Low-sensitivity, low-power active-RC allpole filters using impedance tapering

Abstract

A procedure for the design of allpole filters with low sensitivity to component tolerance is presented. The filters are based on resistance-capacitance (RC) ladder structures combined with single operational amplifiers. It is shown that by the use of impedance tapering, in which L-sections of the RC ladder are successively impedance-scaled upwards, from the driving source to the amplifier input, the sensitivity of the filter characteristics to component tolerances can be significantly decreased. Impedance tapering is achieved by the appropriate choice of component values. The design procedure, therefore, adds nothing to the cost of conventional circuits; component count and topology remain unchanged, whereas the component values selected for impedance tapering account for the considerable decrease in componenttolerance sensitivity.

Low-Noise, Low-Sensitivity Active-RC Allpole Filters Using MATLAB Optimization

“…High-impedance sections are surrounded by dashed rectangles in Figure 7. For illustration, let us consider the following practical design example as one in (Moschytz, 1999): 2 86 kHz; 5; 100 pF.…”

“…It is shown in (Jurisic et al, 2010c) that complementary Biquads have identical noise transfer functions and, therefore, the same output noise. An optimization of both sensitivity and noise performance is possible by varying the general impedance tapering factors (15) of the resistors and capacitors in the passive-RC network of the filters in Figure 7, see (Moschytz, 1999;Jurisic et al, 2010b). By increasing r>1 and/or >1, the R 2 and C 2 impedances are increased.…”

“…They are calculated using Matlab procedures presented in Section 3.1. Referring to Figure 7, the voltage attenuation factor  (0<1), which decouples gains K and  , see (Moschytz, 1999), is defined by the voltage divider at the input of the filter circuits. Note that all filters in Figure 7 have the same expressions for  p , and that the expressions for pole Q, q p are identical only for complementary circuits.…”

“…The relationship between the low sensitivity and low output noise, that are the most important performance of active-RC filters, is investigated, and optimum designs that reduce both performances are presented. A considerable improvement in sensitivity of single-amplifier active-RC allpole filters to passive circuit components is achieved using the design technique called 'impedance tapering' (Moschytz, 1999), and as shown in (Jurisic et al, 2010a) at the same time they will have low output thermal noise. The improvement in noise and sensitivity comes free of charge, in that it requires simply the selection of appropriate component values.…”

Third Order Current-Mode Filter Realization using CMOS Current-Mirror

“…Therefore, the power supply voltage of the circuits must be reduced extremely to low value. In addition to this, the use of portable equipments has restricted the operation to a single battery [8], [9]. Also operation at high frequencies is a key desirable feature for these devices.…”