A System of Two Coupled Oscillators With a Continuously Controllable Phase Shift
Abstract : We present a novel generalization of quadrature oscillators (QVCO) which we call “arbitrary phase oscillator” or APO for short. In contrast to a QVCO which generates only quadrature phases, the APO is capable of continuously generating any desired phase at its output. The proposed structure employs a novel coupling mechanism to generate arbitrary phase shifts between two coupled oscillators without the need for an explicit phase shifter. A rigorous nonlinear dynamic analysis is presented to give a closed-form formula for the generated phase shifts, and the theory is verified by numerical simulation as well as measurement results of a prototype chip fabricated in 130-nm CMOS technology. The prototype APO has a frequency tuning range of 4.90–5.65 GHz and is continuously phase tunable from 0? to 360? across the entire frequency range. The APO structure can be used in designing novel coupled-oscillator-based phased arrays for 5G wireless communications.
? There exist various discrete time numerical integration methods that are used to perform a transient simulation.
? There exist time-domain algorithms such as the shooting methods that minimize the evaluation of the initial transient state in order to efficiently obtain the desired periodic steady state.
? In microwave mixer circuits, a quasi-periodic steady-state solution exists with two or more fundamental frequency components.
? The points of infinite slope are the turning points of the curve, and due to the fact that the synchronization curves are closed, for any frequency or control voltage between them, there exist two solutions for the oscillator power.
? The system is classified as an initial value problem, and the computation of its solution over a given time interval is known as transient simulation.
? Moreover, for large arrays, it becomes difficult to generate the required output power with good spectral purity from a single solid state source at mm-wave frequencies and this problem is further exacerbated by large losses in the feed network.
? The system also suffers from beam squint problem due to variation of phase shifts with frequency modulations.
? The phase reduction technique reduces the original problem to the analysis of oscillator’s phase variables without capturing the dynamics of their amplitudes.
• The nearest-neighbor bilateral and unilateral coupling topologies are relevant to recently proposed power combining and beam-scanning applications.
• We also study the pattern recognition applications of coupled oscillator networks and propose a new alternative that avoids the impractical all to all coupling between the oscillators.
• In order to eliminate the expensive phase shifter blocks, injection locked coupled oscillator arrays have been proposed as an alternative to the more common feed based structures for beamforming.
• The simplicity of the proposed circuit makes it readily implementable on any standard CMOS technology.
? The nonlinear dynamics of coupled oscillators was used to demonstrate a novel way of frequency tuning in a closed loop of unidirectionally coupled oscillators, which avoided using lossy varactors inside oscillator’s tanks.
? However, shrinking cell sizes and advances in CMOS technology has made mm-Wave communications feasible provided that adaptive beamforming is used to compensate for the additional propagation losses.
? A general advantage of coupled oscillator phased arrays is in the scalability of layout for larger arrays as each antenna is fed by a designated, nearby VCO and hence the long interconnects and the complex feed networks in traditional systems are eliminated.
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