceratio,dB
w
k
l
L M S Jilter
SNR = 2OdB
cantly reduced. It is seen that the TB-LMS filter offers significant
performance gains over that of the conventional LMS filter. The
proposed modifications can be readily extended to other
algorithms.
14 July 1995
0 IEE 1995
Electronics Lerrers Online No: I9951077
F. Dominique (Apt #170OF. 1200 Hunt Club Road. Bluckshurz, V A
24060, USA )
It is easy to see that:
(i) when I(K, n) = l((K-l),n), i.e. when not a transition
M
C[I,(Ii)I,(Ii
~ i n ( ~ i )
-
-
111’
3=1
I
I
=o
(11)
irrespective of the value of Win@).Here, 1(K, n ) refers to the nth
component of the vector I at time K .
(ii) when I(K, n )
E
{
#
I((K-I), n), i.e. a transition is present,
M
Win(1i)=y[I,(Ii)
- I,(K
3=1
- 1)]2
=0
(12)
References
WIDROW. B., GLOVER, J , MCCOOL. J., KAUNITZ. I., WILLIAMS, C.,
HEARN. R., ZEIDLER, J., DONG. E . and GOODLIN, R.: ‘Adaptive noise
cancelling: principles and applications’. Proc. IEEE. 1975, 64, pp.
1151-1162
2 DOUGLAS, s.c., and MENG. T.H Y : ‘The optimum scalar data
nonlinearity in LMS adaptation for arbitrary I.I.D. inputs’, IEEE
Trans., 1992. COM-40, pp. 1566-1570
3 HONIG.M L , and MESSERSCHMITT. D.G: ‘Adaptive filters Structures. algorithms, and applications’ (Kluwer Academic, 1985)
I
as Win(n) = 0. Since the data transitions of the SNOIs occur at
different times from those of the SOI, Win(n) = 0 at the transition
times of the SNOI as per its definition in eqn. 8. In a similar fashion
Range extension in optical low coherence
reflectometry achieved by using a pair of
retroreflectors
K. Takada, H. Yamada, Y. Hibino and S. Mitachi
Inde.;ine rerm: OTDR
=O
(14)
The interference component can thus be eliminated almost completely from the total weight error power, depending on the accuracy to which the data clock phase of the SO1 can be estimated.
Results and cunclusiun: Simulations were carried out to investigate
the effectiveness of the proposed scheme. The SO1 is a 7 bit pseudonoise sequence modulated by a uniformly generated binary data
sequence. The SNOIs were represented by other data modulated
pseudonoise sequences. Perfect training is assumed. Fig. 1 shows
the performance gain in the bit error rate of the TB-LMS filter
over the LMS filter. Performance gains of >1 order of magnitude
are achieved, especially at low signal to interference ratios (SIRS).
It has been shown in this Letter how the the number of interferers that contribute to the interference component can be signifi-
ELECTRONICS LETTERS
3lstAugust 1995
Vol. 31
The authors report an optical low coherence reflectometer
(OLCR) with a distance range of 2m. By using a pair of
retroreflectors in the variable optical delay line and bouncing the
local oscillator light off either moving retroreflector ten times, the
distance range could he extended ten-fold from 20cm to Zm as
compared with a conventional OLCR. The complete Rayleigh
backscattering distributions of I .53m long silica-based waveguides
were obtained by translating the retroreflector once for each
waveguide. The measurement error of the loss coefficients was
+0.0025dB/cm.
Introduction: An optical low coherence reflectometer (OLCR) [ I ,
21 is a nondestructive diagnostic tool that provides loss distribu-
tions of planar optical waveguides. The loss coefficients and steplike loss increases in silica-based waveguides have been measured
from their Rayleigh backscattering distributions [3]. The OLCR is
now beginning to play an important role in the field of planar
optical waveguide diagnosis.
No. 18
1565
Two kinds of variable optical delay line have been reported for
use in the OLCR. One uses a moving mirror [2], and the other
uses a moving retroreflector and a fixed mirror [4]. The distance
range R of the OLCR is limited by the maximum translation L of
the stage used for the movement. When n is the refractive index of
a waveguide to be tested, R is given by M L / n , where M = 1 and M
= 2 for these optical delay lines. Since the typical L value of commercially available stages is 30 cm. their respective ranges are R =
20cm and R = 40cm when silica-based waveguides are tested.
We report a range-extended OLCR with a pair of retroreflectors
in the optical delay line. The pair were aligned in a particular way
so that the translation of either retroreflector has a one-to-one
correspondence with the optical delay, which is ten times larger
than that provided by the same translation of the mirror mentioned above. This means that the distance range of the OLCR is
extended ten-fold ( M = IO) and the complete Rayleigh backscattering distribution of any 1.5m long silica-based waveguide can be
obtained by moving the retroreflector once for each waveguide.
waveguide
under test
mirmr 2
mirror 1
signal processing system
:
delay line j.....
retroreflector 1
a
Fig. 1 Configuration ofrungr-ertended O L C R
LO: local oscillator
light was < l d B over a 24h period. This is because of the divergence in its beam profile, which reduced its coupling efficiency
with the LO port fibre.
-40
-1LOl
"
"
I
,
I
'
,
I
I
,
,
1566
I
I
.
,
I
,
I
,
. .
1
50
A polarisation-holding fibre was tested by this range-extended
OLCR, as shown in Fig. 2, to check the variable optical delay line.
The measured reflection distribution was calibrated with the LO
light power as a function of the position of the moving retroreflector. The residual slope of the calibrated Rayleigh backscattering
distribution over 150cm was 4.005dBicm. Repeated measurements showed that the measured slope changes within k0.005dBi
cm, half of which, *0.0025dB/cm, is the measurement error of the
loss coefficient of a silica-based waveguide. Only one peak
appeared at 32cm, corresponding to the end-reflection of the fibre.
There is no possibility that the output beam from the LO port
branches at the optical delay line, and re-enters the LO port after
propagating through a path different from that shown in Fig. 1
-40,
Results and discussion: Since the maximum translation of the stage
was 30cm, the range for silica-based waveguides was extended to 2
m. By introducing the optical delay line into the OLCR, the LO
light power experienced a loss of 15dB at the starting position of
retroreflector 1 and 19dB at the maximum translation of 30cm.
Since the total loss due to the reflection at the two retroreflectors
was 7dB, the residual loss is estimated to he from 8 to 12dB,
depending on the position of retroreflector 1. Because the return
beam from the optical delay line diverged as a result of diffraction, the residual loss mainly results from the degradation in the
coupling efficiency of the return beam into the LO port fibre.
Despite this high loss of the LO power, shot-noise limited detection was achieved hecause we used a high power light source with
an output of -1OmW. The optical power fluctuation of the LO
,
100
I50
200
distance, crn
rn
Fig. 2 Reflection distribution of polarissotion-hold in^ fibre
The dynamic range of the Rayleigh backscattering measurement was
30dB
0
,
,
,
,
,
,
-1401,,
0
,
.
,
,
,
. .
.
,
,
,
~ ~ 50 ~ " 100
~ ~ " 150" " " '
a
-40.
m
rn -6 0
. .
,
Experimental setup: The experimental setup is shown in Fig. 1.
The configuration of an OLCR using a [3x3] coupler isdescribed
in [5]. The dotted square in the Figure outlines the variable optical
delay line designed for range extension. It consists of two mirrors,
and two retroreflectors that bounce any incident light beam back
in the incident direction and parallel to it. The clear apertures of
the retroreflectors are 63mm in diameter and there is a 1 s deviation from parallel between the incoming and outgoing beams.
The light beam from the local oscillator (LO) port is launched
into the retroreflectors I and 2 by using mirror 1. Since the centre
of the aperture of retroreflector 2 is to the left of that of retroreflector I , the launched beam rotates clockwise and approaches the
two centres as it bounces hack and forth between these retroreflectors. When the beam reaches the centre of retroreflector 2, it is
reflected by mirror 2 parallel to the incident direction, and rotates
counter-clockwise between the retroreflectors, following the same
path as that prior to incidence. The beam then reaches mirror 1, is
launched into the LO port, and is used as the LO light for balance
detection. Retroreflector 1 moves on the stage parallel to the
bounce direction. Because the pair of the retroreflectors does not
form an optical cavity, the position of retroreflector I has a oneto-one correspondence with a given optical delay. Since the LO
light bounces ten times at moving retroreflector I , the distance
range of the OLCR is extended ten-fold ( M = 10).
1 UI
noise level
30dB-
.
I
distance.cm
'
'
'
'
'
I
'
5
- -8 0
b
-z -100
r
$ -120
0
50
100
150
b
distance.cm
rn
Fig. 3 Comparison of reflection distributions qf two 1 . 5 3 ~ 1long silicabased waveguides fabricated on one substrate
a Low-loss waveguide
b High-loss waveguide
Spatial resolution was 7 0 0 ~
The reflection distributions of two silica-based waveguides
1.53111 in length and fabricated on one substrate [6] are shown in
Fig. 3a and b. Although one waveguide (a) produced large pointlike reflections owing to defects in the waveguide, the Rayleigh
backscattering floor attenuated at a rate of 0.084dB/cm along its
length. That is, the waveguide has a loss coefficient of 0.042dB/cm
and no significant defects causing step-like loss increases.
The distribution of the other waveguide ( b ) exhibited step-like
decreases of 2dB at point A (17 cm distance), and 6dB at point B
(36cm distance). The distributions of the three sections that are
obtained by dividing the waveguide at the two points attenuated
at the same rate of 0.082dB/cm. In terms of loss, therefore, the
ELECTRONICS LETERS
-
31st August 1995
Vol. 31
No. 18
~
‘quality’ of waveguide a is the same as that of waveguide b, in
which two defects of I and 3dB are produced. From these diagnostic results, the total losses are estimated to be 6.4 and 10.3dB,
respectively. These values agree with the directly measured values
of 6.6 and 11dB.
Conclusion: The distance range of an optical low coherence reflectometer (OLCR) has been extended to ten times that of a conventional OLCR. This was achieved by introducing a pair of
retroreflectors into the variable optical delay line and bouncing
the local oscillator light off either moving retroreflector ten times.
The range for silica-based waveguides was extended from 20cm to
2m, and the complete Rayleigh backscattering distributions of
I .53m long silica-based waveguides were successfully measured.
The measurement error of the loss coefficients was t0.0025dBkm.
The experimental results confirm that the range-extended OLCR
provides useful information for reducing the losses in long silicabased waveguides. The range will be further extended to a few
hundreds of metres by using a recirculating delay line [7], and the
resultant OLCR will be available for short-haul optical fibre fault
location.
years, with the accelerating trend towards greater automation, a
number of low cost high volume applications, e.g. automobile
control and smart shells, have been identified requiring innovative
designs for gyroscopes. To meet this requirement, a number of
approaches have been considered, with the most attractive being
the application of silicon micromachining technology with its
accurate replication facilities, coupled with the potential for further cost reduction by incorporating electronic circuits onto the
same substrate [ I , 21. We report here the operalion of a novel resonant gyroscope which is based on the vibration of a silicon diaphragm loaded with an inertial mass that has been etched from
crystalline silicon. Furthermore. the design approach described
here offers the opportunity to maximise sensitivity by combining
the cubic symmetry of crystalline silicon with the directional
dependence of anisotropic etching to manufacture a mechanically
symmetrical structure.
t Z
y/
r(
WP
0 IEE I995
I 7 July 1995
Electronics Letters Online No: 19951049
K. Takada, H. Yamada, Y. Hibiuo and S. Mitachi (NTT Oprodectronics Laboratories, Nippon Telegraph and Telephone C~~rpur-uriuii,
162. Tokai. Naka-gun, Iharaki-ken 319.1 I , Japan)
Referenees
TAKADA, K.,
YOKOHAMA.1..
CHIDA,K.,
and N0DA.J.: ‘New
measurement system for fault location in optical waveguide devices
based on an interferometric technique’, Appl. Opt., 1987, 26. (9).
pp. 16.3-16.6
DANIELSON. B.L.,
and
WHITTENBURG.
c.w :
‘Guided-wave
reflectometry with micrometer resolution‘, Appl. Opt,, 1987, 26,
(14). pp. 2836-2842
TAKADA. K., YAMADA, H., and HOKIGIJCHI, M.: ‘Loss distribution
measurement of silica-based waveguides by using a jaggedness-free
optical low coherence reflectometer’, Electron. Lett., 1994, 30, (17).
pp. 1441-1442
GILGEN. H.H., BODMEK, G., and Z I M M E R . CH : ‘Optical coherence
domain reflectometry as a test method for integrated optic devices‘.
Proc. 2nd Optical Fiber Measurement Conf., Torino, Italy, 1993,
pp. 143-146
TAKADA, K..
YAMADA, H., and
HORIGUCHI. M.: ‘Optical low
coherence reflectometer using [3x3] fiber coupler’, IEEE Photonic.?
Technol. Lett., 1994, 6 , (8). pp. 101&1016
HIHINO.Y , OKALAKI, H., HIDA. Y , and OHMORI, Y : ‘Propagation loss
characteristics of long silica-based optical waveguides on 5 in Si
wafers’, Electron. Lett., 1993, 29, (21), pp. 1847-1848
BANEY. D.M.. and SORIN. w.v.: ‘Extended-range optical lowcoherence reflectometry using a recirculating delay line’, IEEE
Photonics Technol. Lett., 1993, 5 , (9). pp. 1109-1 112
Vibrating silicon diaphragm
micromechanical gyroscope
A.J. Harris, J.S. Burdess, D. Wood, J. Cruickshank and
G. Cooper
Indexing terms: Electric sensing devices, Micromachining,
Micromechanicul resonators
The design and operation of a micromechanical gyroscope based
on a vibrating diaphragm loaded with an inertial mass is
described. Capacitive actuation and sensing methods are
employed. Preliminary results are presented which show that
mechanical and electrical coupling limit current performance,
which could be improved to give a noise equivalent rate of turn
better than 0.14”is.
Introduction: Historically, rate of turn sensors (i.e. gyroscopes)
have been expensive components that have found a niche market
in high cost and low volume inertial navigation systerns. In recent
ELECTRONICS LETTERS
3lstAugust 1995
Vol. 31
t=
b
a
Fig. 1 Vibrating diuphrazm gyroscope
a Structure:
im: inertial mass, d: square diaphragm, ce: common electrode, pd: primary drive, ps: primary sense, ss: secondary sense, su: secondary null,
gr: guard ring
b Mode of vibration of primary motion
Structure und operation: The structure of the gyroscope is given in
Fig. la. The truncated pyramidal inertial mass with a topside
length of 0.72mm and a height of 300pm is wet etched from a
(100) silicon wafer. It is located symmetrically at the centre of a
thin ( - 2 . 5 ~ )square diaphragm of side length 2.9mm. The diaphragm is created by boron doping the silicon, which acts as an
etch stop to the EDP (ethylene diamine, pyrocatechol and water
mixture) which etches the silicon from the reverse side to form the
diaphragm and inertial mass. The metallisation on the silicon diaphragm, called the common electrode, forms one electrode which
is common to four capacitors which have their other electrodes on
a Pyrex substrate. These electrodes drive and sense the vibrational
motion of the diaphragm. The electrode pattern on the Pyrex substrate is situated in an etched cavity of depth 3pm which acts as a
spacer between these electrodes and the common electrode. The
electrode pattern on the Pyrex and the diaphragndinertial mass
are aligned along the x- and y-axes. This alignment, along with the
four-fold symmetry of the silicon structure, fulfils the mechanical
symmetry required to match the resonant frequencies of the primary and secondary motions and hence to maximise sensitivity.
The gyroscope is operated with the common electrode earthed
and the same DC bias, relative to this earth, applied to all four
capacitors to prevent tilting of the diaphragm. T o produce useful
amplitudes of vibration, the air in the etched pit is removed to
prevent squeeze film damping. Resonance of the primary motion
is monitored using the primary sense and maintained by employing closed-loop control based on phase-locked-loop methods. The
primary motion of the diaphragmiinertial mass is shown in Fig.
I h , which corresponds to a rocking motion of the inertial mass
No. 18
1567
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