Patrick Longhini

DC and RF Measurements of Serial Bi-SQUID Arrays

SQUID arrays are promising candidates for low-profile antennas and low-noise amplifier applications. We present the integrated circuit designs and results of dc and radio frequency measurements of wideband serial arrays based on the integration of linear bi-SQUID cells forming a superconducting quantum interference filter (bi-SQUID SQIF). Various configurations of serial array designs are described. The measured linearity, power gain, and noise temperature are analyzed and compared. The experimental results are matched to results of mathematical modeling. A serial bi-SQUID SQIF arrays are integrated into a coplanar waveguide, and symmetrically grounded to corresponding sides of the coplanar waveguide. The radio frequency output comes out from the central common line, which is also used for dc biasing, and forms a symmetrical balanced output. The signal and dc flux biasing line is designed as coplanar lines passed in parallel over each bi-SQUID cell in a bidirectional fashion concentrating magnetic flux inside of each cell. Serial bi-SQUID SQIF arrays are fabricated on 5 mm × 5 mm chips using a standard HYPRES niobium 4.5 kA/cm2 fabrication process.

Development of 2-D Bi-SQUID Arrays With High Linearity

We develop a two-dimensional (2-D) superconducting quantum interference filter (SQIF) array based on the recently introduced high-linearity tri-junction bi-SQUIDs (superconducting quantum interference device). Our bi-SQUID SQIF array design is based on a tight integration of individual bi-SQUID cells sharing inductances with adjacent cells. We provide extensive computer simulations, analysis, and experimental measurements, in which we explore the phase dynamics and linearity of the array voltage response. The nonuniformity in inductances of the bi-SQUIDs produces a pronounced zero-field single antipeak in the voltage response. The antipeak linearity and size can be optimized by varying the critical current of the additional junction of each bi-SQUID. The layout implementation of the tight 2-D array integration leads to a distinct geometrical diamond shape formed by the merged dual bi-SQUID cells. Different-sized 2-D arrays are fabricated using the standard HYPRES niobium 4.5 kA/cm2 fabrication process. The measured linearity, power gain, and noise properties will be analyzed for different array sizes and the results will be compared with circuit simulations. We will discuss a design approach for the electrically small magnetic field antenna and low-noise amplifiers with high bandwidth based on these 2-D bi-SQUID SQIF arrays. The results from this work will be used to design chips densely and completely covered in bi-SQUIDs that have optimized parameters such as linearity and power gain.

Exploiting Nonlinear Dynamics in Novel Measurement Strategies and Devices: From Theory to Experiments and Applications

This paper is focused on the exploitation of intrinsic nonlinear dynamics toward novel measurement systems and readout methodologies. In particular, sensors that can be represented as nonlinear dynamical systems and are often reducible to systems described by a static nonlinearity are considered; the nonlinear behavior therefore reduces to the dynamics of a system characterized by two or more (meta)stable equilibrium states (or attractors) separated by energetic thresholds to be overcome to transition from one attractor to the other. The presence of a weak unknown target signal is assessed via the monitoring of the “residence times” in the attractors. This operational scenario that is based on the monitoring of suitable “events” avoids an “amplitude-based” readout and provides a very simple and sensitive readout-processing scheme. Many noise effects are also mitigated by the intrinsic decoupling between the amplitude domain of the input signal and the event or time domain of the output signal. We present here the general transduction methodology for this class of “residence-times difference” sensors, together with the experimental results obtained from the working versions of these sensors (in particular, a simple fluxgate magnetometer). We then introduce some novel dynamical behavior that occurs when the active nonlinear (in this case, bistable) elements are coupled using well-crafted coupling topologies. Sensors based on these coupling schemes provide several advantages over their single-element counterparts. We discuss the dynamics of the coupled-element device, summarizing recent theoretical and experimental results. Finally, we describe the construction and performance of working devices (magnetic- and electric-field sensors) based on these concepts.

Voltage response of non-uniform arrays of bi-superconductive quantum interference devices

Multi-loop arrays of Josephson junctions (JJs) with non-uniform area distributions, which are known as superconducting quantum interference filters (SQIFs), are the most highly sensitive sensors of changes in applied magnetic field as well as the absolute magnitude of magnetic fields. The non-uniformity of the loop sizes allows the array to produce a unique collective voltage response that has a pronounced single peak with a large voltage swing around zero magnetic field. To obtain high linear dynamic range, which is critical for a wide variety of applications, the linearity of the slope of the anti-peak response must be improved. We propose a novel scheme for enhancing linearity—a new configuration combining the SQIF array concept with the recently introduced bi-superconductive quantum interference device (SQUID) configuration, in which each individual SQUID loop is made up of three JJs as opposed to using two JJs per loop in standard dc SQUIDs. We show, computationally, that the additional junction offe...

Gluing bifurcations in coupled spin torque nano-oscillators

Over the past few years, it has been shown, through theory and experiments, that the AC current produced by spin torque nano-oscillators (STNO), coupled in an array, can lead to feedback between the STNOs causing them to synchronize and that, collectively, the microwave power output of the array is significantly larger than that of an individual valve. Other works have pointed, however, to the difficulty in achieving synchronization. In particular, Persson et al. [J. Appl. Phys. 101, 09A503 (2007)] shows that the region of parameter space where the synchronization state exists for even a small array with two STNOs is rather small. In this work, we explore in more detail the nature of the bifurcations that lead into and out of the synchronization state for the two-array case. The bifurcation analysis shows bistability between in-phase and out-of-phase limit cycle oscillations. In fact, there are two distinct pairs of such cycles. But as the input current increases, the limit cycles may increase their ampli...

A drive-free vibratory gyroscope

Computational and analytical works have shown that certain coupling schemes can lead to significant enhancements in sensitivity, accuracy, and lower costs for a wide range of sensor devices whose output and performance depends directly on the ability of individual units to generate stable limit cycle oscillations. Vibratory gyroscopes are very good candidates for this new paradigm as their accuracy and sensitivity are directly dependent on the ability of a driving signal to produce and maintain oscillations with stable amplitude, phase, and frequency. To achieve higher accuracy, we show proof of concept of a novel scheme: a drive-free coupled gyroscope system in which the coupling alone can lead to self-regulated limit cycle oscillations in the drive- and sense-axes with stable constant amplitude and phase-locking.

A Bistable Microelectronic Circuit for Sensing Extremely Low Electric Field

Bistable systems are prevalently found in many sensor systems. Recently, we have explored unidirectionally coupled overdamped bistable systems that admit self-sustained oscillations when the coupling parameter is swept through the critical points of bifurcations. Complex behaviors emerge, in addition, from these relatively simple coupled systems when an external signal ac or dc is applied uniformly to all the elements in the array. In particular, we have demonstrated this emergent behavior for a coupled system comprised of mean-field hysteretic elements describing a single-domain ferromagnetic sample. The results are being used to develop extremely sensitive magnetic sensors capable of resolving field changes as low as 150 pT by observing the changes in the oscillation characteristics of the coupled sensors. In this paper, we explore the underlying dynamics of a coupled bistable system realized by coupling microelectronic circuits, which belong to the same class of dynamics as the aforementioned ferromagnetic system, with the nonlinear features and coupling terms modeled by hyperbolic tangent nonlinearities; these nonlinearities stem from the operational transconductance amplifiers used in constructing the microcircuits. The emergent behavior is being applied to develop an extremely sensitive electric-field sensor.

Dynamics, Bifurcations and Normal Forms in Arrays of Magnetostrictive Energy Harvesters with All-to-All Coupling

Modeling and bifurcation analysis of an energy harvesting system composed of coupled resonators using the Galfenol-based magnetostrictive material are presented. The analysis in this work should be broad enough to be applicable to a large class of vibratory-based energy harvesting systems since various types of vibratory harvesters share the same normal forms, e.g. magnetostrictive and piezoelectric materials. A combined model of the mechanical and electrical domains of a single energy harvester is discussed first. Building on this model, the governing equations of the coupled system are derived, leading to a system of differential equations with an all-to-all coupling between the resonators. A bifurcation analysis of the system equations reveals different patterns of collective oscillations. Among the many different patterns, a synchronous state exists and it is stable over a broad region of parameter space. This pattern has the potential to yield significant increases in power output and it will be used as a starting point to guide future experimental work. A Hamiltonian approach is employed to study analytically the nature of the bifurcations and to calculate an expression for the onset of synchronization valid for any number of harvesters.

COLLECTIVE BEHAVIOR OF A COUPLED GYROSCOPE SYSTEM WITH COUPLING ALONG THE DRIVING- AND SENSING-MODES

A critical component of many Inertial Navigation Systems (INS) is the gyroscope — a device used for detecting rotation rates and orientation. Gyroscopes are subject to material imperfections and ma...

Modeling the effects of fabrication spreads and noise on series coupled arrays of bi-SQUIDs

We explore the effects of fabrication spreads and noise in a series array of DC bi-SQUIDs. The investigation is performed through numerical simulations of phase equations derived from circuit diagrams. It has been previously determined that the series coupled bi-SQUID arrays dynamic range increases with the number of bi-SQUIDs in the array and that non-uniform bi-SQUID loops sizes produces a zero-field single anti-peak in the voltage response. Results show the effects of industry standard fabrication spreads to the anti-peak feature are minimal, while the effects to the voltage response of arrays of identical bi-SQUIDs can be drastic. The findings presented here will be used to support the design of an electrically small magnetic field antenna and low-noise amplifier with high bandwidth.