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Journal of Physics Conference Series

Dc SQUID array with nonlinear inductance

Victor K. Kornev, Igor I. Soloviev, N. V. Klenov, Oleg A. Mukhanov

Published Jun 1, 2010• 1 citation
Publisher

Abstract

We show that voltage response of dc SQUID can be substantially linearized by the introduction of a nonlinear inductance. The inductance tuning allows us to achieve the response linearity as high as 120 dB. Such a nonlinear inductance can be easily formed using Josephson junction inductance. To obtain high dynamic range commensurate to the high response linearity, one can use series array of the nonlinear inductance dc SQUIDs.

DOI
10.1088/1742-6596/234/4/042034

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We show that voltage response of dc SQUID can be substantially linearized by the introduction of a nonlinear inductance. The inductance tuning allows us to achieve the response linearity as high as 120 dB. Such a nonlinear inductance can be easily formed using Josephson junction inductance. To obtain high dynamic range commensurate to the high response linearity, one can use series array of the nonlinear inductance dc SQUIDs.
We show that the voltage response of a dc SQUID can be substantially linearized by the introduction of a nonlinear inductance. The inductance tuning allows us to achieve response linearity close to 120 dB. Such a nonlinear inductance can be easily formed using Josephson junction inductance. The additional junction and main inductance form a single-junction SQUID and hence the device can be called a bi-SQUID. To obtain high dynamic range commensurate to the high response linearity, one can use a serial array of nonlinear inductance dc SQUIDs. Experimental studies of a single bi-SQUID and serial arrays of bi-SQUIDs are reported and discussed.
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.
We performed an in-depth numerical analysis of high-inductance bi-SQUIDs with normalized inductance of its one junction loop l ≫ 1. This is desired for better coupling with the external signals and for the high-temperature superconductor implementations. Typically the high linearity (up to 90 dB) can be achieved in bi-SQUIDs at l ≫ 1 at which its flux-to-voltage characteristic has a distinct triangular shape. We showed that the high linearity can be also achieved at l > 1, when the bi-SQUID has a hysteretic response. The critical current of the third Josephson junction is to be of the same order as the one of the other two Josephson junctions, and the inductance lDC of the second (two junction) loop is allowed to be as high as about one-fourth in the presence of the high linearity.
Abstract A superconducting quantum interference device with differential output or ‘DSQUID’ was previously proposed for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of the DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that spur-free dynamic range of the DSQUID magnetic flux-to-voltage transfer function is higher than 100 dB while the total harmonic distortion of a signal is less than 10 −3 % with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, 2Φ a = Φ 0 /8. Analysis of the DSQUID voltage response stability to a variation of circuit parameters shows that DSQUID implementation allows for highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.
We report on the investigation of the effects of the nonlinear inductance of huge Josephson junction arrays on high-quality RF circuits. The inductance of a single junction is far too small for use in many RF applications; however, Josephson junction stacks and especially intrinsic Josephson junctions in crystalline-layered superconductors open new opportunities. The stack inductance can be altered by changing a DC Josephson current either using an external bias current or an external magnetic field applied to a closed superconducting loop containing two stacks connected in parallel. Using stacks of Josephson junctions in the LC resonators, a tunable 4-pole, 15 MHz band-pass filter with a centre frequency at 1.1 GHz was designed. The filter was simulated in the time domain and the response was converted to the frequency domain. It was found that using an input power level of −62 dBm, corresponding to 0.5% of the junctions' critical current, a linear approximation for the stack nonlinear inductance can be used. By changing the applied magnetic field, a tuning range of 20% was demonstrated with a tuning speed of 2 µs or better. An estimate of the losses is also given. In addition, power handling up to −26 dBm is reported using increasing circuit complexity.
A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.