Coupled Oscillator Arrays Research Articles

Dynamics of high-power coupled nonlinear oscillator arrays for electronic beam steering technique: case of the triode based van der Pol oscillator

This paper presents the dynamics of coupled nonlinear oscillator arrays (CNOAs) as phase shifter for electronic beam steering technique. The proposed phase shifter uses oscillators of van der Pol type with a fifth-order nonlinear resistance and is built on the two architectures based injection-locked oscillator array (ILOAs) and coupled oscillator arrays (COAs). The dynamics equations of the phase shifter are proposed in the frequency and time domain. With the help of mathematical tools such as bifurcation diagrams, maximum Lyapunov exponent and Hilbert transform, important cartography of different oscillating states is deduced over large range of system parameters. Different behavior of the CNOAs including chaos, 2D-torus, multistability, locked and unlocked states are depicted. The phase shift between output voltages of each pair of coupled oscillators is presented for both architectures. A detailed analysis of locked states shows that the required phase shift is synthesized by slightly varying the frequency of the injected signal, or simply by detuning the free-running frequencies of the edge oscillators in equal but opposite directions. The proposed circuit of the phased shifter is built using the original van der Pol oscillator based on a vacuum triode. The maximal phase shift reaches 63° and 75° respectively for ILOAs and COAs. With the presence of triode in the circuit, the output voltage of each oscillating element in the array reaches 100V around 60KHz and is boosted by increasing the value of the triode bias potential to more than 420V. This, therefore, increases the total power dissipation of a single oscillator in the array to more than 47dB ( 50.12W ). This circuit is a candidate for high-power electronics beam steering at ultrasonic frequency.

Prediction of chimera in coupled map networks by means of deep learning

Chimera states are Spatio-temporal patterns in coupled oscillator arrays, in which incoherent domains coexist with coherent ones. To characterize chimeras, however, is a nontrivial problem since it is difficult to distinguish between coherent domains and incoherent domains. A useful tool for this task is machine learning, in particular deep learning techniques like reservoir computing and multilayer perceptrons. In this work we use these quantifiers in order to identify chimera states in logistic map lattices with non-local coupling. We compare our results from machine learning techniques with more conventional characterizations, such as Lyapunov exponents and a local order parameter.

A 0.47-THz Ring Scalable Coupled Oscillator–Radiator Array With Miniature Patch Antennas

This article integrates several techniques for large-scale, high power-efficiency, and area-efficiency terahertz (THz) radiators. First, we present a systematic design method to synthesize a high output power harmonic oscillator at a high fundamental to maximum oscillation frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {osc}}/f_{\mathrm {max}})$ </tex-math></inline-formula> ratio by making a quantitative tradeoff between fundamental oscillation and harmonic output power. Then, a ring scalable coupled oscillator array topology is proposed for a flexible and compact layout. Patch antennas are preferred for large-scale radiator arrays, but the size is much larger than the commonly used slot antenna. Therefore, a miniature on-chip patch antenna is proposed for front-side radiation, whose compact size also helps make the design scalable in 2-D. A quartz superstrate is superimposed on the chip to improve the radiation efficiency. A 16-element ring-coupled oscillator–radiator array is designed and fabricated in a 0.8-mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> total area using a 65-nm CMOS process to verify the design methods. Maximum radiated power of −2.8 dBm is measured at 472 GHz. This design achieves an area efficiency of 0.66 mW/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the highest among THz radiator arrays using on-chip patch antennas. It is even higher than most radiator arrays using slot antennas. This design also achieves the state-of-the-art dc-to-THz efficiency and frequency tuning range of 0.12% and 4.2%, respectively. The chip can be easily configured to feed a low-cost Teflon lens. A maximum effective isotropic radiated power (EIRP) of ~30 dBm is measured with a 12-mm diameter lens. The measured directivity is 33.7 dBi. At 472 GHz, the measured phase noise is −71.3 dBc/Hz at the 1-MHz offset.

Noise influenced response movement in coupled oscillator arrays with multi-stability

In this work, the authors explore the influence of noise on the dynamics of coupled nonlinear oscillators. Numerical studies based on the Euler–Maruyama scheme and experimental studies with finite duration noise are undertaken to examine how the response can be moved from one response state to another by using noise addition to a harmonically forced system. In particular, jumps from a high amplitude state of each oscillator to a low amplitude state of each oscillator and the converse are demonstrated along with noise-influenced localizations. These events are found to occur in a region of multi-stability for the system, and the corresponding noise levels are reported. A method for recognizing how much noise is required to induce a change the system dynamics is developed by using the response basins of attraction. The findings of this work have implications for weakly coupled, nonlinear oscillator arrays and the manner in which noise can be used to influence energy localization and system dynamics in these systems.

A 482-GHz 2-D Scalable and Wideband Radiator Array

This letter reports a 2-D scalable coupled harmonic oscillator array achieving coherent spatial power combining at about 500 GHz. This design is implemented using on-chip microstrip lines and microstrip antennas by which the lossy silicon substrate is shielded and, therefore, front side radiation could be obtained. Compared with previously reported scalable array designs, this work not only achieves maximum oscillation at the fundamental frequency, but also decouples the design of oscillator core, radiation element, and coupling structure. Therefore, different parts could be separately optimized to achieve maximum radiated second harmonic power and more design diversity is possible for the antenna part. To demonstrate the design concept, a 2×2 coupled oscillator array is designed and fabricated using 65-nm CMOS process, which achieves a maximum effective isotropic radiated power (EIRP) of 2.6 dBm and radiated power of 162.2 μW (-7.9 dBm) at 482 GHz. It consumes 154-mW dc power and the dc-to-terahertz (THz) efficiency is 0.11%. This design achieves a 6.8% tuning range from 469 to 502 GHz by changing the bias voltages.

Phase-Transition Optical Activity in Chiral Metamaterials.

Optical activity from chiral metamaterials is both fundamental in electrodynamics and useful for polarization control applications. It is normally expected that due to infinitesimally small thickness, two-dimensional (2D) planar metamaterials cannot introduce large optical rotations. Here, we present a new mechanism to achieve strong optical rotation up to 90° by evoking phase transition in the 2D metamaterials through tuning coupling strength between meta-atoms. We analytically elucidate such phenomenon by developing a model of phase-transition coupled-oscillator array. And we further corroborate our ideas with both numerical simulations and experiments. Our findings would pave a new way for applying the concept of phase transition in photonics for designing novel optical devices for strong polarization controls and other novel applications.

Discrete Vortex Filaments on Arrays of Coupled Oscillators in the Nonlinear Resonant Mode

Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant external force applied at the boundary of the domain. Ranges of the parameters of the system and an external signal favorable for the formation of modulationally stable quasi-uniform energy background, which is a decisive factor for the occurrence of this phenomenon, have been qualitatively revealed.

Analysis of Stable Modes of a Scalable Coupled Oscillator Array

This brief proposes a scalable array of actively coupled oscillators based on vertex-shared expansion of multiple sub-arrays. We analytically prove that as a result of this proposed scaling, the expanded array preserves the stable operating modes of the sub-arrays. In addition, we verify the expected transient and steady-state behaviour of the scaled structure using time-domain simulation. Furthermore, we demonstrate that the proposed topology is resilience to element-to-element variation as the dimensions scale. This offers a promising solution for large scale signal distribution in phased arrays.

Full-field laser vibrometer study of dissipation in a beam with a coupled oscillator array

Coupled oscillator systems can be designed to manage the distribution of mechanical energy in vibration or acoustic systems. A specific implementation of an array composed of small damped mass-spring attachments on a primary is here referred to as a subordinate oscillator array. SOAs and their ability to absorb energy from a primary mass are of continued importance in analysis for both structural and acoustic systems. The ability to dissipate energy in a specific frequency band has many potential applications. This work will use laser Doppler vibrometry (LDV) to evaluate a beam mounted on an electromechanical shaker with and without an attached planar SOA composed of much smaller beams. This study is motivated by earlier work that indicated a high sensitivity to disorder in the form of fabrication error. The apparatus allows for the controlled introduction of various levels of disorder to quantify its effect and compare to a numerical model. We will show full-field forced response from the LDV with and without the SOA and the resulting apparent damping within the band of the SOA for various levels of disorder.

A 70-GHz LO Phase-Shifting Bidirectional Frontend Using Linear Coupled Oscillators

A 70-GHz two-element bidirectional frontend is demonstrated with linear coupled oscillators in a 90-nm silicon–germanium BiCMOS process. The transmitter has a measured peak output power of 7.2 dBm and a peak conversion gain of 14.5 dB while consuming 47 mA from a 1.8-V supply. The receiver has a peak conversion gain of 9.9 dB and a minimum noise figure of 8.6 dB with a nominal current consumption of 18 mA from a 1.5-V supply. The frontend is integrated with a two-element linear coupled oscillator array and achieves a maximum phase scanning of ±80°.

Experimental excitation and propagation of nonlinear localized oscillations in an air-levitation-type coupled oscillator array

Experimental excitation and propagation of nonlinear localized oscillations in an air-levitation-type coupled oscillator array

Various coupling configurations on the performance of two‐dimensional coupled oscillator arrays

Coupled oscillator arrays (COAs) can be used to control the phase distribution across the aperture of an array antenna in such a manner as to affect steering of the beam without the use of phase shifters. Given the various possible planar configurations of COAs, a systematic design approach is necessary. In this study, the authors present a comprehensive comparison of various configurations of planar COAs based on their sensitivity to random errors in their free running frequencies. The parameters considered are (a) the beam pointing error of the array, (b) the locking probability, (c) the side lobe level, and (d) the beam width of the radiation pattern. These results can serve as a design strategy for choosing optimal configurations of planar COAs based on the needs of each particular application.

Transients in the synchronization of asymmetrically coupled oscillator arrays

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

Analytical statistical study of beam‐pointing error in two‐dimensional coupled oscillator arrays

In this study, the authors investigate the effect of the random free-running frequency distribution of oscillators in two-dimensional (2D) coupled oscillator arrays (COAs) on the phase error of the elements, and consequently on the beam-pointing angle of the array. They derive an analytic formulation for the standard deviation of the beam-pointing error (BPE) in terms of the statistical parameters of the free-running frequencies of the elements and array configuration. The results show that in order to decrease the BPE in 2D COAs, one can use COAs with a larger size (greater number of elements) and decrease the deviation of the free-running frequency of the oscillators.

Suppressing Activity of an Array of Coupled Fitzhugh-Nagumo Oscillators

An extremely simple method for stabilizing unstable steady states in an array of coupled neuronal FitzHugh– Nagumo type oscillators is described. A two-terminal electronic feedback controller has been developed. The feedback circuit, when coupled to an array of oscillators, damps the spiking neurons, thus does away with the effect of synchronization. Both, numerical simulations and hardware experiments with the electronic circuits have been performed. The results for an array of three mean-field coupled FitzHugh–Nagumo oscillators are presented.

M707 空気浮上を用いた連成振動子列の作成および非線形局在モードの励起実験(GS10 流体関連振動・流動励起振動,修士研究発表セッション)

M707 空気浮上を用いた連成振動子列の作成および非線形局在モードの励起実験(GS10 流体関連振動・流動励起振動,修士研究発表セッション)

Comparison of Injection-Locked and Coupled Oscillator Arrays for Beamforming

Injection-locked oscillator arrays (ILOAs) and coupled oscillator arrays (COAs) are analyzed using Adler’s equation, and their performance to drive phased arrays for beam-steering is compared. The Monte Carlo simulation results indicate that COAs render smaller beam-pointing error when the locking range of oscillators is narrow (high $Q$ ), while ILOAs render smaller beam-pointing error when the locking range is wide (low $Q$ ). An ILOA with a frequency tripler connected to the oscillators’ output is designed to increase the achievable range of inter-element phase shift, and a chip is fabricated in the TSMC 0.18- $\mu$ m CMOS technology to verify the design concept, with the measured maximum phase shift around 240 $^\circ$ .

A Self-Steering Receiver Array Using Jointly Coupled Oscillators and Phased-Locked Loops

This paper presents an analog circuit scheme to steer phased-array receivers in the direction of an incoming signal. The proposed circuit technique utilizes a coupled-oscillator array along with a coupled-phased-locked loop to auto-align an N-element receive array towards the direction of the incident RF signal. A four-element receiver array is implemented in 45-nm CMOS SOI process and achieves auto-steering range of ±35° from broadside. A three-element version of the array demonstrates higher auto-steering angle covering ±70° range. The receiver also performs signal demodulation for the incident modulated RF signal, allowing high-data rate communication. A 60-Mbps 64-QAM modulated RF signal is demodulated with error-vector-magnitude (EVM) less than 4% across the steering angle range. The chip area is 3.45 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> including a pad frame with 30-mW/element power consumption. To the best of authors' knowledge, this is the first demonstration of an analog self-steering array in an integrated circuit.

A PUSH-PUSH OSCILLATOR ARRAY USING RESONATOR TYPE COUPLING CIRCUITS

A coupled oscillator array using push-push oscillators and resonator type coupling circuits is presented. In the proposed oscillator array, the coupling circuit operates at the fundamental frequency and the output signal is the 2nd harmonics. The adjacent oscillators are connected via the coupling circuits. The coupling circuit is used to synchronize the oscillators and control the phase difference of the output signals. In this study, a three elements push-push oscillator array has been designed in Ku band. The measured phase shift between the output signals of the adjacent oscillators is 511 degrees at the maximum.

ANALYSIS ON STRONGLY COUPLED OSCILLATOR ARRAYS USING MODIFIED Y-PARAMETERS APPROACH

A modifled Y -parameters approach is proposed to model the behavior of coupled oscillator arrays (COA's). A coupling network with tunable coupling strength is proposed, which has a near- constant input conductance, to ensure the oscillation condition under difierent attenuation levels. The parameters of oscillators and the coupling network are derived on the TSMC 0.18m technology, and their Y parameters are extracted around 10GHz for illustration. After being verifled with full- circuit simulations and other behavior models, including the Adler's equation and the conventional Y - parameters approach, this method is applied to estimate the maximum allowable number of oscillators that can be coupled together. The inter-element phase shift of a COA is controlled by tuning the free-running frequencies of oscillators at both ends. Injection signals with proper phases are proposed to synchronize multiple COA's into a bigger COA.