Abstract
It is shown that the characteristic equation (CE) of an nth-order, 'single-pumping', continuous-time periodic system is an nth-order polynomial equation in the z-plane, whose coefficients (for zero-mean, symmetric pumping of magnitude K) are power series in K/sup 2/. For cisoidal cases, the expressions for the K/sup 2/, K/sup 4/ and K/sup 6/ terms have been obtained. Further, for non-cisoidal systems, the K/sup 2/ term has also been obtained. Such CEs allow one, for the first time in literature, to study analytically the behaviour of periodic systems for any pumping frequency and even for large values of K. The K behaviour of several frequency-normalised, cisoidal systems has been studied to illustrate this point. The study further reveals that, (i) particularly for high-frequency systems, the K/sup 2/ terms of the power series are alone capable of describing the system behaviour over a wide domain, and (ii) as the value of K is increased, the roots, in general, move in an oscillatory fashion. >
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