B. C. Sarkar

A new dynamic gain control algorithm for speed enhancement of digital-phase locked loops (DPLLs)

A dynamic gain modification algorithm of a class of DPLLs has been proposed to improve its transient characteristics and tracking behavior. In this technique, rather taking a time invariant gain, the gain of the loop digital filter is made a function of the sampled value of the signal at every sampling instant. It has been shown analytically as well as numerically that the new structure is faster than the conventional one in its acquisition time and at the same time, it has a broader acquisition range.

STUDIES ON THE DYNAMICS OF BILATERALLY COUPLED X-BAND GUNN OSCILLATORS

The dynamics of a system comprising of two bilaterally coupled Gunn oscillators (BCGOs) has been examined using a circuit theoretic model of the Gunn oscillator (GO). The efiects of coupling factors (kij) between i-th and j-th oscillators on the frequency-range of synchronized operation and the magnitude of common frequency of oscillation have been examined semi-analytically and by numerical solution of the system equations. The occurrence of chaotic oscillations at the verge of synchronization bands is observed in numerical simulation. The experimental response of the BCGO operating in the X-band is obtained and the results are found to be qualitatively similar to the analytical and numerical predictions.

Chaos, intermittency and control of bifurcation in a ZC2-DPLL

Nonlinear dynamics of a dual sampler-based zero crossing digital phase lock loop (ZC2-DPLL) has been investigated. Analysis supported by detailed numerical studies shows that the system enters a chaotic state through a cascade of period doubling bifurcation. The dynamics of the system have been quantified with the dynamical measures of Lyapunov exponent and correlation dimension. Further, it has been found that for certain system parameters intermittency occurs in the system. The occurrence of intermittency has been proved using the Pomeau–Manneville principle. The phenomenon of bifurcation control in a ZC2-DPLL using time delay feedback has been explored. It has been found that for some suitably chosen control parameters bifurcation phenomena can be controlled such that the stable locked zone of a bifurcation controlled ZC2-DPLL can be extended, which enhances the application potentiality of a ZC2-DPLL.

Some Numerical and Experimental Observations on the Growth of Oscillations in an X-Band Gunn Oscillator

The dynamics of the onset of oscillations in a wave guide cavity based Gunn Oscillator (GO) has been critically examined through numerical simulations and experimental studies. The transition of the GO from a non-oscillatory to an oscillatory state and the same in the reverse direction occurs at different critical values of the dc bias voltage applied to the GO. In presence of a weak RF field in GO cavity, oscillations with broad band continuous spectrum and multiple discrete line spectrum are observed at the GO output for different values of dc bias below the above mentioned critical values. Analysing the numerically obtained time series data, chaos quantifiers have been obtained to prove the occurrence of the chaotic oscillations in the GO. Experimental results and observations of numerical simulation show good qualitative agreement.

Nonlinear dynamics of a class of symmetric lock range DPLLs with an additional derivative control

Nonlinear dynamics of a class of symmetric lock range digital phase-locked loops (SLR-DPLLs) has been investigated using nonlinear dynamical theoretical and computational tools. It has been observed that the system shows a period doubling route to chaos. For certain system parameters the loop exhibits intermittent behavior. The analytical bifurcation analysis shows that inspite of the broader frequency acquisition range than a conventional one the stability of the loop degrades appreciably when the input signal frequency is less than the nominal frequency of the digitally controlled oscillator. The system dynamics have been characterized by measuring the Lyapunov exponent and the correlation dimension. Further it has been shown that the stability range of a SLR-DPLL can be extended using a modified loop filter incorporating time delay feedback technique. The modified SLR-DPLL (MSLR-DPLL) with this additional derivative control along with the loop digital filter (LDF) shows faster convergence than the unmodified one for proper choice of system design parameters. Consequently, the MSLR-DPLL becomes more suitable for practical applications.

Phase error dynamics of a class of modified second-order digital phase-locked loops in the background of cochannel interference

The present paper examines the dynamics of a nonuniform sampling second-order digital phase-locked loop (NUS-DPLL) with an effectively modified loop filter. Through an analytical study of the system response around the steady state, supported by detailed simulation results, the paper establishes the better performance of the modified DPLL. It has been shown by a simulation study as well as explained qualitatively, that the modified DPLL will be able to withstand the adverse effects of cochannel interference signals better than the conventional NUS-DPLL.

Phase error dynamics of a class of DPLLs in presence of cochannel interference

Nonlinear dynamics of a class of conventional digital phase-locked loops (DPLLs) and its modified structure using loop digital filter modification has been studied analytically as well as through computer simulation. The presence of an interference signal considerably disturbs the dynamical stability of the conventional DPLL but the modified structure is capable of withstanding this disturbance to a larger extent. A qualitative explanation of the observation has been given using bifurcation theory.

Studies on the Dynamics of Two Bilaterally Coupled Periodic Gunn Oscillators Using Melnikov Techniques

Dynamical stability of a system of bilaterally coupled periodic Gunn oscillators (BCPGO) has been studied employing Melnikovs global perturbation technique. In the BCPGO system, a fractional part of the output signal of one oscillator is injected into the other through a coupling network. The injected signal is considered as a perturbation on the free running dynamics of the receiving oscillator and the amount of perturbation is quantifled by a parameter named coupling factor (CF). The limiting values of CFs leading to chaotic dynamics of the BCPGO system are predicted analytically by calculating the Melnikov functions (MFs) in the respective cases. Also the efiect of the frequency detuning (FD) between the Gunn Oscillators (GOs) on the computed values of MFs has been examined. A thorough numerical simulation of the BCPGO dynamics has been done by solving the system equations. The obtained results are in qualitative agreement with the analytically predicted observations regarding the roles of the system parameters like CF and FD.

Design of Chaotic and Hyperchaotic Time-Delayed Electronic Circuit

The present paper reports a first order nonlinear retarded type time-delayed chaotic and hyperchaotic electronic circuit. The proposed circuit has three distinct advantages over the existing time-delayed circuits. First, it has a nonlinearity that is expressed by closed form mathematical functions, which makes the analysis and design of the circuit easier. Second, the time-delay part of the proposed circuit is realized with an active All-Pass Filter (APF), in which no inductor is used, and the variation of delay is obtained simply by the variation of a resistor, which is more advantageous than to vary the inductor in LCL delay blocks that is widely used in all the time-delayed circuits existing in the literature. Third, the circuit shows hyperchaos even for a moderate time-delay. We describe the systematic design procedure of the circuit, and whenever necessary, the experimental results are corroborated by the numerical computations. We show that the circuit shows limit cycle oscillation, bifurcation scenario, chaotic and hyperchaotic oscillations.

CONVENTIONAL AND EXTENDED TIME-DELAYED FEEDBACK CONTROLLED ZERO-CROSSING DIGITAL PHASE LOCKED LOOP

This article investigates the effect of the conventional and extended time-delayed feedback control techniques of chaos control on a first-order positive zero-crossing digital phase locked loop (ZC1-DPLL) using local stability analysis, two-parameter bifurcation studies and two-parameter Lyapunov exponent spectrum. Starting from the nonlinear dynamics of a ZC1-DPLL, we at first explore the time-delayed feedback control (TDFC) algorithm on a ZC1-DPLL in the parameter space. A condition for the optimum value of the system control parameter is derived analytically for a TDFC based ZC1-DPLL. Next, the extended time-delayed feedback control (ETDFC) technique on a ZC1-DPLL is described. It is observed that the application of the delayed feedback control (DFC) technique on the sampled values of the incoming signal inside the loop finally results in the nonlinear DFC of the phase error dynamics. We prove that, for some suitably chosen control parameters, an ETDFC based ZC1-DPLL has a broader stability zone in comparison with a ZC1-DPLL and its TDFC version.