frequencies f 01 and f 02 of the two differential oscillators Hence since the

Frequencies f 01 and f 02 of the two differential

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frequencies f 01 and f 02 of the two differential oscillators. Hence, since the inter-stage phase shift is independent of the number of oscillators in the array [4,7,9], the proposed tool can also help the
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designer to rapidly find the free-running frequencies of the two outermost oscillators of the array required to achieve the desired phase shift. Indeed, without such a tool, a transient analysis of the oscillator array for different couples of oscillators’ free-running frequencies must be performed in order to find the phase shift required for the targeted application. The proposed CAD tool can of course be used for other differential oscillators architectures and in strong and weak coupling cases. IV. Conclusion This paper presents a new CAD tool which provides, in a considerably shorter analysis time a cartography giving the phase shifts, synchronization frequencies and amplitudes of the differential output voltages of two differential oscillators coupled through a broadband network. Starting from a new expression of the equations describing the locked states of two van der Pol oscillators coupled through a resistor, a simpler system of three equations with three unknowns was obtained. Solving this system on Matlab using nonlinear programming technique has led to the elaboration of the cartography of the locked states of the two differential oscillators coupled through a resistive network. The reliability and the accuracy of the developed CAD tool was verified using Agilent’s ADS software, where two differential NMOS oscillators coupled through a resistor were simulated. The obtained results were in accordance with those generated by the presented CAD tool, showing the usefulness of such a tool for the design of an array of differential oscillators coupled through a broadband network. References
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[1] M. R. Kuhn and E. M. Biebl, “Power combining by means of harmonic injection locking”, IEEE MTT-S Int. Microw. Symp. Dig, vol. 1, pp. 91–94, June 2004. [2] S. Nogi, J. Lin, and T. Itoh, “Mode analysis and stabilization of a spatial power combining array with strongly coupled oscillators”, IEEE Transactions on Microwave Theory and Techniques , vol. 41, n° 10, pp. 1827–1837, October 1993. [3] T. Health, “Beam steering of nonlinear oscillator arrays through manipulation of coupling phases”, IEEE Transactions on Antennas and Propagation , vol. 52, n° 7, pp. 1833–1842, July 2004. [4] P. Liao and R. A. York, “Beam Scanning With Coupled VCOs”, In Proc. Antennas Propagation Soc. Int. Symp ., vol. 2, pp. 836–839, June 1994. [5] P. Liao and R.A. York, “A new phase-shifterless beam-scanning technique using arrays of coupled oscillators”, IEEE Transactions Microwave theory and techniques, vol. 41, n°10, pp. 1810-1815, October 1993. [6] S. Toon, A. Banai, F. Farzaneh, “Evaluation of beam steering in circular planar array of coupled microwave oscillators”, International Journal of RF and Microwave Computer-Aided Engineering , vol. 21, n°4, pp. 383-391, July 2011. [7] R. A. York, “Nonlinear analysis of phase relationships in quasioptical oscillator arrays”, IEEE Transactions on Microwave Theory and Techniques , vol. 41, n°10, pp. 1799–1809, October 1993. [8] R. A. York and T. Itoh, “Injection and phase-locking techniques for beam control”,
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  • LC circuit, R. A. York

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