Study on synchronisation capability enhancement of optoelectronic oscillator using dynamic control bandpass filter
2018; Institution of Engineering and Technology; Volume: 12; Issue: 6 Linguagem: Inglês
10.1049/iet-opt.2018.5025
ISSN1751-8776
AutoresKousik Bishayee, Shantanu Mandal, Arindum Mukherjee, Baidyanath Biswas, Chandan Kumar Sarkar,
Tópico(s)Photonic and Optical Devices
ResumoIET OptoelectronicsVolume 12, Issue 6 p. 280-288 Research ArticleFree Access Study on synchronisation capability enhancement of optoelectronic oscillator using dynamic control bandpass filter Kousik Bishayee, Corresponding Author Kousik Bishayee kousikbishayee@gmail.com orcid.org/0000-0001-8814-8656 Department of ECE, University Institute of Technology, Burdwan University, Bardhaman, WB, 713104 IndiaSearch for more papers by this authorShantanu Mandal, Shantanu Mandal Department of ECE, University Institute of Technology, Burdwan University, Bardhaman, WB, 713104 IndiaSearch for more papers by this authorArindum Mukherjee, Arindum Mukherjee Department of ECE, Central Institute of Technology, Kokrajhar, Assam, IndiaSearch for more papers by this authorB. N. Biswas, B. N. Biswas Sir J.C. Bose School of Engineering, SKFGI, Mankundu, WB, IndiaSearch for more papers by this authorChandan K. Sarkar, Chandan K. Sarkar Department of ETE, Jadavpur University, Kolkata, WB, IndiaSearch for more papers by this author Kousik Bishayee, Corresponding Author Kousik Bishayee kousikbishayee@gmail.com orcid.org/0000-0001-8814-8656 Department of ECE, University Institute of Technology, Burdwan University, Bardhaman, WB, 713104 IndiaSearch for more papers by this authorShantanu Mandal, Shantanu Mandal Department of ECE, University Institute of Technology, Burdwan University, Bardhaman, WB, 713104 IndiaSearch for more papers by this authorArindum Mukherjee, Arindum Mukherjee Department of ECE, Central Institute of Technology, Kokrajhar, Assam, IndiaSearch for more papers by this authorB. N. Biswas, B. N. Biswas Sir J.C. Bose School of Engineering, SKFGI, Mankundu, WB, IndiaSearch for more papers by this authorChandan K. Sarkar, Chandan K. Sarkar Department of ETE, Jadavpur University, Kolkata, WB, IndiaSearch for more papers by this author First published: 01 December 2018 https://doi.org/10.1049/iet-opt.2018.5025Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study introduces the concept of dynamic controlled bandpass filter (BPF) to achieve improved synchronisation capability of a single-loop optoelectronic oscillator (OEO) under the effect of externally applied angle modulated signal. The governing equation for synchronisation ability of an OEO using dynamic control BPF has been derived. Theoretical study and comparison of locking capability enhancement using this dynamic BPF over a conventional static BPF are provided which is properly validated by simulation. Finally, the ability of frequency modulation to amplitude modulation conversion has been compared by measuring the total harmonic distortion values of the reconstructed signals. 1 Introduction Numerous works have been reported in the past two decades on an optoelectronic oscillator (OEO) which was proposed by Nakazawa et al. [1] in 1984. Its practical construction, a vivid study on its operation, characteristics and benefits was reported by Yao and Maleki [2–4]. Before the invention of OEO, microwave or mm-wave signal was generated by the beating of two laser beams or by optical injection locking method [5, 6]. Those systems were lacking in terms of spectral purity, phase noise and frequency-tunability which are essential in modern satellite, radar, and wireless communication applications. OEO is the most advanced method for generating extremely low phase noise microwave oscillators. The reason is that an optical cavity is used here as a microwave resonator, which provides low loss and an extremely high Q factor. A generic OEO, as shown in Fig. 1, works in a loop where the optical signal is modulated by an electro-optic modulator (Mach–Zehnder modulator – MZM), passes through the long optical fibre which produces the required time delay of the signal, and then detected by a photo detector. The detected electrical signal is then filtered, amplified and fed back to the modulating grid of the optical modulator. When the loop gain is larger than the loss and the round-trip phase shift of signal is an integer multiple of 2π, the OEO can generate a certain frequency determined by the centre frequency of the bandpass filter (BPF) and oscillation modes which depends upon the amount delay introduced by the optical fibre [7–10]. In the last two decades, several works have been reported on OEO either for advancement or behavioural pattern studies under different circumstances [11–18]. For a single frequency of oscillation in an OEO, a sharp cut off BPF is required so that only a single mode can persist in the system. Such a filter can only be realised using a single frequency tuned circuit. However, to achieve frequency tunabality feature, a dynamic BPF needs to be used having a tuned circuit whose capacitor is replaced by a varactor diode so that the centre frequency can be varied with external DC control voltage [19]. Performance and accuracy of such a dynamic BPF can be enhanced over the static BPF using a feedback control system; referred to as dynamic control system which the authors report in this communication. Fig. 1Open in figure viewerPowerPoint Schematic diagram of a synchronised single-loop OEO [20] This work closely follows the earlier work of Mukherjee et al. [20], on synchronisation effects by an angle modulated signal in a single-loop OEO having a static BPF. When a frequency modulated signal shines on a BPF, the output of it is a frequency modulation to amplitude modulation (FM–AM) signal. In the closed-loop dynamic control system, the modulating signal is extracted using a square-law detector, the output of which serves as a control voltage to the varactor used in the tuned circuit of the BPF (Fig. 2). Fig. 2Open in figure viewerPowerPoint OEO with FM sync signal using dynamic control filter This control signal of the dynamic BPF changes the centre frequency of the filter in accordance to the amplitude of the modulating signal, thereby allowing more linear region for the FM–AM conversion by the tuned circuit. In this communication, the expression for locking range of OEO using dynamic control BPF under the influence of FM synchronisation signal is derived first. Then the variation of practical locking range with different parameters, i.e. fibre delay, injection amplitude, modulation index and RF gain has been studied using this dynamic control scheme and compared with earlier work [20] both theoretically and numerically using Matlab® simulation. Finally, the ability of AM-to-FM conversion of this new scheme has also been compared with previous work by measuring the total harmonic distortion (THD) values of the reconstructed signals. 2 Theoretical analysis The proposed system works in a closed-loop structure is depicted in Fig. 2. Here the optical signal of a laser source gets intensity modulated by an MZM in accordance with the electrical signal provided at the modulating input of the MZM. The intensity modulated light is then passed through a long optical fibre which works as a resonator and is detected by a photo detector. This electrical signal is then combined with an external FM signal having carrier frequency nearly similar to the steady state frequency of the closed loop without any external signal. The mixed signal is then passed through the dynamic control BPF and amplified before feeding to the modulating input terminal of the MZM. This system will produce a stable oscillation at the FM carrier frequency if the FM frequency is within the locking range of the loop. The control signal for dynamic BPF is generated by extracting the message signal used in FM modulation. For that purpose, the output of dynamic BPF which is an AM–FM signal, passed through a square-law detector. The quality of this detected signal is tested by measuring its THD values before feeding to the control input of the dynamic filter. 2.1 Need of dynamic control in single-tuned circuit for FM detection For improvement in the detection of the FM signal, a large linear region is desired in the tuned circuit and at the same time, the output THD should be kept at a minimum. This also implies that a large conversion gain is required and consequently the tuned circuits will be able to handle an FM signal with large frequency deviation. The output THD for fixed centre frequency tuned circuits are constant and if the conversion-gain increases, signal handling capacity decreases. Hence a tracking dynamic filter is proposed which automatically tunes the instantaneous centre frequency of the tuned circuit in accordance with the detected modulating signal in such a way that the effective linear region for the FM-to-AM conversion process or the conversion gain becomes large and the signal handling capacity also increases. The basic principle behind the dynamic tuning of the centre frequency is illustrated in Figs. 3 and 4. Here the output detected wave is used to perform two things simultaneously: (i) the centre frequency is changed in such a way to bring the operating point in the more linear region and (ii) the effective modulation index is reduced. Thus the operation is confined to the linear part of the RF tuned circuit. Fig. 3Open in figure viewerPowerPoint Dynamic tuning principle Fig. 4Open in figure viewerPowerPoint Schematic arrangement for dynamic control of centre frequency of the tuned circuit It may be noted that the diagram is an exaggerated version. It has been shown in simulation findings that the output THD of the tuned circuits can be reduced by judiciously selecting the feedback gain, which controls the shift of the centre frequency of the tuned circuit. Detailed mathematical derivation of the dynamic control action is given in the Appendix. 2.2 System equation of single-loop OEO with dynamic control BPF under the influence of angle modulated synchronisation signal As shown previously [20], the closed-loop equation of OEO under the influence of FM synchronising signal is (1)where the parameters are defined as is the RF input applied to the modulating input of the MZM; is the external FM synchronising signal having input phase modulation where is phase sensitivity constant of modulator. So it may be mentioned that the instantaneous phase of the OEO is considered as where is the photo voltage of the photo detector, and is the half-wave voltage and bias voltage of MZM, is the extinction ratio of the modulator and is the time delay of the long optical fibre used in the loop; G is the gain of the RF amplifier and is the transfer function of the variable centre frequency tuned circuit or dynamic BPF introduced here. If the frequency detuning factor is considered as , where ; is the free-running frequency of the OEO. Then the modified transfer function of the variable centre frequency tuned circuit is given by [19] (2)For dynamic control action, the reconstructed message signal is fed as a control signal to the detuning port of the dynamic filter (let us say it is and 'A' has the unit of Hz/V). The purpose is to restrict the FM–AM conversion by the tuned circuit to the linear zone of the response characteristics of the BPF, thereby linearising the FM–AM conversion process. Thus, the transfer function of the dynamic control filter will be given by (3)As , the last term in can be neglected. In order to have the oscillation frequency at , which is equivalent to and , we can consistently assume the parameters of MZM as [16] and if then for an OEO ; application of these values leads to (4)Now, the complex frequency can be written as (5) (6)and (7)Rewriting (1) with the help of (5)–(7) gives (8)Equating the real part of (8) and considering in total synchronism, i.e. one gets (9)Similarly, equating the imaginary part of (8) and considering provides (10)However, the instantaneous frequency of OEO can be given as (11)Now it can be assumed that OEO is operating under a locked condition with an average phase error '' which is a measure of the initial detuning and also a component at the modulating frequency. So the solution of (11) can conveniently be written as (12)where M is the input output index error and . Now using Jacobi–Anger relation one can show that (13)Using (11)–(13) and neglecting the higher order terms like () because of the high Q BPF, it is not difficult to show (14)where in steady state, the term bearing non-linearity is assumed to be a constant ('C'). Considering under driven oscillator can be substituted. Moreover, in the steady state, it can be approximated as Now using harmonic balance method, the DC balance equation gives (15)Defining the normalised lock range as , (15) becomes (16)Similarly, using harmonic balance method harmonic terms (14) gives (17)i.e. (18)Now from (16) and (18), it can be written as (19) 2.3 Evaluation of lock range Locking range of any injection synchronised oscillator can be considered as the range of incoming frequency over which the free running signal of the OEO and external signal are combined to produce a single frequency. Locking range of an oscillator to an FM sync signal implies that the average value of the instantaneous frequency error is zero, i.e. . Where can be written as (20)Towards finding the average value one can neglect the harmonic terms in (20). So in steady state form taking is given by (21)i.e. (22)Now substituting in (19) one can write (23)Equations (21) and (23) are coupled equations. Therefore, the value of 'M' obtained from (23) has been substituted to (22) to find the theoretical normalised lock range of OEO using dynamic control BPF which has been shown in the results section. 3 Results and observations 3.1 System design To validate the theoretical findings Matlab® Simulink® environment is used. One significant entity needs to be mentioned here that the laser light frequency is of the order of few hundred THz. So for time-domain simulation analysis of such high frequency signal, a large amount of memory is required in PC which is not available to the authors. To overcome this problem, the operating frequency of laser source in a simulation study has been directly scaled down. Correspondingly, the oscillation frequency of the simulated OEO has also been scaled down proportionately. As per our observation, such frequency scaling does not affect the system performance of OEO. The designed circuit of OEO using dynamic control BPF is already shown in Fig. 2. Simulink realisation of the dynamic BPF shown in Fig. 5 is actually the block implementation of the transfer function considered for the dynamic filter. In modern communication applications like software defined radio (SDR) require a frequency tunablity feature in its local oscillator section. Use of dynamic BPF in OEO can introduce such frequency tunability in the system. Fig. 5Open in figure viewerPowerPoint Block diagram of dynamic BPF Frequency response comparison of this dynamic filter with the earlier static one is shown in Fig. 6 and corresponding linear variation of the centre frequency of dynamic filter with frequency detuning () is shown in Fig. 7. Fig. 6Open in figure viewerPowerPoint Frequency response comparison of static and dynamic filter Fig. 7Open in figure viewerPowerPoint Centre frequency variation of the dynamic filter with frequency detuning () 3.2 Improvement of locking capability using dynamic control BPF over static one An externally injected FM signal having slightly different carrier frequency than the OEO free running frequency, tries to perturb the synchronisation of the system which provides limited lock range as obtained in earlier work using static BPF. However, the presence of dynamic control action in the system helps to adjust the centre frequency of the dynamic filter in such a way that it becomes equal to the instantaneous frequency of FM signal and system becomes resynchronised for wider frequency range to provide a larger locking range. The theoretical variation of lock range with fibre delay, injection amplitude, FM modulation index and RF gain are calculated using Mathematica 11.1®. It is worthwhile to mention here that (22) and (23) are the coupled equations of two unknowns, i.e. locking range () and I/O index error (M). Hence the normalised lock range () has been obtained by solving the two equations numerically using Mathematica 11.1® and the consequent validation has been made using MATLAB® simulation. To provide a comparative study of the static BPF, the theoretical and simulated variations of the lock range with different parameters are shown in Fig. 8. Fig. 8Open in figure viewerPowerPoint Variation of lock range with fibre delay (a) Theoretical, (b) Simulated In Fig. 8 a, it is witnessed that for a given fibre delay of 7 µs, the theoretically obtained value of normalised lock range using dynamic control BPF is 0.9079 but for a static BPF is 0.8199, whereas the simulated results for the same are 0.3746 and 0.298, respectively, as shown in Fig. 8 B. The corresponding simulation data is given in Table 1. Table 1. Lock range measurement with fibre delay for the static and dynamic filter using RF Amp gain = 2, free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, modulating signal freq. = 20 kHz, and modulation index = 0.5 Fibre delay, µs Normalised lock range for static BPF Normalised lock range for dynamic control BPF 1 1.000 1.000 3 0.574 0.6350 5 0.390 0.5614 7 0.298 0.3746 10 0.241 0.3351 Likewise, for additional three parameters, i.e. injection amplitude, FM modulation index and RF gain the same locking range variation (both theoretical and simulated) for static and dynamic control BPF are shown in Figs. 9, 10–11, respectively. In all these cases, a very good agreement in the nature of graphs between theoretical and simulation plots have been witnessed. As instances, from Figs. 9 a and b, it can be seen that for an injection amplitude value of 0.4, theoretically obtained value of normalised lock ranges are 0.8504 and 0.4323 whereas corresponding simulated lock range values are 0.7069 and 0.5370 for dynamic control and static BPF, respectively. Similarly, from Figs. 10 a and b, it is evident that for a modulation index value of 0.5, theoretically obtained value of normalised lock ranges are 0.9778 and 0.9639, whereas simulated values are 0.9812 and 0.979. Finally, for an RF gain value of 2.2, theoretical values are 0.7222 and 0.5461, whereas the simulated values are 0.9944 and 0.993 as shown in Figs. 11 a and b. Simulation results are given for each case correspondingly in Tables 2–4. Table 2. Lock range measurement with injection amplitude for the static and dynamic filter using RF Amp gain = 2, free running frequency = 12.002 MHz, Q factor = 76.9, fibre delay = 10 µs, modulating signal freq. = 20 kHz and modulation index = 0.1 Injection Amp(E) Normalised lock range for static BPF Normalised lock range for dynamic control BPF 0.1 0.0925 0.1029 0.2 0.2037 0.5485 0.3 0.3888 0.6217 0.4 0.5370 0.7069 0.5 0.6666 0.7901 0.6 0.7407 0.8653 0.7 1.0000 1.0000 Table 3. Lock range measurement with modulation index for the static and dynamic filter using RF Amp gain = 2, free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, fibre delay = 1 µs and modulating signal freq. = 20 kHz Modulation index(β) Normalised lock range for static BPF Normalised lock range for dynamic control BPF 0.3 1 1 0.5 0.991 0.9950 0.7 0.979 0.9812 0.9 0.964 0.9650 1.0 0.945 0.9537 Table 4. Lock range measurement with RF gain for the static and dynamic filter having free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, fibre delay = 5 µs, modulating signal freq. = 20 kHz and modulation index = 0.5 RF gain(G) Normalised lock range for static BPF Normalised lock range for dynamic control BPF 2.0 1.0000 1.0000 2.2 0.7708 0.8095 2.4 0.6042 0.6310 2.6 0.4583 0.5714 2.8 0.3333 0.4643 3 0.1875 0.3214 Fig. 9Open in figure viewerPowerPoint Variation of lock range with injection amplitude (a) Theoretical, (b) Simulated Fig. 10Open in figure viewerPowerPoint Variation of lock range with modulation index (a) Theoretical, (b) Simulated Fig. 11Open in figure viewerPowerPoint Variation of lock range with RF gain (a) Theoretical, (b) Simulated Therefore, it can be concluded that in all cases the implication of dynamic control has helped to achieve a better locking range than a normal static filter. 3.3 Reduction of distortion using dynamic control over static BPF When an OEO is in synchronisation with an externally injected FM signal, the characteristic property of the OEO is to transform the injected FM signal into AM which has been investigated in earlier work of Mukherjee et al. [20]. The converted AM signal can be easily demodulated using a conventional square-law detector to retrieve the message signal. The spectral purity of the retrieved message signal can be judged by measuring the THD of the output. A comparative study of THD values of an output message signal using dynamic control and static BPF is made here. Set up for THD measurement using MATLAB® has been shown in Fig. 2 with corresponding measurement tables for different parameters like fibre delay, injection amplitude, FM modulation index and RF gain are given in Tables 5–8. Table 5. Lock range measurement with fibre delay for the static and dynamic filter using RF Amp gain = 2.1, free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, modulating signal freq. = 20 kHz and modulation index = 0.5 Fibre delay, µs Normalised THD for static BPF Normalised THD for dynamic control BPF 3 1 1 4 0.8938 0.8817 5 0.9163 0.886 6 0.8597 0.8442 7 0.8239 0.7991 8 0.8189 0.7818 9 0.7584 0.7296 10 0.7567 0.7231 Table 6. Lock range measurement with injection amplitude for the static and dynamic filter using RF Amp gain = 2, free running frequency = 12.002 MHz, Q factor = 76.9, fibre delay = 5 µs, modulating signal freq. = 20 kHz and modulation index = 0.5 Injection Amp(E) Normalised THD for static BPF Normalised THD for dynamic control BPF 0.1 0.3421 0.3194 0.2 0.5083 0.4875 0.3 0.6694 0.6565 0.4 0.7936 0.7856 0.5 0.8841 0.8797 0.6 0.9508 0.9487 0.7 1 1 Table 7. Lock range measurement with modulation index for the static and dynamic filter using RF Amp gain = 1.8, free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, fibre delay = 5 µs and modulating signal freq. = 20 kHz Modulation index(β) Normalised THD for static BPF Normalised THD for dynamic control BPF 0.3 1 1 0.5 0.9950 0.991 0.7 0.9812 0.979 0.9 0.9650 0.964 1.0 0.9537 0.945 Table 8. Lock range measurement with RF gain for the static and dynamic filter having free running frequency = 12.002 MHz, Q factor = 76.9, injection amp = 0.3, fibre delay = 5 µs, modulating signal freq. = 20 kHz and modulation index = 0.5 RF gain(G) Normalised THD for static BPF Normalised THD for dynamic control BPF 0.3 1 1 0.5 0.9950 0.991 0.7 0.9812 0.979 0.9 0.9650 0.964 1.0 0.9537 0.945 It can be mentioned that the actually obtained THD values are normalised here for graphical comparison. Since it has been found that a general variation of THD values for static and dynamic filters occur at the first decimal point. Whereas THD variation with an individual parameter like fibre delay, injection amplitude, FM modulation index and RF gain occurs at the third decimal point for both static and dynamic cases. Therefore, the plots of actual THD values of the two cases will show two lines parallel to the 'x'-axis, which will not reflect the variation of THD values with the intended parameter. The combined Figs. 11 a –d show the comparative study of the improvement achieved by means of dynamic control filter over earlier static one for different parameter variations. The nature of the curves obtained for different parameter variation can be justified as follows: For an OEO the phase noise decreases quadratically with the loop delay time [20], so the THD values should also decrease with delay as obtained in Fig. 12 a. Fig. 12Open in figure viewerPowerPoint Variation of THD for static and dynamic control BPF with different parameters (a) Fibre delay, (b) Injection amplitude, (c) Modulation index, (d) RF gain Externally injected signal of different frequency always tries to disturb synchronisation of any PLL system. Therefore, with the increase of injection amplitude, THD values increase which are evident from Fig. 12 b. Wideband FM starts at modulation index and improves modulation quality with the increase of index values. Better modulation ensures better detection. So the increase of modulation index reduces the THD values as shown in Fig. 12 c. Higher RF gain makes the system overdamp, thereby increasing THD values of the detected signal as found in Fig. 12 d. At last, it can be resolved that the reduction of THD values using dynamic control seems nearly similar for all the cases. This can be instantiated as for a delay value of 10 µs of Table 5, an approximate 4% improvement of THD values over static filter which is also evident from Fig. 12 a. 4 Conclusion It has been established here theoretically as well as with simulation results that the dynamic controlling action of the BPF enhances the synchronisation capability of an injection locked OEO. Profound improvement of detection capability using this dynamic control BPF over static filter has been observed (around 4%) by measuring the THD values. It has also been perceived that further improvement in synchronisation capability can be made using dual parallel dynamic control BPF approach, which will be communicated in future. 5 Acknowledgment The authors were thankful to the management of University Institute of Technology, the University of Burdwan, Burdwan, West Bengal and Central Institute of Technology, Assam for giving an opportunity to carry out this work and also the management of Sir J.C. Bose School of Engineering for carrying out the work in Sir J.C. Bose Creativity Centre of Supreme Knowledge Foundation Group of Institution, Mankundu, Hooghly. 7 Appendix 7.1 Dynamic control action of the single-tuned circuit The instantaneous frequency of a periodic wave is defined as . Therefore, when the instantaneous amplitude is and the instantaneous frequency is , then it is not difficult to show . Now, the input impedance of the tank circuit is . Where ; and when ; then . It is to be noted that '' is static centre frequency of the single-tuned circuit and '' is that for dynamic BPF where '' is the shift in the centre frequency in response to a control voltage, typically , '' being the voltage-phase conversion gain. From Fig. 13, it is not difficult to show , where is the instantaneous output voltage and is the input FM current. Thus, one gets for a dynamic BPF: . Fig. 13Open in figure viewerPowerPoint A single tuned circuit with injection synchronisation Expressing the instantaneous output voltage and the input current of the tuned circuit as and , respectively where is the instantaneous phase difference between the output and the input Equating the real and the imaginary components, one gets The above two coupled equations can be solved numerically to obtain the instantaneous amplitude equation '' as a function of ''. The control signal responsible for changing the centre frequency of the dynamic BPF is obtained by using square-law detection technique to obtain the instantaneous output amplitude and then this voltage is fed back to the control input of the BPF (Fig. 2). The centre frequency shift of the BPF in accordance with the amplitude of the control signal shown in Fig. 14. Fig. 14Open in figure viewerPowerPoint BPF centre frequency shift with control signal 6 References 1Nakazawa M. Nakashima T., and Tokuda M.: 'An optoelectronic self-oscillatory circuit with an optical fibre delayed feedback and its injection locking technique', J. Lightwave Technol., 1984, LT-2, (5), pp. 719– 730 2Yao X.S., and Maleki L.: 'Optoelectronic microwave oscillator', J. Opt. Soc. Am. B, 1996, 13, (8), pp. 1725– 1735 3Yao X.S., and Maleki L.: 'Optoelectronic oscillator for photonic systems', IEEE J. Quantum Electron., 1996, 32, (7), pp. 1141– 1149 4Yao X.S. Maleki L., and Devis L.: 'Coupled optoelectronic oscillators for generating both RF signal and optical pulses', J. Lightwave Technol., 2000, 18, (1), pp. 73– 78 5Goldberg L. Taylor H.F., and Weller J.F. et al.: 'Microwave signal generation with injection locked laser diodes', Electron. Lett., 1983, 19, (13), pp. 491– 493 6Gliese U. Nielsen T.N., and Nørskov S. et al.: 'Multifunctional fiber-optic microwave links based on remote heterodyne detection', IEEE Trans. Microw. Theory Tech., 1998, 46, (5), pp. 458– 468 7Gonorovsky I.: ' Radio circuit and signals' ( Mir Publisher, Moscow, 1974) 8Biswas B.N.: ' Phase lock theories and applications' ( Oxford and IBH, New Delhi, 1988) 9Biswas B.N. Roy S.K., and Pramanik K. et al.: 'Injection locked tunable filters and amplifiers', IEEE Trans. Circuits Syst., 1980, CAS-27, (9), pp. 833– 836 10Biswas B.N. Chatterjee S., and Pal S.: 'Laser induced microwave oscillator', Int. J. Electron. Commun. Eng. Technol., 2012, 3, (1), pp. 211– 219 ISSN 0976–6464(Print), ISSN 0976–6472(Online), © IAEME 11Mukherjee A. Chatterjee S., and Das N.R. et al.: 'Laser induced microwave oscillator under the influence of interference', Int. J. Microw. Wirel. Technol., 2014, 6, (6), pp. 581– 590 12Mukherjee A. Ghosh D., and Das N.R. et al.: 'Harmonic distortion and power relations in a single loop optoelectronic oscillator', Opt. – Int. J. Light Electron Opt., 2015, 127, pp. 973– 980 13Mukherjee A. Ghosh D., and Biswas B.N.: 'On the effect of combining an external synchronizing signal feeding the Mach–Zehnder modulator in an optoelectronic oscillator', Opt. – Int. J. Light Electron Opt., 2015, 127, pp. 3576– 3581 14Mukherjee A., and Biswas B.N.: 'On synchronisation issues pertaining of a noisy angle modulated signal in an OEO', Int. J. Electron. Lett., 2017, pp. 1– 14 ISSN: 2168-1724(print), 2168-1732(online) 15Maleki L.: 'Sources: the optoelectronic oscillator', Nat. Photonics, 2011, 5, pp. 728– 730 16Ghosh D. Mukherjee A., and Chatterjee S. et al.: 'A comprehensive theoretical study of dual loop optoelectronic oscillator', Opt. – Int. J. Light Electron Opt., 2016, 127, pp. 3337– 3342 17Mukherjee A. Varseney A., and Mehta T. et al.: ' Locking characteristics of a modified heterodyne phase lock loop'. IEEE Conf. URSI AP-RASC, Seoul, Korea, 20 October 2016 18Bishayee K. Mandal S., and Mukherjee A. et al.: 'Locking phenomenon in a single loop OEO', Int. J. Electron. Commun. Technol., 2014, 5, (2), pp. 97– 101, Spl-1, ISSN: 2230-7109 (online) | ISSN: 2230-9543(print) 19Mukherjee A. Ghosh D., and Das N.R. et al.: 'On a single loop optoelectronic oscillator using variable centre frequency dynamic filter', Int. J. Electron. Commun. Technol., 2015, 6, (1), pp. 152– 155, Spl-1, ISSN: 2230-7109 (online) | ISSN: 2230-9543 (print) 20Mukherjee A. Biswas B.N., and Das N.R.: 'A study on the effect of synchronization by an angle modulated signal in a single loop optoelectronic oscillator', Opt. – Int. J. Light Electron Opt., 2015, 126, (19), pp. 1815– 1820 Citing Literature Volume12, Issue6December 2018Pages 280-288 FiguresReferencesRelatedInformation
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