An explicit form of all-pole filter function with decreasing envelope of the summed sensitivity function

In this paper, the all-pole lowpass filter function with the decreasing envelope of the summed sensitivity in the pass-band is considered. The filter transfer function with maximal number of the ripples of the summed sensitivity in the pass-band is obtained in the explicit form, by the application of the Chebyshev polynomials of the first kind. The slope of the decrease of the summed sensitivity envelope can be controlled by a free-parameter alpha. We derived a new approximation function in order to achieve small summed sensitivity in the filter pass-band. Consequently, the sensitivity analysis was carried out and a comparison of the summed sensitivity and the group delay with respect to the classic all-pole filters was given. The approach presented in this paper is based on that the minimization of the summed sensitivity is important for the reduction of the deviation of the magnitude response caused by temperature changes of the continuous-time active filters implemented into the analog front end or as programmable chips. Copyright (C) 2010 John Wiley & Sons, Ltd.