## 1 Introduction  
The design and synthesis of active frequency-selective filters have a very significant role in the areas of continuous-time signal processing, instrumentation and measurement applications, and wireless communication. In recent years, the design of general mixed-mode universal biquadratic filters with input voltages and/or currents and output voltages and/or currents has received a lot of attention from researchers. Considering the nature of input and output signals, the filters can be classified into four possible modes, i.e., voltage mode (VM), current mode (CM), transmittance mode (TAM), and transimpedance mode (TIM). The VM and CM operations perform frequency filtering behavior on voltage and current signals, respectively. The TAM and TIM operations can be used as bridges for connecting a VM filter to any of the CM circuits and vice versa. Accordingly, the mixed-mode universal filters that provide all generic filtering responses in all four modes increase the versatility and flexibility of practical filtering applications and requirements. Consequently, these filters are worthy of investigation and research. Therefore, in the recent past, several structures realizing mixed-mode universal biquadratic filters with a variety of high-performance active elements have appeared in the literature [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; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. Table 1 presents a comparative study of earlier-reported mixed-mode universal filters based on various types of high-performance active components. A deep investigation of the available literature reveals that several exemplary filter topologies introduced in [1; 12; 16; 19; 21; 26; 29; 31; 32; 37; 39; 43; 44] do not provide the different filtering responses in all four modes of operation. In [1; 2; 3; 40; 17; 18; 20; 25; 27; 28; 29; 30; 32; 36; 38; 40; 41], they require more than two active components for the design. The use of more active components results in higher power dissipation and a large chip area. Additionally, a multitude of the previously discussed mixed-mode filters [3; 4; 5; 6; 10; 12; 16; 18; 22; 23; 25; 27; 31; 35; 36; 38; 41; 42; 44; 45] employ an excessive number (at least five) of passive components. It has been observed that the realizations of [3; 4; 5; 6; 10; 12; 14; 15; 16; 18; 21; 22; 24; 26; 27; 31; 33; 35; 37; 38; 41; 42; 43; 45; 46] still used some floating passive components, which is unfavorable from integrated circuit (IC) implementation viewpoint. To obtain various filtering responses or to change the operating mode, the designs in [5; 27; 32; 42] need structural modification with a programmable switching technique. This technique needs to employ some external switches, which practically lead to increasing switching noise. The filter structures given in [3; 4; 5; 6; 10; 12; 16; 18; 22; 23; 25; 31; 35; 36; 38; 41] do not provide the feature of inbuilt tunability of filter parameters. Furthermore, the important filter parameters, i.e., natural angular frequency (\(\omega_{o}\)) and quality factor (\(Q\)), for the circuits [1; 5; 6; 10; 12; 13; 15; 16; 17; 19; 20; 23; 30; 33; 34; 37; 38; 41] are interactive. Although the circuits of [4; 13; 22; 25; 27; 30; 31; 32; 38] allow the realization of different functions of the universal filter with the same topology, they employ two different types of active components, which are not modular, and increase the complexity of the resulting circuit. In other works [8; 16; 19; 24; 26; 33; 39; 43; 45; 46], some mixed-mode universal filters based on a single active element were previously reported. However, the active devices used for these realizations are complex active components, resulting in a complicated internal structure [8; 24; 33; 39; 43; 45; 46]. Furthermore, the single active element-based filter circuits [16; 26; 39; 43] function only in dual modes of operation.