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Register a new userRealization of Biquadratic Impedance as Five-Element Bridge Networks
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This report includes the original manuscript and the supplementary material of Realization of Biquadratic Impedance as Five-Element Bridge Networks.
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This report presents some supplementary material to the paper entitled Passive controller realization of a biquadratic impedance with double poles and zeros as a seven-element Series-parallel network for effective mechanical control [1].
This is a supplementary material to Realization of three-port spring networks with inerter for effective mechanical control [1], which provides the detailed proofs of some results. For more background information, refer to [2]-[32] and references therein.
Integrating nano-scale objects, such as single molecules or carbon nanotubes, into impedance transformers and performing radio-frequency measurements allows for high time-resolution transport measurements with improved signal-to-noise ratios. The realization of such transformers implemented with superconducting transmission lines for the 2-10 GHz frequency range is presented here. Controlled electromigration of an integrated gold break junction is used to characterize a 6 GHz impedance matching device. The real part of the RF impedance of the break junction extracted from microwave reflectometry at a maximum bandwidth of 45 MHz of the matching circuit is in good agreement with the measured direct current resistance.
We present a resistance bridge which uses a SQUID to measure the shot noise in low impedance samples. The experimental requirements are high DC bias currents (typically 10mA) together with high AC sensitivity (pA/VHz). This system is used to investigate the shot noise in Superconductor/Normal/Superconductor junctions where Andreev reflection enhanced shot noise is expected. Because our setup has an intrinsic noise much smaller than the thermal noise of the resistance bridge at 4.2K, reliable results can be obtained on impedances out of the range of classical measurement schemes.
We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4~aF$/sqrt{textrm{Hz}}$ at 77 K on a comb-drive actuator, while maintaining a small excitation amplitude of 15~$k_text{B} T/e$. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60~mK with a probe signal of 12.8~$k_text{B} T/e$.
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