Distributed Nonlinearities in Microwave Superconducting Devices

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