Periodic steady-state behaviour of cross-coupled LC-tank oscillator is of critical importance in ultra-low power, lowvoltage transceiver circuits. Understanding the major factors affecting amplitude, oscillation frequency and power consumption would lead to more optimised oscillator design particularly for short-range wireless transceivers. This study presents a new approach for evaluating the amplitude of the main component, oscillation frequency and power consumption of cross-coupled LC-tank oscillator. Three major factors, affecting oscillator functionality are examined. In order to obtain a general design methodology, the effects of oscillator parameters such as transistors' sizes, inductor and capacitor values are investigated. An intuitive discussion about oscillator behaviour and a design procedure are presented. The theoretical results are verified by circuit simulations in the 0.18 µm CMOS process.

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a b s t r a c tThe solution of a Volterra type screw dislocation problem in an orthotropic rectangular plane with finite length and width and various boundary conditions is obtained by means of a separation of variables technique. A distributed dislocation method is employed to obtain integral equations of the plane with cracks and cavities under an anti-plane traction. The ensuing equations are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the applicability of the proposed solution.

Linear behaviour of bootstrap switches is of critical importance in low-voltage analogue circuits and understanding the major factors affecting the linearity helps design a better switch. This study presents a theoretical approach for evaluating the distortion of bootstrap switches in the frequency domain based on the Volterra series. Five major factors affecting the linearity of the bootstrap switch are examined. In order to obtain a general design guideline the analysis is done in two parts. First, the distortion because of the nonlinear I-V characteristic of the main transistor of the switch is considered. In the second part, the distortion because of sampling errors, such as clock feed-through and charge injection, are added to the analysis. The theoretical results are verified by circuit simulations in a 0.18 mm CMOS process, using HSpice. 2 Volterra series and harmonic distortion The non-linearity of a system can be obtained using the Volterra series. A non-linear system with input x(t) and output y(t) can be represented by Volterra series as the sum of infinite number of operators as the following [5] y(t) ¼ H 1 [x(t)] þ H 2 [x(t)] þ H 3 [x(t)] þ Á Á Á (1) where H n [x(t)] is the nth-order operator with kernel h n and is

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