Dražen Jurišić

Low-noise active-RC low-, high- and band-pass allpole filters using impedance tapering

It is shown that low-sensitivity active resistance-capacitance (RC) filters are also low in output thermal noise. The design procedure of second- and third-order low-sensitivity allpole filters, using impedance tapering, has already been published. The component values selected for impedance tapering account for the considerable decrease in output thermal noise. The method of Zurada and Bialko (1975) was used to determine output noise spectral density and total RMS output noise of filters. Passive elements and operational amplifiers are represented by substitute noise models. The noise contribution of each device to the output node is calculated using noise transfer functions. The noise analysis was performed on the second-order (class 4) Sallen and Key low-pass, high-pass and band-pass filter sections using MATLAB. The extension to third- and higher-order filters follows the same principles. It was found that the filters with minimum noise coincide with the filters with minimum sensitivity to component tolerances.

Use of "lossy" LP-BP-transformation in active second-order BP filter design procedure

The design of second-order band-pass (BP) active RC filters using a modified low-pass to band-pass (LP-BP) frequency transformation is presented. The transformation is applied to a first-order low-pass (LP) filter as the (odd-order-)prototype, from which a single-amplifier second-order BP filter is constructed. The operational amplifier is added to the first-order LP circuit in order to provide a low output impedance and supply a positive feedback loop to enable a pole shifting process needed in the realization. It is shown that a BP filter can be realized by substitution of resistor and capacitor in the low-pass prototype filter, by serial parallel RC circuits in the resulting band-pass structure. Schoeffler sensitivity is used as a measure of the magnitude sensitivity to component tolerances. A step-by-step design procedure is verified for several second-order band-pass filter circuits, using different impedance scaling ratios, resulting by different sensitivities. It is shown that the circuit with equal impedance scaling ratios yields the best results. Obtained results are double-checked using PSPICE.

Low-Sensitivity Active-RC Allpole Filters Using Optimized Biquads

In this paper we present an optimal design procedure for second-and third-order active resistance-capacitance (RC) single-amplifier building blocks that are used to build a high-order tolerance-insensitive allpole filter. The design procedure of low-sensitivity, low-pass second- and third-order active-RC allpole filters, with positive feedback, has already been published. The design was extended to the high-pass and band-pass filters, as well as, to the filters using negative feedback. In this paper we summarize all these previously presented designs in the form of a tabulated step-by-step design framework (cookbook). The low passive sensitivity of the resulting circuits, as well as low active sensitivity features are demonstrated on the high-order Chebyshev filter examples. The resulting low passive sensitivity is investigated using the Schoeffler sensitivity measure, whereas the low active sensitivity is investigated with Matlab using finite and frequency dependent opamp gain.

Low-sensitivity, low-power 4/sup th/-order low-pass active-RC allpole filter using impedance tapering

The analytic design procedure of low-sensitivity, low-power, low-pass (LP) 2/sup nd/- and 3/sup rd/-order class-4 active RC allpole filters, using impedance tapering, has already been published (Moschytz, 1999). In this paper the desensitisation using impedance tapering is applied to the design of LP 4/sup th/-order filters. The numerical design procedure was performed by Newtons iterative method. Analytically designed unity-gain LP 4/sup th/-order filters (Jurisic et al., 2004) can provide initial values for Newtons method. The sensitivities of a filter transfer function to passive components tolerances, as well as active gain variation are examined by the Schoeffler sensitivity and Monte Carlo PSpice simulation. Butterworth and Chebyshev 0.5dB filter examples illustrate the design method.

GIC based third-order active low-pass filters

Third-order low-pass filters are analyzed. Two different configurations of general impedance converter (GIC) based filters are compared to two Sallen and Key (SAK) based structures. For GIC-based third-order filters, realization procedures are given. The transfer functions and the component values for the third-order filters with Butterworth response are presented. Sensitivity analysis is done, and the results of Monte Carlo runs, as well as Schoeffler sensitivities are shown. The best results are obtained with the GIC-based filter which uses four capacitances for the realization.

General purpose biquads optimized for dynamic range and low noise

In this paper two general-purpose (GP) biquadratic filters are analyzed and optimized. The design equations for both filters are given, and the methods used to optimize the dynamic range and reduce the noise are described. On one example of the 2nd-order Butterworth filter, PSpice analyses were carried out, and a comparison of noise, referred to the input, is given. The dynamic range is optimized such as to have the same signal level at each amplifier output. Both optimization procedures are highly effective and can be applied to the similar filter design problems

Real amplifier influence on impedance tapere 2nd-order filters

In this paper, an influence of real parameters of operational amplifier to the impedance tapered filter transfer function is analyzed. As an example, a second-order-low-pass (LP) and high-pass (HP) Sallen and Key filters with Butterworth and Chebyshev transfer function approximations are considered. Design tables with normalized element values for both cases are given. The filter elements were calculated using three different design criteria: equal resistors, capacitors and impedance tapered elements. Filter transfer functions are obtained using ideal and real operational amplifier. Real model of common operational amplifier is presented. Active sensitivities for all presented filters are shown. The results obtained by the analysis show significant influence of real amplifier in the frequency ranges higher than 100 kHz. Reduction of active sensitivities is obtained using impedance tapering, which fortunately, reduces the passive sensitivities as well.

Low-sensitivity, low-power fourth-order band-pass active-RC allpole filter using impedance tapering

The design of low sensitivity band-pass (BP) active resistance-capacitance low (RC) filters using impedance tapering is presented. 4/sup th/-order band-pass filters are considered. The design procedure for low-sensitivity low-pass (LP) prototype second-order class 4 Sallen and Key active-RC allpole filters, using impedance tapering, has already been published. In this paper a low-pass to band-pass (LP-BP) transformation is applied to an impedance tapered 2/sup nd/-order LP filter, and a 4/sup th/-order BP filter is constructed. The component values, selected for impedance tapering, account for the considerable decrease in sensitivity to component tolerances for the LP as well as for the BP filter. As an example, a Chebyshev 4/sup th/-order BP filter is realized, and the sensitivities are analysed. Schoeffler sensitivity measure is used as a basis for comparison, and Monte Carlo runs are performed as a double-check. A considerable improvement in sensitivity is achieved, both for the BP filter as well as well as for the original LP prototype.

Impedance tapering effects on "low-Q" SAB band-pass active-RC filter

The design procedure of low-sensitivity active resistance-capacitance (RC) allpole filters, using impedance tapering, has already been published. The low-sensitivity filter sections already described in publications are class 4 (TT-SABB) Sallen and Key (1955) sections. In this paper class 3 (SAB) sections for low pole-Q realization are considered. Impedance tapering is applied on L-sections, which are situated in the negative-feedback of the operational amplifier in open-loop mode. L-sections are impedance scaled upwards, from the driving source to the negative amplifier input. A second-order band-pass filter is considered. Pole-Q factors for low-Q building blocks take their values up to, say, 5. The sensitivity to component tolerances of the circuit is shown to be small for any type of impedance tapering regardless of the gain-sensitivity product (GSP) value.

Frequency domain approach to fault diagnosis of analog filters

This paper presents fault location technique for testing analog filters using a fault dictionary. The single hard faults of the filter passive elements can be located and identified. To enable the efficient testing, an initial fault dictionary is optimised in order to get the minimal size of the dictionary with maximum number of uniquely recognised faults. After a simulation, the procedure tests the circuit and locates the failed element using adequate fault isolation criterion. The performances of the described method are illustrated with an analog filter fault diagnosis example performed in the frequency domain. The fault detection problem has also been considered.