Suvra Sarkar

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.

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.

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.

Experimental and Numerical Studies on the Dynamics of X-Band Gunn Oscillator Based Angle Modulator–Demodulator System with Chaotic Modulating Signal

We have studied the performance of a Gunn oscillator (GO) based angle modulator–demodulator system in transmitting chaotic signals in the X-band microwave frequency channel. The principle of bias t...

Studies on the Dynamics of a System of Bilaterally Coupled Chaotic Gunn Oscillators

Experimental studies on a system of two bilaterally coupled chaotic Gunn oscil- lators (BC-CGO) indicate the efiect of coupling coe-cient (Kij) on the dynamical state of the system. For some values of Kij, spectrally similar chaotic outputs are obtained from the GOs, while the transition of chaos to signals with discrete components is noted for other values of Kij.

Unstable PLL-Controller as FM Modulator and Detection of Modulating Self-Oscillations

Phase locked loops are well known nonlinear feedback control circuits extensively used in different electronic systems, particularly in communication and control. Generally they are used in stable mode of operation where loop error magnitude is small and system nonlinearity can be replaced by linear approximation. However, PLL designers over the years observed that due to variation of signal and loop parameters, dynamics of a PLL enters in a region which is not stable in conventional sense, even though predictable and controllable through parameter tuning. Hence attention has been given to explore so called unstable mode of PLL dynamics. PLLs operating in such mode produce periodic or chaotic self-oscillatory signals. In this chapter we focus on generation of self-oscillations in PLLs operating in their unstable mode and examine the possibilities of using these PLLs as modulators of periodic as well as chaotic oscillations. We consider a third order PLL with resonant type loop filter since in continuous time domain third order system is susceptible to chaotic self oscillations and gain as well as phase shift of a resonant filter could be tuned through a single parameter. We estimate the influence of loop design parameters in determining stable operating zone and hence find conditions of self-oscillation of third order PLL. With the variation of a design parameter, PLL is found to undergo a sequence of period doubling oscillations and ultimately chaotic oscillation of control signal results. In this condition, PLL is treated as an FM modulator of self-generated chaotic signal. We also report the effectiveness of PLL-based demodulators in detecting chaotically modulated signals. We consider second order and third order PLLs as chaos detecting loops for this purpose and obtain their relative responses. Detection of chaotically self-modulated signal is found to be difficult compared to that with periodically self modulated signal. We describe a circuit modification algorithm to PLL in order to enhance its response as a demodulator. Modified loop is shown to have increased stable zone of operation and faster transient response which makes it a better FM demodulator. Besides analytical and numerical simulation results, we have reported hardware experimental results on this problem.

Effects of Chaotic Perturbation on a Periodic Gunn Oscillator

We have studied dynamics of a periodic X-band Gunn oscillator (GO) forced by microwave chaotic signals through numerical simulation and by hardware experiment. The chaos used as forcing signal is generated in a periodically driven non-oscillatory GO. Numerical simulation results indicate that the forced periodic GO becomes chaotic for a moderate strength of forcing chaos. The generated chaos in driven GO is found to become phase or general synchronized to the forcing chaos depending on strength of the latter one. Hardware experiments are performed in X-band of microwave frequency. It shows generation of chaos in driven GO due to forcing. Moreover, synchronization between forcing and generated chaos is indirectly verified.