Active RC realizations of l and fdnr and some applications in filters

An ~ctive le circuit is one which consists of resis-tors, capacitors and some form of active elements. Thus,by definition, it is ti circuit which do e s not conbafn in-ductors. In pr~ctice, a convcnt.f.ona l, wire - wound in-ducto r is not suitable at low r requenct e s, as in control,d at a COIDir.’:’.r-’ ~:ition systems, analog computer and biomedicalengf.nee.rLng npp lications. Moreover, a fundamental limi-tation cxt sc s t~ the realizations. Their limitations arebulky size} lo’w auality of inductors and their associatedmagnetic fiel~ and also their nonlinear behavior. For allthese reaScns, the concept of eliminating inductors fromnetwork reR.~-iz!!ttions without giving up any of the proper-ties thAt such inductors provide, is a most attractiveone.There are basically three approaches to active fil-ter design :1- Simulated Inductance Approach :In this approach an inductorless filter is obtAinedby first designing a conventional passive RIC filter andthen replAcing each inductance in the design by an activeRC net’,o/Ork simulating an inductance of equa L value.2- Freouency - Dependent Negative Resistance Approach :The b~sic idea here is to transform a passive RLCnetwork using Bruton’s tr~nsformation to an equivalent CRDnetvo rk , The new network is obta.ined by converting aninductance to a resistance, a resistance to a CapaCitance,and A cApacit~nce to an aLemenf having an input impedanceof the form KI 52 (kno en as ItFDNR”) •