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Distributed Nonlinearities in Microwave Superconducting Devices

Join Professor Dr. Fardmanesh's seminar on the principles of applied superconductivity, focusing on distributed nonlinearities in microwave superconducting devices. This session covers high-temperature superconductive devices, the analysis of nonlinearities, and their implications in superconductor characterization and harmonic balance simulations. We will explore analytical and phenomenological models, nonlinear transmission lines, and the effects of intrinsic nonlinearities on device performance. This seminar is a must for anyone looking to deepen their understanding of advanced superconducting technologies.

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Distributed Nonlinearities in Microwave Superconducting Devices

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  1. Seminar for the Course: Principles of Applied Superconductivity Professor: Dr. Fardmanesh June 2010 Distributed Nonlinearities in Microwave Superconducting Devices Main Reference: Analysis and Simulation of the Effects of Distributed Nonlinearities in Microwave Superconducting Devices; C. Collado, J. Mateu, and J. M. O’Callaghan; IEEE Transactions on Applied Superconductivity, March 2005 M. M. Assefzadeh assefzadeh@ee.sharif.edu

  2. Outline • Introduction • High Tc Superconductive Devices • Nonlinearity Drawbacks • Nonlinearities in Superconductors • Analytical and Phenomenological • Superconductor Films • IMD and Third-Harmonic Generation in SDevices • Nonlinear Transmission Line • Line Resonators • Superconductor Characterization with IMD Measurements • Harmonic Balance for Simulation of Superconducting Devices • Conclusion

  3. Introduction • Motivations to use SC (esp. HTS) in electronics: • Low Surface Resistance • Reaching to High Currents in Devices • Reduced Power Dissipation and Delay • Unique Quantum Accuracy • Low Noise from Cryogenic Operation Taken from HTS Microwave Devices Lecture, Colorado University

  4. Introduction • HTS Microwave Devices such as: • Planar Filters • Resonators • Microstrip and Stripline Transmission lines • Benefits of SC Filters: • Low volume • Reduced insertion losses • High selectivity • Drawbacksof High Powers: Nonlinearities • Recognize Them • Simulate Them • Predict Them! Large-Area Double-Sided YBCO Thin Films Taken from The Web Page of Semiconductor Physics Group of Leipzig University Taken from HTS Microwave Devices Colorado; Northrop Grumman

  5. Nonlinearities in Superconductors • Intrinsic Concept of Nonlinearity in Superconductors • Assumptions • Microwave Frequencies (Low Surface Resistances) • Two Fluids Model (Nonlinearly) • Studying Intrinsic Nonlinearity • 1. Nonlinear Conductance and Penetration Depth • Intrinsically: Less Cooper Pairs when we have applied current. • Phenomenological: Experimental works claiming the current dependent penetration depth • 2. Dependence of Electric Field on Surface Current

  6. Nonlinear Conductance and Penetration Depth • Analytical Approach • Basis: • Nonlinearity characterization function • Taylor expansion: • Approaching to: • Phenomenological Approach • Measuring current dependent penetration depth and after fitting Data: Small Signal values (J~0): Linear Conductance Linear Penetration Depth No Dependence On J Large Current Magnitudes: Increased note that this is the resistive conductance in the two fluid model Increased

  7. Superconducting FilmsFrom Nonlinear Electric Field to Nonlinear Surface Impedance • Time Domain Equation Between E and Js: assuming quasi exponential decay of the electromagnetic fields: • Nonlinear inductive equation: • Assuming E in two linear and NL components: • Deriving nonlinear parts of surface resistance and inductance: Talking about JS Talking about Jo

  8. Nonlinear Distributed Parameters in Transmission Lines • Intrinsic Nonlinearities in SC affecting Parameters in Transmission Lines: • These nonlinearities follow the same nonlinear rules as the nonlinearity function f(T,J). • Quadratic Nonlinearities: • Modulus Nonlinearities: Nonlinear equivalent circuit of a superconducting transmission line segment with length dz; Taken from the main reference.

  9. IMD & Third Harmonic GenerationDerivation from intrinsic nonlinearities • Definitions: • Third Harmonic: An effect of nonlinear devices creating freq. of 3f. • IMD: The unwanted amplitude modulation of signals containing different frequencies. • In our work, we consider the products f12 = (2f1 – f2) & f3 = 3f1for a signal with two frequencies f1& f2. The spectrum of an RF signal containing two fundamental frequencies From Wikipedia

  10. IMD and 3rd Harmonic Generation in Nonlinear Transmission Lines • Matched Transmission Line • Experimental use of Transmission Lines: • 1) Quadratic or modulus nonlinearity? • Spurious powers against sources powers slope: 3:1 and 2:1 for Quadratic and Modulus • 2) Resistive or inductive nonlinearities? From The Main Reference

  11. IMD and 3rd Harmonic Generation in Nonlinear Resonators • The Same Theory Analysis Applies for • Line Resonators • Disk Resonators and Cavities • Hairpin Resonator, measurements fit theory (dots are measured) • Quantitative results: Taken From The Main Reference In the Order of Jc

  12. Results of Harmonic Balance Simulation • Harmonic Balance: A high performance method to simulate nonlinear circuits • Linear part in Freq. domain • NL part in Time domain • Current Distribution Along a SC Matched Line • Simulation (Dots) Versus Theory Taken From the Main Reference

  13. Results of Harmonic Balance Simulation • Matched SC Line: Powers Delivered to the output • Dashed lines from the theory, solid lines simulated • Inset chart: The error between calculations and simulations 10% Error for Input Power of 45dBm (=33W); The Effect of Higher Order Nonlinearities. Taken From the Main Reference At the fundamental frequency At the IMD 12 frequency

  14. Conclusion • Nonlinearities due to high powers • Theory and phenomenological approaches • SC thin film devices: Theoretical solutions • Resulting intermodulation distortion and 3rd harmonic generation • Simulations reveal the effects of extra high powers; Higher order nonlinearities

  15. References [1] Carlos Collado, J. M. (MARCH 2005). Analysis and Simulation of the Effects of Distributed Nonlinearities in Microwave Superconducting Devices. IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY , 26-39. [2] T. Dahm and D. Scalapino, “Theory of intermodulation in superconducting microstrip resonator,” J. Appl. Phys. , vol. 81, no. 4, pp. 2002–2002, 1997. [3] T. Dahm, D. Scalapino, and B. Willemsen, “Phenomenological theory of intermodulation in HTS resonators and filters,” J. Supercond., vol. 12, pp. 339–339, 1999. [4] B. A. Willemsen, T. Dahm, and D. J. Scalapino, “Microwave intermodulation in thin film high-Tc superconducting microstrip hairpin resonators: Experiment and theory,” Appl. Phys. Lett., vol. 71, no. 29, pp. 3898–3898, 1997. [5] HTS Materials and Devices. (n.d.). Retrieved from Colorado; Northrop Grumman: http://boulder.research.yale.edu/Boulder-2000/transparencies/talvacchio-lecture1/colorado-rf.pdf Thank You For Your Attention

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