## 1 Introduction  
In control and instrumentation, and speech applications, inverse filters are crucial circuit components used to correct distorted output signals resulting from linear or nonlinear transformations caused by signal processors or transmission systems. This filter has a frequency response that is inversely proportional to the frequency response of the system, leading to distortion. The design of inverse filters is also necessary in several communication applications, such as monitoring the relative cleanness of a signal and de-emphasizing FM systems. In control systems, it is necessary to employ inverse lowpass, highpass, and bandpass filter functions for the implementation of proportional-integral, proportional-derivative, and proportional-integral-derivative controllers. For these reasons, the authors in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] explicitly discuss the design and implementation of inverse filters utilizing different modern active components. The previous studies operate in various modes such as voltage mode (VM) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], current mode (CM) [2, 3, 4, 5, 6, 7, 12, 14, 15, 17, 30], and transadmittance mode [16]. In addition, the authors in [5; 6; 7; 23; 29; 31] specifically developed first-order inverse filters, whereas the works referenced as [1; 2; 3; 4; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 26; 27; 28; 29; 30] deal with second-order inverse filters. In [1], a comprehensive approach utilizing nullors as fundamental components was introduced to derive the inverse transfer function for linear dynamic systems and the inverse transfer characteristic for nonlinear resistive circuits. An example of a Sallen-Key HP filter and the inverse of a half-wave rectifier has also been used to illustrate this approach. The previous study described in [2] provided a procedure for transforming a VM op-amp-based RC filter into a CM, four-terminal floating nullor (FTFN)-based inverse filter. The realization approach employs a network representation that utilizes nullors and RC:CR dual transformation. The work in [3] demonstrates a general method for deriving FTFN-based CM inverse filters from well-known VM filters, as well as generating a CM inverse filter from the Friend-Delyannis biquad. Since FTFN is not available commercially, one can realize it using two second-generation current conveyors (CCIIs) or two current feedback operational amplifiers (CFOAs). A number of CM inverse filter implementations using a single FTFN have been described in [4], where the simulation results reported in this study were obtained by synthesizing the FTFN using two CCIIs. Numerous additional inverse filters were given in [5; 6; 7; 8; 16; 20; 21; 22; 23; 24; 25]. Each configuration provides a single inverse filter function. Multifunction second-order inverse filter realizations employing more than two active components are suggested in [8; 9; 10; 11; 14; 15; 16; 17; 19; 26; 27; 29]. Some of them also require a significant number of passive components for their realizations, i.e., at least seven passive components [17; 20; 21; 24; 25; 29; 30]. In [12], it is observed that the output current of the CM inverse filter is sensed through the passive components, requiring an additional buffer stage to connect to the next stage. The output voltage terminals of the second-order VM inverse filter designs in [13; 14; 18; 19; 20; 21; 23; 24; 28] do not explicitly have a low impedance level. Thus, these filters are not appropriate for cascadable connections. This study emphasizes the use of the second-generation voltage conveyors (VCIIs) as active components in designing multifunction inverse filters. Four configurations implementing first-order and second-order inverse filters in both VM and CM are presented.