Projeto de um filtro analógico gerador de pulsos prolato esferoidais para uso em sistemas ultra wideband

Abstract

This paper presents the design of a pulse generator prolate spheroidal systems for use in UWB (Ultra Wideband). A large bandwidth, greater than 500 MHz, combined with low power consumption and pulse based data transmission, make UWB communication system attractive for use on applications requiring high data transfer rates, low power consumption and simple circuits as in Wireless Sensor Network (WSN) and biomedical applications, for example. Among the various types of pulses that can be implemented for use in UWB, this paper proposes the use Prolate Spheroidal Pulse (PSWF). PSWF pulses do not have a closed form, and are then used as a discrete approximation. Based on this approach, numerical approximations are performed in the time domain and Laplace to obtain a transfer function to be implemented through an optimal representation in State Space. This representation will then be implemented on the circuit by means of a Gm-C filter. Using this approximation, other approximations are realized in the time domain which achieves a function in the time domain representing this type of pulse. This function is then manipulated in the Laplace domain, and applying the method of Padé, used to obtain a transfer function. This transfer function is then represented through the orthonormal State Space representation, which has a near optimal behavior in terms of dynamic range and sparsity, besides having low sensitivity to changes in values, compared to conventional representations, as the canonical forms. Using transconductance cells also developed in this work, the orthonormal representation is implemented by means of a Gm-C filter. This filter is used in a proposed m-ary communication, combining PAM (Pulse Amplitude Modulation) with OPM (Orthogonal Pulse Modulation), for use in UWB systems. Ideally, it is desired to obtain a pulse generator that generates pulses PSWF first and second orders to applications in sub-giga, from 500 MHz to 1 GHz with pulses that have duration of 10 ns. However, due to limitations of the technology, the frequency response of the circuit of the filter is less than specified initially (lasting 5 mS and banda 1 MHz - 2 MHz). However, the obtained filter was able to generate PSWF pulses of first and second order, which represents a functional response of the whole system, thus validating the proposed method.