DOĞRUSAL OLMAYAN OPTOELEKTRONİK GERİ BESLEMELİ LAZER DİYODUN ÜÇ TON KÜÇÜK İŞARET GİRİŞLİ İNTERMODULASYON DİSTORSİYON SİSTEM TEORİSİ

Yıl 2007, Cilt: 22 Sayı: 2, 417 - 430, 01.03.2013

Remzi Yıldırım

Öz

Bu çalışmada doğrusal olmayan optoelektronik geribeslemeli lazer diyot sistemi için Volterra güç seri açınımı kullanılarak üç ton küçük işaret girişi için sistemin distorsiyon analizi yapılmıştır. Analiz için intermodülasyon distorsiyon (IMD) uygulamalarında kullanılan frekans bileşenleri seçilmiştir. Bunlar; ( 1 2 ) ω −ω , ( ), 1 2 ω +ω ( ) 1 3 ω +ω , ( ), 1 3 ω −ω ( ), 2 3 ω −ω ( ) 2 3 ω +ω , ( ) 1 2 3 ω +ω +ω , ( ), 1 2 3 ω +ω −ω ( ) 1 2 3 −ω +ω +ω ve ( ) 1 2 3 ω −ω +ω IMD frekans bileşenleridir. Bu frekans bileşenlerin genliklerinin hesaplanmasında sistem yaklaşımı yapılarak, lazer diyot oran eşitlikleri üçüncü dereceye kadar seri açınımı yapılmıştır. Volterra operatöründen H1, H2 ve H3 Volterra çekirdekleri ve bunlardan seçilmiş olan IMD frekans bileşenlerinin transfer fonksiyonları elde edilmiştir. Bu IMD frekans bileşenlerinin genlikleri geribesleme sabiti (K) ve zaman gecikmesine ( o t )’a bağlı olarak elde edilmiştir. Analiz sonucunda bazı IMD frekans bileşenleri arasında asimetrik durum bulunmuştur.

Anahtar Kelimeler

lazer diyot, volterra serisi, intermodülasyon, harmonik distorsiyon, doğrusal olmayan distorsiyon, optoelektronik geribesleme, elektronik geribesleme, kenarband asimetrisi, doğrusal olmayan geribesleme.

INTERMODULATION DISTORTION SYSTEM THEORY OF THE THREE-TONE SMALL SIGNAL INPUT LASER DIODE WITH NON-LINEAR OPTOELECTRONIC FEEDBACK

Öz

In this study, Volterra power series expansion is performed successfully in order to analyse the distortion for
three tone small signal with non-linear optoelectronic feedback laser diode system input. The frequency components which are used in intermodulation distortion (IMD) applications are selected in the analysis. These are
( ) ω1 −ω2 , ( ), ω1 +ω2 ( ) ω1 +ω3 , ( ), ω1 −ω3 ( ), ω2 −ω3 ( ) ω2 +ω3 , ( ) ω1 +ω2 +ω3 , ( ), ω1 +ω2 −ω3 ( ) −ω1 +ω2 +ω3 and
( ) ω1 −ω2 +ω3 During the calculation of the amplitudes of these selected frequency components, system approach is performed and series expansion of the laser diode rate equations is obtained up to third order degree.
From the Volterra operator, H1, H2 and H3 Volterra kernels are computed. Then the transfer functions of the
IMD frequency components are obtained. The amplitudes of the IMD frequency components is found with respect to feedback constant (K) and time delay ( ot ). At the end of the analysis asymmetry is determined in some
of the IMD frequency components. 

Anahtar Kelimeler

Laser diode, volterra series, intermodulation, harmonic distortion, non-linear distortion, optoelectronics feedback, electronics feedback, sideband asymmetry, non-linear optoelectronic feedback

Kaynakça

• Schetzen, M. and Yıldırım,R. “System theory of the
• single-mode laser-diode” Opt. Commun, 219, 341-
• , 2003.
• Yıldırım, R. and Schetzen,M. “ Application of the
• Single–mode Laser Diode System Theory” Opt.
• Commun, 219, 351-355, 2003.
• Aydin, E. and Yıldırım,R. ”Optimizing the Performance
• of Single-mode Laser Diode System Using
• Genetic Algorithm”, Optics.and Laser in Eng., 42,
• -46, July 2004.
• Çelebi, F.V.and Yıldırım, R. ”Distortion System
• Theory of the Two-tone Small signal Input laser Diode“
• J. of the Faculty of Engineering and Architecture
• Gazi University, Vol 20, No 3, pp373,
• -
• Ohtsu, M. and S.Kotajima, "Linewidth Reduction of
• a Semiconductor Laser by Electrical Feedback"
• IEEE J.QE., Vol 21, pp 1905- 1912, Dec. 1985.
• Sharaf, K. and Ibrahim,M.M "The Effect of Electronics
• Feedback on Semiconductor lasers" IEEE
• J.QE., Vol. 26, pp 1347- 1352, Aug . 1990.
• Saboureau, P., Foing J.P. and Schanne, P. " Injection-
• locked Semiconductor Lasers with Delayed
• Optoelectronic Feedback" IEEE J.QE., Vol 30, pp
• - 1591, Sept . 1997.
• Fukushima, T. and Sakamoto, T. " Chaos in Coupled
• Semiconductor Lasers with an Electronic Delayed
• Feedback Caused by Injection Locking" IEEE
• J.QE., Vol 34, pp 750- 758, May 1998.
• Grigorieva,E.V., Haken H. and Kaschenko, S.A.
• "Theory of Quasiperiodicity in Model of Lasers
• with Delayed optoelectronic Feedback" Optics
• Comm. Vol 165, pp 279- 292, July 1999.
• Giacomeli, G. M. Calzavara and Arecchi, F.T. "
• Instabilies in a Semiconductor laser with delayed
• optoelectronic Feedback, Optics Comm., Vol:74 pp
• - 101, Dec. 1989.
• Lee,C.H., Shin,S.Y. " Selfpulsing, Spectral Bistability,
• and Chaos in a Semiconductor Laser Diode with
• Optoelecronic Feedback" Appl Phys. Lett. Vol:62,
• pp 922- 924 May 1993
• Loiko, N.A. and Samson, A.M. " Posible Regimes
• of Generation of a Semiconductor Laser with a Delayed
• Optoelectronic Feedback" Optics Comm.
• Vol:93 pp 66- 72 Sept. 1992
• H. D.I.Abarbanel,M. B. Kennel, l. Illing, H.F. Chen,
• and J.M. Liu," Synchronization and Communication
• Using Semiconductor Lasers with Optoelectronic
• Feedback" IEEE J.QE. Vol:37, pp 1301- 1311,
• Oct. 2001
• Tang, S. and Liu, J.M. " Chaotic Pulsing and Quasi-
• Periodic Route to Chaos in a Semiconductor with
• Delayed Optoelectronic Feedbabck" IEEE J.QE.,
• Vol 37, pp 1301- 1311, March 2001.
• Schetzen, M.” The Volterra and Wiener Theories
• of Nonlinear Systems”, Malabar, Fla., R.E. Krieger Publishing Co., 2006, reprint edition with
• additional material.
• Hassine, L. et al., “Volterra Functional Series Expansions
• for Semiconductor Lasers Under Modulation,”
• IEEE Journal of Quantum Electronics, Vol 30,
• No 4, pp. 918-928, April 1994.
• Tucker, R.S. “High-Speed Modulation of Semiconductor
• Lasers,” J. Lightwave Tech. LT-3, No. 6,
• pp. 1180-1192, Dec. 1985.
• Olshansky, Lanzisa, R. V. W.V. Powazinik,“ Universal
• Relationship Between resonant Frequency and
• Damping Rate of 1.3 μm InGaAsP Semiconductor
• Laser” Apl. Phys. Letters., 50 (11), pp.653-
• ,1987.
• Navid,R., Clark,J.R.,Demirci, M. and Nguyen,
• C.T.C. ”Third-order Indermodulation distortion in
• Capasitively- Driven CC-beam Micromechanical
• Resonators”, Micro Electro Mechanical Systems,
• MEMS 2001.The 14 th IEEE International
• Conference on, 21-25Jan 2001 pp.228 - 231
• Pipes, L.A. and Harvill, L. R.” Applied Mathematics
• for Engineers and Physicists, Third edition”,
• McGraw-Hill International Book Comp., 1983, Tokyo.
• Bussgang, J.J. and Ehrman, L.,” Analysis of Nonlinear
• Systems with Multiple Inputs” Proc. IEEE, Vol
• , pp.1088-1119, Aug.1974.
• Bedrosian, E. and Rice,S.O.” The Output Properties
• of Volterra Systems (Nonlinear Systems with Memory)
• Driven by Harmonic and Gaussian Inputs”,
• Proc. IEEE, Vol 59, pp.1688-1707, Dec. 1971.
• Nam, S. and Power,E. J. ”On the Selective Counting
• of Third-Order Products,” IEEE Trans.Commun.,
• Vol 43, pp.2405-2413, Aug. 1995.
• Weiner, D.D. and .Spina, J.E” Sinusodial Analysis
• and Modeling of Weakly Nonlinear Circuits”,
• Van Nostrand Reinhold Comp.1980, New York
• Borges de Carvalho, N. and J.Carlos Pedro, “A
• Comprehensive Explanation of Distortion Sideband
• Asymmetries”, IEEE Trans. Microwave Theory
• Tech., vol 50, pp.2090-2101, Sep. 2002.
• Bosh, W. and .Gatti, G “ Measurement and simulation
• of memory effects in predistortion linearizers”,
• IEEE Trans. Microwave Theory Tech., vol 37,
• pp.1885-1890, Dec. 1989.
• Sevic, J.F., Burguer, K.L. and Steer, M.B. “ A novel
• envelope-termination load-pull methods for ACPR
• optimization of RF/ Microwave power amplifies“,
• In IEEE MTT-S Int.Microwave Semp. Dig., Baltimore,
• MD, 1998, pp. 601-605.
• Borges de Carvalho, N. and Pedro,J.Carlos “ Twotone
• IMD asymmetry in microwave power amplifiers
• ”, In IEEE MTT-S Int.Microwave Semp. Dig.,
• Boston , MA, 2000, pp. 445-448.
• McIntosh, P.M. and Snowden, C.M.” The effect of a
• variation in tone spacing on the intermodulation performance
• of A and class AB HBT power amplifiers,”
• ”, In IEEE MTT-S Int.Microwave Semp.
• Dig., 1997, pp. 371-374.
• Rugh,W.J. “ Nonlinear System Theory” The Johns
• Hopkins University Press.Baltimore, 1981.
• “EAGLE-WARE GENESYS” -software handbook–
• Enterprıse-2003.