Muri

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MURI talk on December 10th, 2010

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Muri

  1. 1. Nonlinear Microwave Oscillators: Dynamics and Synchronization Hien Dao (Chemical Physics Program) John C. Rodgers (IREAP) Thomas E. Murphy (ECE & IREAP)
  2. 2. Outline <ul><li>Motivation </li></ul><ul><li>Dynamics of a nonlinear microwave system </li></ul><ul><li>Synchronization of coupled microwave oscillators </li></ul><ul><li>Conclusion </li></ul>
  3. 3. Motivation <ul><li>Nonlinear time-delayed feedback loops can produce high dimensional chaos. </li></ul>nonlinearity Example: An optoelectronic chaotic oscillator A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 101 , 154102 (2008)  H (s)  gain delay filter
  4. 4. <ul><li>Microwave transmission systems are used everywhere; and many of those rely on microwave carrier recovery with voltage controlled oscillator is key component. </li></ul>Motivation <ul><li>Our microwave chaotic system is based on time-delayed feedback loop </li></ul><ul><li>architecture working in the frequency band, 2 GHz-4 GHz. </li></ul><ul><li>A chaotic signal in this band would potentially offer advantages such as lower probability of detection, less susceptible to noise and jamming, less likely to interfere with existing communication channels… </li></ul>Phase- locked- loop using VCO could exhibit chaotic signal. Sandia report, March 2004
  5. 5. VCO splitter  d mixer   Bias at operating point H ( s ) low pass filter gain delay Experimental setup
  6. 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. 7. v VCO  d Mixer Splitter delay Nonlinear function is created using delay-line frequency discriminator output
  8. 8. VCO Splitter  d Mixer bidirectional coupler combiner
  9. 9. VCO splitter  d mixer   Bias at operating point H ( s ) low pass filter gain delay Experimental setup
  10. 10. L=5  H C=1nF  u =0.1  s/unit; <ul><li>= 1.2  s </li></ul><ul><li>f cutoff ~ 3 MHz </li></ul>Loop feedback delay  is built in with transmission line design L/N L/N L/N C/2N C/2N C/2N C/2N C/2N C/2N N units
  11. 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
  12. 12.  =1.6  =2.2  =6.5 Experiment Simulation
  13. 13. Phase portrait of system plotting phase of envelope signal versus its derivative can tell us about dynamics of system  =1.6  =2.2  =6.5
  14. 14. Simulation Experiment Bifurcation diagram of system Vtune [V] Vtune [V] -2 -1 2 1 0 -2 -1 2 1 0 1 2 3 4 6 5 7 
  15. 15. Vtune [V] Vtune [V] increasing  decreasing  Historesis effect 1 2 3 4 6 5 7  -2 -1 2 1 0 -2 -1 2 1 0
  16. 16. Vtune [V] Maximum Lyapunov exponent -2 -1 2 1 0 1 2 3 4 6 5 7  -0.2 0.4 0.2 -0.1 0.1 0 0.3 0.5
  17. 17. Synchronization of coupled microwave oscillators
  18. 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. 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
  20. 20. <ul><li>Phase synchronization (PS) is achieved when two RF signals has locking of phases. </li></ul><ul><li>Envelope Synchronization (ES) happens when two tuning voltage signals synchronized while two microwave signals can stay uncorrelated </li></ul>VCO Tuning signal RF signal RF signal
  21. 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
  22. 22. VCO Tuning signal RF signal  =1.2 and  =0.1
  23. 23. t (  s) 0 100 50 200 250 150 0 100 200
  24. 24. VCO Tuning signal RF signal  =2.1 and  =0.1
  25. 25. 0 3000 6000 0 100 50 200 250 150 t (  s)
  26. 26. Conclusion <ul><li>We designed and modeled a nonlinear microwave circuit which can exhibit chaotic signal. The circuit is very applicable due to range of operating frequency, small size and reasonable price. </li></ul><ul><li>We also coupled two microwave systems and achieved envelope synchronization and some promising data indicated phase synchronization between RF signals. </li></ul><ul><li>To avoid delay loop in coupling part, we will try unidirectional coupling case and increase coupling strength as well. </li></ul><ul><li>Improve modeling of coupled systems. </li></ul>

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