1. 1 Basics of Microwave Measurements Steven Anlage http://www.cnam.umd.edu/anlage/AnlageMicrowaveMeasurements.htm

2. 2 Electrical Signals at Low and High Frequencies

3. 3 Transmission Lines Transmission lines carry microwave signals from one point to another They are important because the wavelength is much smaller than the length of typical T-lines used in the lab You have to look at them as distributed circuits, rather than lumped circuits The wave equations V

4. 4 Transmission Lines Wave Speed Take the ratio of the voltage and current waves at any given point in the transmission line: = Z 0 The characteristic impedance Z 0 of the T-line Reflections from a terminated transmission line ZLZL Z0Z0 Reflection coefficient Some interesting special cases: Open Circuit Z L = ∞,  = 1 e i0 Short Circuit Z L = 0,  = 1 e i  Perfect Load Z L = Z 0,  = 0 e i  These are used in error correction measurements to characterize non-ideal T-lines

5. 5 Transmission Lines and Their Characteristic Impedances

6. 6 The power absorbed in a termination is: Transmission Lines, continued Model of a realistic transmission line including loss Traveling Wave solutions with Shunt Conductance

7. 7 How Much Power Reaches the Load?

8. 8 Waveguides Rectangular metallic waveguide H

9. 9 Network Analysis Assumes linearity!

10. 10 N-Port Description of an Arbitrary Enclosure N – Port System N Ports  Voltages and Currents,  Incoming and Outgoing Waves Z matrixS matrix V 1, I 1 V N, I N  Complicated Functions of frequency  Detail Specific (Non-Universal)

11. 11 Linear vs. Nonlinear Behavior

12. 12 Network vs. Spectrum Analysis

13. 13 Resonator Measurements Sample Microwave Resonator Cavity Perturbation input output Traditional Electrodynamics Measurements H rf rf currents inhomogeneities ~ microwave wavelength These measurements average the properties over the entire sample frequency transmission f0f0 ff f0’f0’  f’  f = f 0 ’ – f 0   (Stored Energy)  (1/2Q)   (Dissipated Energy) Quality Factor Q = E stored /E dissip. Q = f 0 /  f T1T1 T2T2 B sample

14. 14 Electric and Magnetic Perturbations Sample E  1 - i  2  /t R s + i X s Varying capacitance (  1 ) and inductance (  1 ) change the stored energy and resonant frequency  f  f = f 0 ’ – f 0   (Stored Energy)  (1/2Q)   (Dissipated Energy) Varying sample losses (  /t, tan    ,  2 ) change the quality factor (Q) of the microscope Magnetic Field Pert.  1 + i  2  t R s + i X s Sample E Electric Field Pert. BB

15. 15 The Variable-Spacing Parallel Plate Resonator Principle of Operation: Measure the resonant frequency, f 0, and the quality factor, Q, of the VSPPR versus the continuously variable thickness of the dielectric spacer (s), and to fit them to theoretical forms in order to extract the absolute values of and R s. Vary s s: contact – ~ 100  m in steps of 10 nm to 1  m The measurements are performed at a fixed temperature In our experiments L, w ~ 1 cm

16. 16 The VSPPR Experiment Films held and aligned by two sets of perpendicular sapphire pins Dielectric spacer thickness (s) measured with capacitance meter

17. 17 VSPPR: Theory of Operation V. V. Talanov, et al., Rev. Sci. Instrum. 71, 2136 (2000) US Patent # 6,366,096 Superconducting samples Quality Factor fringe effect SC Trans. line resonator Resonant Frequency Assumes: 2 identical and uniform films, local electrodynamics, R s (f) ~ f 2 f* is a reference frequency

18. 18 High-T c Superconducting Thin Films at 77 K fit: 257 ± 25 nm R s fit: 200 ± 20  @ f* = 10 GHz L = 9.98 mm, w = 9.01 mm, film thickness d = 760 ± 30 nm, T c = 92.4 K Mutual Inductance Measurements ( 1 + 2 )/2 = 300 ± 15 nm