Oscillator array dynamics with broadband N-port coupling networks

York, R.A.; Liao, Po‐Yung; Lynch, J.J.

doi:10.1109/22.330116

Cited by 124 publications

(126 citation statements)

References 18 publications

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“…The phase equation in (1) is referred to as Adler's equation [7] in the microwave literature, and predicts an interesting result: the phase difference between the injected signal and the oscillator is a function of the relative detunings, according to the equation: Several unit cells can be embedded in a coupling network to achieve the synchronization of an array of oscillators. Usually at high frequencies the nearestneighbor coupling is most convenient to realize with the use of transmission lines that have broadband properties [4]. In this case the system is governed by the equations, for i = 1…N:…”

Section: Coupled Oscillator Arraysmentioning

confidence: 99%

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Synchronization of Oscillating Systems for Microwave Antennas and RF Electronics

York¹,

Maccarini²,

Buckwalter³

2003

AIP Conference Proceedings

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Abstract. During the past decade we have demonstrated that coupled nonlinear systems (oscillator arrays) can offer simple methods for phase control in microwave antenna arrays, and hence provides alternatives to conventional electronic beam scanning capability. Numerous experiments have been carried out at microwave frequencies to verify the analysis, and the experimental work proved valuable in guiding parallel theoretical efforts and demonstrating the advantages and limitations of such techniques for practical systems. During the course of this work, models have been developed and refined and used to explore new dynamical phenomena, such as "mode-locked" quasi-periodic states for pulse generation, phase noise reduction in oscillator array systems (verified experimentally at X-band), and other practical design issues. More recently, efforts have focused on the potential for coupled phase-locked-loop systems that promise more robust locking bandwidths and phase-control. We present an overview of our experimental efforts in exploiting the synchronization of oscillating systems for microwave antennas and RF electronics.

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Section: Coupled Oscillator Arraysmentioning

confidence: 99%

“…Usually in practice the variable capacitor controls of the oscillation frequency of the VCO. This simple parallel model is commonly used to derive the COAs' properties [1]- [4]. An equivalent series model can also be used, for which current and voltages can be interchanged to obtain analogous equations [5].…”

Section: Coupled Oscillator Arraysmentioning

confidence: 99%

Synchronization of Oscillating Systems for Microwave Antennas and RF Electronics

York¹,

Maccarini²,

Buckwalter³

2003

AIP Conference Proceedings

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show abstract

“…In [6], it is shown that the in-phase power-combining mode can be sustained by inserting a resistor at the center of the coupling network to attenuate undesired modes, or by placing two resistors at both ends of a transmission-line segment [7,8]. In [9], an one-dimensional coupling network is proposed, which consists of one-wavelength transmissionline segments and series/shunt resistors.…”

Section: Introductionmentioning

confidence: 99%

“…The time evolution of frequency and phase can be obtained by solving a set of differential equations. In [8], a Y -parameters approach is used to analyze the COA's. Harmonic-balance technique has been used to derive the steady-state response of COA's [7].…”

Section: Introductionmentioning

confidence: 99%

Analysis on Strongly Coupled Oscillator Arrays Using Modified Y-Parameters Approach

Lo¹,

Kiang²

2014

PIER B

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Abstract-A modified 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 nearconstant input conductance, to ensure the oscillation condition under different attenuation levels. The parameters of oscillators and the coupling network are derived on the TSMC 0.18 µm technology, and their Y parameters are extracted around 10 GHz for illustration. After being verified with fullcircuit simulations and other behavior models, including the Adler's equation and the conventional Yparameters 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.

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“…Concerning the frequency domain approaches, R. York made use of simple van der Pol oscillators to model microwave oscillators coupled through either a resistive network or a broadband network [6,16,17]. Since these works are limited to cases where the coupling network bandwidth is much greater than the oscillators' bandwidth, he used more accurate approximations based on a generalization of Kurokawa's method [18] to extend the study to the case of a narrow-band circuit [19].…”

Section: Introductionmentioning

confidence: 99%

New Formulation of the Equations Describing the Locked States of Two Van der Pol Oscillators Coupled through a Broadband Network – Application to the Design of Two Differential Coupled VCOs

et al. 2013

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In this paper, a new expression of the equations describing the locked states of two van der Pol oscillators coupled through a broadband network and allowing an accurate prediction of the oscillators' amplitudes is presented. To do so, the York's theory is improved using a more accurate van der Pol model in order to obtain a new system of four equations with four unknowns describing the locked states of two van der Pol oscillators coupled through a resonant network. Then, the case of a resistive coupling circuit is deduced from this new system of equations. The theory regarding the prediction of the oscillators' amplitudes is verified using Agilent's ADS software for the practical case of an array made of two differential Voltage Controlled Oscillators (VCOs) coupled through a resistive network.

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Oscillator array dynamics with broadband N-port coupling networks

Cited by 124 publications

References 18 publications

Synchronization of Oscillating Systems for Microwave Antennas and RF Electronics

Synchronization of Oscillating Systems for Microwave Antennas and RF Electronics

Analysis on Strongly Coupled Oscillator Arrays Using Modified Y-Parameters Approach

New Formulation of the Equations Describing the Locked States of Two Van der Pol Oscillators Coupled through a Broadband Network – Application to the Design of Two Differential Coupled VCOs

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