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Applied Physics Letters

Input impedance of an amplifier based on a dc superconducting quantum interference device

Claude Hilbert, John L. Clarke

Published Oct 1, 1984• 15 citations
Publisher

Abstract

The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.

DOI
10.1063/1.95370

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IEEE Transactions on Applied Superconductivity•Jun 1, 1999•1 citation
The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.
Computer models are presented for a microstrip amplifier based on a dc superconducting quantum interference device (SQUID). In this device, the signal is applied between one end of the spiral input coil and the square washer on which it is deposited. The amplifier exhibits substantial power gain when the signal frequency is such that a half wavelength is approximately equal to the length of the microstrip formed by the coil and the groundplane. The resonant frequency is lowered significantly by the inductance of the square washer transformed into the input coil; this reduction is consistent with predictions of a simple model and with analog simulations. With the washer grounded, the gain of the amplifier peaks at a frequency that is lowered from the unloaded resonant frequency by the damping of the resistance associated with the source. The position and magnitude of the peak are in good agreement with both a lumped circuit model and with a model representing the microstrip as a transmission line. When the counter electrode of the SQUID is grounded and the washer floats, feedback from the output of the SQUID to the input via the capacitance of the microstrip plays a major role and is well described by simulations using the transmission line model. Measurements of the input impedance of the microstrip amplifier show that the return loss can be positive or negative, depending on the sign of the feedback and whether the frequency is above or below the resonant frequency. This behavior is in good accord with simulations.
The coupling effects of a commercial dc superconducting quantum interference device (SQUID) to an electrical LC resonator which operates at audio frequencies (≈1 kHz) with quality factors Q≈106 are presented. The variations of the resonance frequency of the resonator as functions of the flux applied to the SQUID are due to the SQUID dynamic inductance in good agreement with the predictions of a model. The variations of the quality factor point to a feedback mechanism between the output of the SQUID and the input circuit.
We optimized the design and operation of a low-Tc direct current superconducting quantum interference device (dc SQUID) with an integrated coupling coil of 1.5 muH inductance taking into account typical effects observed for similar devices. Numerical simulations were performed on a model including the capacitance of the Josephson junctions, thermal noise of the integrated shunt- and damping- resistors as well as a complex frequency dependent impedance of the SQUID loop originating from the integrated coils. The experimentally and numerically determined characteristics and sensitivity are in good agreement. A minimum additional coupled energy resolution of 700 (h/2p) and 250 (h/2p) was measured at a temperature of 4.2 K and 1.5 K, respectively.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.
The power gain of a dc superconducting quantum interference device (SQUID) amplifier, with tuned input and output circuits, is computed as a function of the current and magnetic biases. A gain of 20300 is found at 1.5 GHz and 3470 at 3.0 GHz, implying a frequency dependence to the gain of approximately ω−2. The gain, as derived from the resistively shunted junction model, is compared with the gain of a simplified model based on the dc magnetic response Vφ. This comparison shows that the Vφ description of the SQUID can lead to large errors.
The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.