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Basics of Microwave Measurements Steven Anlage http://www.cnam.umd.edu/anlage/AnlageMicrowaveMeasurements.htm 1 Electrical Signals at Low and High Frequencies 2 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 V The wave equations 3 Transmission Lines Take the ratio of the voltage and current waves at any given point in the transmission line: Wave Speed = Z0 The characteristic impedance Z0 of the T-line Reflections from a terminated transmission line Z0 ZL Reflection coefficient Vleft Vright b Z L Z0 a Z L Z0 Open Circuit ZL = ∞, = 1 ei0 Some interesting special cases: Short Circuit ZL = 0, = 1 eip Perfect Load ZL = Z0, = 0 ei? These are used in error correction measurements to characterize non-ideal T-lines 4 Transmission Lines and Their Characteristic Impedances 5 Transmission Lines, continued The power absorbed in a termination is: Model of a realistic transmission line including loss Shunt Conductance Traveling Wave solutions 6 with How Much Power Reaches the Load? 7 The Need for Care with SMA Connectors 8 Microwave Connectors “Compatible” with Found in 60 2.4 mm Corbino expt. 2.4 mm 60 V PNA K (2.92 mm) 40 3.5 mm*, SMA* BlueFors fridge 3.5 mm 26.5 K, SMA* PNA SMA 18 or 25 3.5 mm, K All over… Connector Name Bandwidth (GHz) 1 mm 110 V (1.85 mm) * Means “mates with damage” See https://www.microwaves101.com/encyclopedias/microwave-connectors#overview 9 Waveguides H Rectangular metallic waveguide 10 Network Analysis Assumes linearity! 11 N-Port Description of an Arbitrary Enclosure N Ports V1 V1 V1 , I1 Voltages and Currents, N – Port Incoming and Outgoing Waves System VN V N S matrix V 1 V 1 V 2 V 2 [S ] V N V N 12 VN , IN Z matrix V1 I1 V I 2 2 [ ] VN I N S ( Z Z 0 ) 1 ( Z Z 0 ) Z ( ), S ( ) Complicated Functions of frequency Detail Specific (Non-Universal) Linear vs. Nonlinear Behavior 13 Network vs. Spectrum Analysis 14 Resonator Measurements Traditional Electrodynamics Measurements input ~ microwave wavelength l output Microwave Resonator Cavity Perturbation B sample Hrf Sample transmission T1 df f0 15 T2 df’ f0’ rf currents Quality Factor Q = Estored/Edissip. Q = f0 / df inhomogeneities These measurements average the properties over the entire sample frequency Df = f0’ – f0 D(Stored Energy) D(1/2Q) D(Dissipated Energy) Electric and Magnetic Perturbations Electric Field Pert. E Magnetic Field Pert. E Sample e1 - i e2 s, r/t Rs + i Xs Sample B B m1 + i m2 s, r/t Rs + i Xs Varying capacitance (e1) and inductance (m1) change the stored energy and resonant frequency Df Varying sample losses (r/t, tand e2/e1, m2) change the quality factor (Q) of the microscope Df = f0’ – f0 D(Stored Energy) D(1/2Q) D(Dissipated Energy) 16 The Variable-Spacing Parallel Plate Resonator Vary s s: contact – ~ 100 mm in steps of 10 nm to 1 mm Brf Principle of Operation: Measure the resonant frequency, f0, 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 l and Rs. 17 The measurements are performed at a fixed temperature In our experiments L, w ~ 1 cm The VSPPR Experiment Films held and aligned by two sets of perpendicular sapphire pins Dielectric spacer thickness (s) measured with capacitance meter 18 VSPPR: Theory of Operation Superconducting samples Resonant Frequency f 0,SC Quality Factor f 0, PC 1 1 2leff / s 1 s SC Trans. line resonator f 0, PC fringe effect c 2L e r leff l coth( d / l ) 1 2 0.423 ln sf m e pL 0 0 1 1 1 1 QSC Q Qd Qrad * Reff f SC 1 tan d s * * QSC pm0 f ( s 2leff ) f Reff * f 0 , SC * Reff f 2 f* is a reference frequency 1/ L Assumes: 2 identical and uniform films, local electrodynamics, Rs(f) ~ f2 19 V. V. Talanov, et al., Rev. Sci. Instrum. 71, 2136 (2000) US Patent # 6,366,096 High-Tc Superconducting Thin Films at 77 K 1200 VSPPR, T=77 K 12.4 LN2 dielectric spacer 1000 12.2 800 12.0 600 11.8 Q-factor Resonant Frequency (GHz) 750nm-YBCO/LAO 400 11.6 200 11.4 0 0 20 40 60 80 100 Dielectric Spacer Thickness ( m m) l fit: 257 ± 25 nm Rs fit: 200 ± 20 m @ f* = 10 GHz 20 Mutual Inductance Measurements (l1+l2)/2 = 300 ± 15 nm L = 9.98 mm, w = 9.01 mm, film thickness d = 760 ± 30 nm, Tc = 92.4 K