This paper presents the design and the implementation of a fully monolithic coupled-oscillator array, operating at 6 GHz with close to zero coupling phase, in 0.25 μm BICMOS SiGe process. This array is made of four LC-NMOS differential VCOs coupled through a resistor. The single LC-NMOS VCO structure is designed and optimized in terms of phase noise with a graphical optimization approach while satisfying design constraints. At 2.5 V power supply voltage, and a power dissipation of only 125 mW, the coupled oscillators array features a simulated phase noise of -127.3 dBc/Hz at 1 MHz frequency offset from a 6 GHz carrier, giving a simulated phase progression that was continuously variable over the range -64° < Δphi <64 ° and -116° < Δphi < 116°. This constant phase progression can be established by slightly detuning the peripheral array elements, while maintaining mutual synchronization.

/pdf/design-and-implementation-of-a-6-ghz-array-of-four-5d4n5c25u7.pdf

Design and Implementation of A 6-GHz Array of Four Differential VCOs Coupled Through a Resistive Network

This article presents the homodyne detection in a self-oscillation system, which represented by a short-range radar (SRR) circuit, that is analysed using a multi-time forced oscillator (MTFO) model. The MTFO model is based on a forced oscillation perspective with the signal and system theory, a second-order differential equation, and the multiple time variable technique. This model can also apply to analyse the homodyne phenomenon in a difference kind of the oscillation system under same method such as the self-oscillation system, and the natural oscillation system with external forced. In a free oscillation system, which forced by the external source is represented by a pendulum with an oscillating support experiment, and a modified Colpitts oscillator circuit in the UHF band with input as a Doppler signal is a representative of self-oscillation system. The MTFO model is verified with the experimental result, which well in line with the theoretical analysis.

/pdf/homodyne-detection-of-short-range-doppler-radar-using-a-4j9cyx573e.pdf

Homodyne detection of short-range Doppler radar using a forced oscillator model.

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.

/pdf/a-new-method-for-the-determination-of-the-locking-range-of-48698foudo.pdf

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

During the past decade, coupled oscillators have shown their efficiency as simple methods for phase control in microwave antenna arrays, and hence as alternatives to conventional electronic beam steering methods. This paper describes the design and the implementation of a fully monolithic coupled-oscillator array, operating at 6 GHz in 0.25 μm BICMOS SiGe process. A novel and original method, based on the use of a MOS transistor, for coupling the differential oscillators is developed and presented. At 2.5 V power supply voltage, and a power dissipation of only 62.5 mW, the coupled oscillators array features a simulated phase noise of −124.8 dBc/Hz at 1 MHz frequency offset from a 6.01 GHz carrier, giving a simulated phase progression that was continuously variable over the range −84 ° < Δ□ < 84 ° and −96° < Δ□ < 96°.

Design and implementation of a 6-GHz array of two differential oscillators coupled through a MOS transistor network

Injection-locking technique is receiving increasing interest in industrial applications, which is especially suitable for smart antenna array, but relative experiments are complicated. The article focuses on the theory and experiment of the technique. Firstly, section 2 reviews the theory of injection-locking technique, and summarizes two useful conclusions on injection-locking bandwidth and phase difference adjusting bound of the phenomena. Secondly, section 3 describes experiments using commercial microwave integrated circuit (MMIC) voltage controlled oscillator (VCO), which is reduces the experimental conditions. Experiments results perform very well.

Theory and Experiments of Injection-Locked Oscillator

According to the phase dynamics and desired phase gradient in the nearest-neighbor coupled oscillator array, conditions that the natural frequencies of oscillator elements should be satisfied are gotten in the article From the conditions we must tune natural frequency of the first element lower and tune natural frequency of the last element higher, if the desired phase gradient of the linear array is positive But an opposite conclusion can be got according to corresponding consequence of other several articles Rightness of our conclusion can be proved by simulations and experiments So conditions that the oscillator elements' natural frequencies should satisfied for desired phase gradient in our article is right

Study on Natural Frequencies Tuning Method of Nearest-Neighbor Coupled Oscillators

Van der Pol oscillator can be used to model microwave negative oscillator, and injection locked oscillator can be looked as forced Van der Pol oscillator. The article studies the amplitude and phase dynamics of the forced Van der Pol oscillator, and gets conditions under which injection locking phenomena can occur. Injection locked Van der Pol oscillator is also realized with a simple modern semiconductor circuit in the article. At last OrCAD PSpice is used to simulate the circuit and testify the conclusions got by theory analyzing.

Injection locking phenomena of Van der Pol oscillator

Large profile, high price, low efficiency in realization prevent phased array from being broadly used in automobile radar and communication systems, though phased array has high performance The article puts forward a new kind of shifterless phased array based on coupled oscillators The article studies the dynamics of nearest-neighbor coupled oscillators after reviewing the principles of electrical beam-scanning According to the need of beam-scanning the desired solutions of phase dynamics are established From that, we determine how the accessible parameters of coupled oscillators can be adjusted The article also determines conditions under which those solutions are stable, ie, physically realizable Computer simulations are used to testify the usefulness of the method Then in the last part of the article a complete transmit-receive scheme for vehicle radar and communication systems is given out

Low profile, low cost and high efficiency phased array for automobile radar and communication systems

In this paper, set of equations for the oscillator amplitude and phase dynamics are presented by describing the coupled series-resonant oscillator array in term of Z-parameters, and they are simplified for nearest-neighbor coupling topologies For beam-scanning using, equations of phase dynamics are analyzed under the phase model; the free-running frequencies of oscillators are controlled for certain relations The usefulness is illustrated through simulations

http://ieeexplore.ieee.org/iel5/9668/30550/01411496.pdf

Analysis of oscillator array dynamics for phase-shifterless beam-scanning

Beam scanning and beam forming can be achieved by nonlinear antenna array technology without the need of phase shifters. The architecture and settling time of phase distributions of nonlinear antenna array is studied in this paper. A general equation describing the phase dynamic of external locking array, unilateral locking array and mutual locking array is deduced. Transient response of nonlinear antenna array is analyzed. The analytic formula of settling time is presented.

Tang Zhikai

Papers

Study on Natural Frequencies Tuning Method of Nearest-Neighbor Coupled Oscillators

Injection locking phenomena of Van der Pol oscillator

Low profile, low cost and high efficiency phased array for automobile radar and communication systems

Analysis of oscillator array dynamics for phase-shifterless beam-scanning

Analysis of Settling Time of One Dimension Nonlinear Antenna Array