Proceedings Article | 21 April 2003
KEYWORDS: Bandpass filters, Digital filtering, Computer aided design, Telecommunications, Capacitors, Computer programming, Filtering (signal processing), Optimization (mathematics), Algorithms, Distortion
In this paper, we present a design approach for the high-level synthesis of programmable continuous-time Gm-C and active-RC filters with optimum trade-off among dynamic range, distortion products generation, area consumption and power dissipation, thus meeting the needs of more demanding baseband filter realizations. Further, the proposed technique guarantees that under all programming configurations, transconductors (in Gm-C filters) and resistors (in active-RC filters) as well as capacitors, are related by integer ratios in order to reduce the sensitivity to mismatch of the monolithic implementation. In order to solve the aforementioned trade-off, the filter must be properly scaled at each configuration. It means that filter node impedances must be conveniently altered so that the noise contribution of each node to the filter output be as low as possible, while avoiding that peak amplitudes at such nodes be so high as to drive active circuits into saturation. Additionally, in order to not degrade the distortion performance of the filter (in particular, if it is implemented using Gm-C techniques) node impedances can not be scaled independently from each other but restrictions must be imposed according to the principle of nonlinear cancellation. Altogether, the high-level synthesis can be seen as a constrained optimization problem where some of the variables, namely, the ratios among similar components, are restricted to discrete values. The proposed approach to accomplish optimum filter scaling under all programming configurations, relies on matrix methods for network representation, which allows an easy estimation of performance features such as dynamic range and power dissipation, as well as other network properties such as sensitivity to parameter variations and non-ideal effects of integrators blocks; and the use of a simulated annealing algorithm to explore the design space defined by the transfer and group delay specifications. It must be noted that such design space also includes most common approximation methods and network synthesis approaches as optimization variables, in order to make as widespread as possible the search for optimum solutions. The proposed methodology has been partially developed in MATLAB, taking advantage of the routines available in the signal processing and control toolboxes, and C++. The validity of the methodology and companying software will be demonstrated at the Conference and reported in the paper, using as a tailoring example the design of a programmable bank of filters for a high-performance powerline modem.
