In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit ...theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.
U radu je predstavljena realizacija nisko-propusnog aktivnog-RC filtra trećeg reda koji upotrebljava novu "leap-frog" (LF) topologiju. Nova struktura je pojednostavljena LF struktura s elementima ...koji se računaju direktno iz koeficijenata prijenosne funkcije. Nekoliko inačica krugova je prikazano i obavljena je usporedba. Napravljena je usporedba tako.er i s drugim uobičajenim filtarskim sekcijama trećeg reda. Novi LF filtar ima smanjeni broj komponenata, smanjenu kompleksnost i jednostavniji postupak projektiranja u usporedbi s klasičnim filtrima. Za ilustraciju učinkovitosti predstavljenog novog LF filtra, provedena je analiza osjetljivosti pomoću Schoefflerove mjere osjetljivosti i analiza termičkog šuma na izlazu na primjerima s prijenosnim funkcijama po Butterworthu i Chebyshevu s valovitošću u području propuštanja od 0.5 dB. Pomoću PSpice-a s modelom pojačala TL081, filtarska svojstva su simulirana, uspore.ena i potvr.ena mjerenjima na filtrima realiziranim pomoću diskretnih elemenata na štampanoj pločici. U radu su dane sve potrebne jednadžbe u postupku projektiranja korak po korak.
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.
This paper presents the realization of third-order low-pass active-RC filters using a new Leap-Frog (LF) topology. New structure is a simplified LF structure with the elements calculated directly ...from the transfer function coefficients. Several versions of the circuits are presented and compared. The comparison to other common third-order filter sections is done, as well. The new LF filter has the reduced number of components, reduced complexity and straightforward design procedure compared to classical filters. As an illustration of the efficiency of the proposed new LF filter, the sensitivity analysis using Schoeffler sensitivity measure as well as output thermal noise analysis was performed on examples with Butterworth and Chebyshev 0.5dB pass-band ripple transfer functions. Using PSpice with a TL081 opamp model, the filter performance is simulated and the results compared and verified by measurements on a discrete-component breadboard filter. All equations needed for the step-by-step design are given.
In this paper it is shown that active-RC filters can be designed to have low-sensitivity to passive components and at the same time possess low output thermal noise. The design procedure of low-noise ...and low-sensitivity, positive-feedback, second- and third-order low-pass allpole filters, using impedance tapering, has already been published. The noise analysis in this paper was extended to the high-pass and band-pass filters and those with negative-feedback. The optimum designs, regarding both noise and sensitivity of most useful filter sections were summarized in the table form (as a cookbook) and demonstrated on examples. The classical methods were used to determine output noise spectral density and total rms output noise of filters. It was found that low-sensitivity filters with minimum noise have reduced resistance levels, low Q-factors, low-noise operational amplifiers and use impedance tapering design.
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