1) The document discusses a nonlinear microwave oscillator system that can exhibit chaotic behavior based on a time-delayed feedback loop architecture operating in the 2-4 GHz frequency band.
2) It presents the experimental setup of the system using a voltage controlled oscillator (VCO), splitter, mixer, and delay line. Mathematical models are developed to simulate the system dynamics.
3) Experiments show the system can transition from periodic to chaotic behavior as a nonlinearity parameter is increased. Synchronization is also achieved by bidirectionally coupling two similar microwave oscillator systems.
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...
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1. Nonlinear Microwave Oscillators: Dynamics and Synchronization Hien Dao (Chemical Physics Program) John C. Rodgers (IREAP) Thomas E. Murphy (ECE & IREAP)
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5. VCO splitter d mixer Bias at operating point H ( s ) low pass filter gain delay Experimental setup
6. Voltage Controlled Oscillator (VCO) is a device that converts an input analog voltage into a signal whose frequency is linearly proportional to the magnitude of voltage VCO Tuning signal v (t) RF signal and with is named tuning sensitivity (VCO gain) and 0 is bias frequency. Slowly varying phase 0 =2.65 GHz =175 MHz/v
7. v VCO d Mixer Splitter delay Nonlinear function is created using delay-line frequency discriminator output
9. VCO splitter d mixer Bias at operating point H ( s ) low pass filter gain delay Experimental setup
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11. Mathematical model for tuning signal system equation H (s) nonlinearity gain delay low pass filter v(t) f cutoff =3 MHz s 1.2 s Varying from 0.5-9.5 5 ns 175 MHz/V Value Parameters
18. Chaotic synchronization had been achieved by coupling two optoelectronic systems. How to couple two microwave systems and what kind of synchronization we should observe? x 1 (t): x 1 (t) – x 2 (t): x 2 (t):
19. Two systems are coupled bi-directionally in microwave band, VCO Splitter d Mixer Bias VCO Splitter d Mixer Bias H(s) H(s) is coupling strength v 1 (t) v 2 (t) Behavior depends on whether the VCO difference frequency exceeds the filter bandwidth
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21. RF signal collected from scope Analytic signal Hilbert transform Analytic signal Where is Hilbert transform of Using Hilbert transform to estimate phase RF signal Constant amplitude Phase varies around a bias value 0