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A simple 2-D oscillator to determine the correct decomposition of perturbations into amplitude and phase noise

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1 Author(s)
Coram, G.J. ; Analog Devices Inc., Wilmington, MA, USA

This paper presents a simple, analytically solvable example showing that the so-called “orthogonal decomposition” of noise in an oscillator yields the wrong result. The orthogonal decomposition assumes that the right eigenvectors of a matrix are orthogonal, and hence the projection along one of them may be computed by a simple inner product. However, this assumption is not always valid; for the example in this paper, the eigenvectors are not orthogonal and the projection must instead be determined by solving a linear system, or equivalently, computing an inner product with the left eigenvector

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:48 ,  Issue: 7 )