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PIEZOELECTRIC OPTICAL DEFLECTOR WITH ADAPTIVE MIRROR
DOI 10.24411/2072-8735-2018-10109
Mehman H. Hasanov,
Azerbaijan Technical University, Baku, Azerbaijan, Keywords: piezoelectric optical deflector, adaptive mirror,
[email protected] piezoelectric bimorph element, fiber-optic technology.
In a relatively short history of the development of optical networks, a huge number of different types of optical signal deflectors based on a variety of physical principles have been developed. The main task of optical deflectors is to ensure the highest possible speed for the terabit optical communication lines being developed [3], efficiency [2] and to provide the lowest possible unit cost, as well as to reduce power consumption in comparison with existing electronic analogues. Due to the simplicity of the designs, piezoelectric transducers associated with miniaturization and integrated versions find wide application in fiber-optic technology [1-5]. Proceeding from this, we developed a piezoelectric optical deflector with an adaptive mirror. The proposed work considers one of the possible principles for the creation of piezoelectric optical deflectors with adaptive mirrors, for the purpose of using in the development and operation of a piezoelectric deflector for a light beam in fiber-optic technology.
The article presents a block diagram of control with electronic blocks and a mutual arrangement of the elements of a piezoelectric optical deflector with an adaptive mirror and describes the operation principle of the proposed device. A mathematical model of the bimorph piezoelectric element used in the deflector of the light beam is developed. The results of these studies can be used in the development and operation of a piezoelectric deflector for a light beam in fiber optic technology.
Information about author:
Mehman H. Hasanov, Candidate of Technical Sciences, PhD, Department of "Multi-channel telecommunication systems", Baku Technical University, Baku, Azerbaijan
Для цитирования:
Гасанов М.Г. Пьезоэлектрический оптический дефлектор с адаптивным зеркалом // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №6. С. 56-60.
For citation:
Hasanov M.H. (2018). Piezoelectric optical deflector with adaptive mirror. T-Comm, vol. 12, no.6, pр. 56-60.
q(t)
* X M dx -»
*-L
?
a+û<J
Q+<3Q
a) b)
Fig. 3. Diagram of the rod of the bimorph piezoelement (a) and ihe forces acting on the piezoelectric clement (b)
The work of a piezoelectric optical deflector
with an adaptive mirror
The piezoelectric optical deflector with an adaptive mirror works as follows: at the beginning of the operation, a constant voltage from the source output - 11 is applied to the electrodes-
12 piezoelectric bimorph elements-4, which leads to bending deformation. The electrical signals from the generator output -
13 through the matching device - 15 are fed to the input of the LRD-16 by a given law of change, which after the conversion generates a signal emitted in the form of a beam - 17 light (in the figure, tig. 1 is shown conditionally) directed to the internal mirror surface - 9 piezoelectric separate sections of the hemisphere - 7. This signal from the output of the electrical signal generator is fed to the input of the power amplifier - 25 at the same time, setting its frequency.
From the output of the power amplifier, the supply voltage is applied to the electrodes - 14 separate sections of the hemisphere - 7. As a result of radial mechanical oscillations of the separate sections - 8 piezoelectric elements of the hemisphere - 7 beam -17 beams of light are focused in the center of the piezoelectric hemisphere by means of a focusing mirror - 19. The emitted signal is incident on the end surface of the optical-fiber-cord -2 cables - 1 is transmitted aiong it to the photoelectric receiver -21 through the focusing lens - 20.
When the intensity of the radiation at the output of the optical cable - 1 after converting the photoelectric receiver - 21 is reduced, the amplification in the block - 22 of the formation in the block - 23 and detection in the block - by the feedback circuit, this signal passes through an average metal core — 3 cables - I to the control input of the source is I i DC voltage, changing its gain factor, at which the bimorph piezoelectric element — 4 bending occupies a new position, the latter leads to a change in the position of the light beam relative to The electrical signal from the second output of the driver - 23 pulses is applied to the input of the amplifier - 25, the power changing its amplification factor according to the law of signal change resulting in an increase in the amplitude of the radial mechanical vibrations of the section-8 piezoelectric hemispheres - 7, light rays in accordance with a given law of change directed to the inner mirror surface of the hemisphere - 7, in the form of a beam ka - 17 diffuse light is focused in the center of the hemisphere by means of a mirror -19; leads to an increase in the intensity of the radiation of the useful signal.
Mathematical model of a piezoelectric optical deflector
Next, we will consider the development of a mathematical model of the bimorph piezoelectric element used in the dellector of a light beam |4J.
In Fig. 3 a. a diagram of the rod of a bimorph piezoelectric element OA of length I with one clamped end is shown. The uniformly distributed loads q(t) act on the piezoelectric rod under the influence of the supply voltage and the gravitational force P of the mirror fixed at the end A of this piezoelectric element. Loadq(t) is represented as:
/A F (I) ebu(l) ebun / ; q(l) = —— =-— =--cos( col + (p„ )
I
I
I
(0
where F(l) is the exciting force, e is the piezoelectric voltage constant, h is the width of the rod, £f„ is the voltage, <p{¡, - is the
phase, and (0 is the frequency of the supply voltage.
Suppose that the longitudinal displacements of the points of the rod OA are very small, and the stiffness does not change during bending. We choose the coordinate system OXY so that the axis, X is directed along the axis of the rod. Let us isolate the element of the rod M of length dx with the abscissa X and consider the forces acting on this element (Fig. 3b). As can be seen from the figure, the following forces will act on the element: Q and Q + dQ, the transverse forces of the discarded part
of the piezoelement acting in the planes of the cross section, M and M + dM are the bending moments acting on the element dx in its cross sections, q(l) - uniformly distribttled load acting
d2
on this element, ddx-—— is the inertia force of the rod element dr~
in its lateral motion: (S is the mass of a unit of the rod, y is its deflections).
On the basis of the Dalembert principle [61, the forccs mentioned above and the moments of forces acting on the element dx of the rod must form a flat balanced system of forces. Projecting these forces on the Y - axis and writing the moment equation of the indicated system offerees relative to the ccnter of the are of this element, we obtain the following equations:
¿1
Qcosa ~(Q+ dQ)cos(a + cl a) - £ -q(l)dx = 0
(2)
where a is the angle of rotation of the cross-section of the rod. In view of the smallness of tlx and da , the following assumptions can be made:
cos a; = cos(cr + da) = 1. dQdx - 0
Then from equation (2) we obtain:
dQ xd2y ... Q-™
dx
(3)
Due to the smallness of the movements, from the course of resistance of materials we give the following dependencies:
M - EJ
dlv ÔM . dQ „.6\v
—y; aM = -—dx\ ~=--EJ—~ dx' dx dx dx
(4)
8*y S d2y ebua . ,
—T- +--, =--L cos (col + &n )
3x4 EJ dl- ¡EJ
(5)
The solution of this differential equation is represented in the following form:
y = u(x) cos {o)l + <pn) (6)
where i/(x) is the amplitude function that determines the form
of the osci llation.
Substituting expression (6) in equation (5), we obtain an ordinary differential equation for the amplitude function:
dAu ,4 —T — k u =-a
dx
(7)
Where k4 =
dor ~EJ
a =■
ebut) ~EJl
To solve this differential equation, we add to it the boundary conditions of the problem posed:
5
ai jc=0, « = 0, — = 0
dx
2 du rjd2u 2 ci^11
at x-i, J/o — = m/o U--EJ—-
dx dx' dx j
(8)
where mz and arc the mass and moment of inertia of the
cross section of the mirror with respect to the transverse axis. The general solution of equation (7) is as follows:
it = it, + us
(9)
where ux is the general solution of the homogeneous equation corresponding to the homogeneous equation (7), and it-, is the particular solution of the inhomogeneous equation (7).
The roots of the characteristic equation corresponding to (7) are equal. In accordance with this, the solution of the homogeneous equation ut — is expressed in the following form:
w, = Ç, cos kx + C2smkx + Cyfr + CAe
(10)
where EJ is the stiffness of the rod material.
After the transformation of equation (3), taking into account expressions (1) and (4), we have the differential equation of transverse oscillation of the piezoelectric element OA :
where, C,,C,C,,C4 are unknowS integration variables.
The particular solution uof the inhomogeneous equation (7) is represented in the following form:
u2=AX+B (11)
where A and B are unknown constants to be determined.
Substituting expression (II) into equation (7), we have the identity:
-k\AX+B)=~a
Hence we find: A = 0,
kA dm2
Then, the general solution of equation (7) by expression (9) is represented in the following form:
u - C. cos kx + C\ siti kx + Cjé + C.e +
ebuQ
(12)
To determine the unknown constants, C,,C2,C,,C4 we can
use the boundary conditions (8). From these conditions we obtain the following four equations:
da'
Ck + CJc -C,k = 0
1 J 4
J/o2(-Ctk si nkl + C2k cos kl - CAkek') = - EJ(-qk2 coskl-C2k2 sinkl + Cyk2eli,C,k2el") =
= w3<y:(C, cos kl + GsinA7 + C/' + CAek' + =
(13)
CCD"
= -EJ(-Qc5 sin kl - C2ks cosjti+CJcW - Cpe")
Four unknown constants, C|,C2,C^,C4 enter into the system of four equations (13). As a result of the joint solution of equations (13), the above-mentioned unknown quantities are determined.
Thus, we find the equation for the transverse oscillatory motion of the piezoelectric element OA, and as a result, finally, it is
possible to determine the rotation angle a — — oi the cross
dx
section of the piezoelectric cell. The results of these studies can be used in the development and operation of a piezoelectric deflector for a light beam.
7TT
Referen ees
Conclusion
The paper proposes a piezoelectric optical deflector with adaptive mirrors, for use in the development and operation of a piezoelectric deflector for a light beam in liber optic technology.
Also shown is a block diagram of control with electronic blocks and a relative arrangement of the elements of a piezoelectric optical deflector with adaptive mirrors and the operating principle of the proposed device is given.
A mathematical model of the bimorph piezoelectric element used in the deflector of the light beam is developed.
The results of these studies can be used in the development and operation of a piezoelectric deflector for a light beam in fiber optic technology.
1. Gayvorovskaya G.S., Ryabsov A.V. (2011). Features of using optical commutators in modern information networks. Applicable Information Models. Sofia, ITHEA, No 22. pp. 169-181.
2. Hasanov M.H. (2010). Efficiency of a piezoelectric deflector for a light beam in communication technology, Baku, pp. 44-46,
3. Gasanov M.G. (2017). Multichannel piezoelectric switch of adaptive optical networks. Bulletin of the Azerbaijan Engineering Academy. Vol. 9 No. 4, pp. 107-113.
4. Vaqif M. Maharramov, Mehman H. Hasanov (2018). About the same transmission principle information flows. Scientific-practical journal of the Institute of Information Technology of ANAS. DOl:
10.25045 / jpit.v09.i 1.03. pp. 25-31.
5. Mehman H. Hasanov. Konul R. Haciyeva, Shalala F.Qodjaeva. (2018). Multifunctional adaptive piezoelectric switch of optical channels. T-Comm. Vol. 13, No. 29. pp. 64-68.
6. Biderman V.L. (1980). Theory of mechanical oscillations. Moscow. 408 p.
ПЬЕЗОЭЛЕКТРИЧЕСКИЙ ОПТИЧЕСКИЙ ДЕФЛЕКТОР С АДАПТИВНЫМ ЗЕРКАЛОМ
Гасанов Мехман Гусейн, Азербайджанский Технический Университет, г. Баку, Азербайджан, [email protected] Аннотация
Рассматривается один из возможных принципов создания пьезоэлектрических оптических дефлекторов с адаптивными зеркалами, с целью для использования при разработке и эксплуатации пьезоэлектрического дефлектора светового луча в волоконно-оптической технике. Приведена структурная схема управления с электронными блоками и взаимное расположение элементов пьезоэлектрического оптического дефлектора с адаптивным зеркалом и описан принцип работы предложенного устройства. Разработана математическая модель биморфного пьезоэлектрического элемента, применяемого в дефлекторе светового луча. Результаты этих исследований могут быть использованы при разработке и эксплуатации пьезоэлектрического дефлектора светового луча в волоконно-оптической технике.
Ключевые слова: пьезоэлектрический оптический дефлектор, адаптивное зеркало, пьезоэлектрический биморфный элемент, оптический кабель.
Литература
1. Гайворовская Г.С., Рябцов A.B. Особенности применения оптических коммутаторов в современных информационных сетях. Applicable Information Models. Sofia. ITHEA, 2011. No 22, pp. 169-181.
2. Гасанов М.Г. Эффективность пьезоэлектрического дефлектора светового луча в технике связи // Ученые-записки АзТУ. №2 (66). Баку 2010. C. 44-46.
3. Гасанов М.Г. Многоканальный пьезоэлектрический коммутатор адаптивных оптических сетей // Вестник Азербайджанской Инженерной Академии. 2017. Том 9. №4. С. 107-113.
4. Maharramov V.M., Hasanov M.H. About the same switching principle information flows. Scientific-practical journal Institute of Information Technology of ANAS, 2018. DOI: l0.25045/jpit.v09.il.03. pp. 25-31.
5. Hasanov M.H., Haciyeva K.R., Qodjaeva S.F. Multifunctional adaptive piezoelectric switch of optical channels. T-Comm. Vol. 13. № 29. 2018.
6. Бидерман В.Л. Теория механических колебаний. Москва, 1980. 408 с.
Информация об авторе:
Гасанов Мехман Гусейн, к.т.н., доцент кафедры "Многоканальные телекоммуникационные системы" Азербайджанского Технического Университета, г. Баку, Азербайджан
