Super-harmonic injection locking of nano-contact spin-torque vortex oscillators

Super-harmonic injection locking of single nano-contact (NC) spin-torque vortex oscillators (STVOs) subject to a small microwave current has been explored. Frequency locking was observed up to the fourth harmonic of the STVO fundamental frequency $f_{0}$ in microwave magneto-electronic measurements. The large frequency tunability of the STVO with respect to $f_{0}$ allowed the device to be locked to multiple sub-harmonics of the microwave frequency $f_{RF}$, or to the same sub-harmonic over a wide range of $f_{RF}$ by tuning the DC current. In general, analysis of the locking range, linewidth, and amplitude showed that the locking efficiency decreased as the harmonic number increased, as expected for harmonic synchronization of a non-linear oscillator. Time-resolved scanning Kerr microscopy (TRSKM) revealed significant differences in the spatial character of the magnetization dynamics of states locked to the fundamental and harmonic frequencies, suggesting significant differences in the core trajectories within the same device. Super-harmonic injection locking of a NC-STVO may open up possibilities for devices such as nanoscale frequency dividers, while differences in the core trajectory may allow mutual synchronisation to be achieved in multi-oscillator networks by tuning the spatial character of the dynamics within shared magnetic layers.Comment: 21 pages, 8 figure

A new method for the determination of the locking range of oscillators

A time-domain method for the determination of the injection-locking range of oscillators is presented. The method involves three time dimensions: the first and the second are warped time scales used for the free-running frequency and the external excitation, respectively and the third is to account for slow transients to reach a steady-state regime. The locking range is determined by tuning the frequency of the external excitation until the oscillator locks. The locking condition is determined by analyzing the Jacobian matrix of the system. The method is advantageous in that the computational effort is independent of the presence of widely separated time constants in the oscillator. Numerical results for a Van Der Pol oscillator are presented

Injection locking of an electro-optomechanical device

The techniques of cavity optomechanics have enabled significant achievements in precision sensing, including the detection of gravitational waves and the cooling of mechanical systems to their quantum ground state. Recently, the inherent non-linearity in the optomechanical interaction has been harnessed to explore synchronization effects, including the spontaneous locking of an oscillator to a reference injection signal delivered via the optical field. Here, we present the first demonstration of a radiation-pressure driven optomechanical system locking to an inertial drive, with actuation provided by an integrated electrical interface. We use the injection signal to suppress drift in the optomechanical oscillation frequency, strongly reducing phase noise by over 55 dBc/Hz at 2 Hz offset. We further employ the injection tone to tune the oscillation frequency by more than 2 million times its narrowed linewidth. In addition, we uncover previously unreported synchronization dynamics, enabled by the independence of the inertial drive from the optical drive field. Finally, we show that our approach may enable control of the optomechanical gain competition between different mechanical modes of a single resonator. The electrical interface allows enhanced scalability for future applications involving arrays of injection-locked precision sensors.Comment: Main text: 10 pages, 7 figures. Supplementary Information: 5 pages, 4 figure

Architectures and Circuits Leveraging Injection-Locked Oscillators for Ultra-Low Voltage Clock Synthesis and Reference-less Receivers for Dense Chip-to-Chip Communications

High performance computing is critical for the needs of scientific discovery and economic competitiveness. An extreme-scale computing system at 1000x the performance of today’s petaflop machines will exhibit massive parallelism on multiple vertical fronts, from thousands of computational units on a single processor to thousands of processors in a single data center. To facilitate such a massively-parallel extreme-scale computing, a key challenge is power. The challenge is not power associated with base computation but rather the problem of transporting data from one chip to another at high enough rates. This thesis presents architectures and techniques to achieve low power and area footprint while achieving high data rates in a dense very-short reach (VSR) chip-to-chip (C2C) communication network. High-speed serial communication operating at ultra-low supplies improves the energy-efficiency and lowers the power envelop of a system doing an exaflop of loops. One focus area of this thesis is clock synthesis for such energy-efficient interconnect applications operating at high speeds and ultra-low supplies. A sub-integer clockfrequency synthesizer is presented that incorporates a multi-phase injection-locked ring-oscillator-based prescaler for operation at an ultra-low supply voltage of 0.5V, phase-switching based programmable division for sub-integer clock-frequency synthesis, and automatic calibration to ensure injection lock. A record speed of 9GHz has been demonstrated at 0.5V in 45nm SOI CMOS. It consumes 3.5mW of power at 9.12GHz and 0.052 of area, while showing an output phase noise of -100dBc/Hz at 1MHz offset and RMS jitter of 325fs; it achieves a net of -186.5 in a 45-nm SOI CMOS process. This thesis also describes a receiver with a reference-less clocking architecture for high-density VSR-C2C links. This architecture simplifies clock-tree planning in dense extreme-scaling computing environments and has high-bandwidth CDR to enable SSC for suppressing EMI and to mitigate TX jitter requirements. It features clock-less DFE and a high-bandwidth CDR based on master-slave ILOs for phase generation/rotation. The RX is implemented in 14nm CMOS and characterized at 19Gb/s. It is 1.5x faster that previous reference-less embedded-oscillator based designs with greater than 100MHz jitter tolerance bandwidth and recovers error-free data over VSR-C2C channels. It achieves a power-efficiency of 2.9pJ/b while recovering error-free data (BER 200MHz and the INL of the ILO-based phase-rotator (32- Steps/UI) is <1-LSB. Lastly, this thesis develops a time-domain delay-based modeling of injection locking to describe injection-locking phenomena in nonharmonic oscillators. The model is used to predict the locking bandwidth, and the locking dynamics of the locked oscillator. The model predictions are verified against simulations and measurements of a four-stage differential ring oscillator. The model is further used to predict the injection-locking behavior of a single-ended CMOS inverter based ring oscillator, the lock range of a multi-phase injection-locked ring-oscillator-based prescaler, as well as the dynamics of tracking injection phase perturbations in injection-locked masterslave oscillators; demonstrating its versatility in application to any nonharmonic oscillator

Bistable phase control via rocking in a nonlinear electronic oscillator

We experimentally demonstrate the effective rocking of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by pi, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcationComment: 7 pages, 10 figure