# VDGA-Based Resistorless Mixed-Mode Universal Filter and Dual-Mode Quadrature Oscillator
## 1 Introduction  
Active frequency-selective universal filters play an important part in several signal processing systems, as they can implement multiple filtering functions simultaneously. Analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) utilize active universal filters for diverse signal processing functions, including noise elimination, phase adjustment, and aliasing prevention. They are also an integral part of audio processing, telecommunications, and instrumentation systems. Image processing uses analog universal filters to eliminate noise or enhance the edges of images. Additionally, sinusoidal quadrature oscillators (QOs) produce two identical sinusoidal output signals, which have equal amplitude and frequency with a 90\({}^{\circ}\) phase shift. They are widely employed in numerous electrical engineering applications, including communication, information, and measurement systems, such as communication receivers, zero-IF and image rejection receivers, soil measurement systems, and phase-sensitive detection. Therefore, the design and synthesis of active analog universal filters and QOs have attracted the interest of researchers during the past decades. In the technical 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], there are numerous analog universal filters and QO realizations that utilize a variety ofactive components. In addition, the circuits mentioned above are examined to provide further insight on certain aspects of circuit design and integrated circuit (IC) fabrication as follows:  
* Modern analog signal processing circuits may process signals in a mixed mode, integrating both voltage or current operations. Many configurations, as reported in [1; 2; 3; 4; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 23; 24; 25; 26; 28], are designed for only a single mode of operation. * Circuit designs that use floating capacitors generally suffer from the perspective of IC fabrication [9; 21]. The design structures referenced in [1; 2; 3; 4; 5; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 23; 25; 26; 28] further employ external passive resistors for their implementations. * The electronic tuning feature is a crucial characteristic of modern analog signal processing circuits. The filter architectures described in [2; 9; 11; 22; 25; 26] lack the characteristic of electronic tunability. * Configurations capable of operating as both a mixed-mode universal filter and QO with the same structure seem to be more useful and versatile in signal processing circuits and solutions. It was intended for the circuit configurations presented in [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 15; 16; 17; 18; 19; 20; 21; 22; 23; 26; 27; 28] to function solely as universal filters or as QO circuits. * Experimental measurements are a crucial method for assessing the feasibility of the circuit for acceptance purposes. In [4; 5; 7; 8; 9; 11; 12; 13; 16; 23; 24; 25; 27; 28], the features and applications of the circuits were evaluated by only computer simulations. In the present scenario, mixed-signal processing systems necessitate interaction between current-mode (CM) and voltage-mode (VM) circuits. To enable a distortion-free interface between CM and VM sections, transimpedance-mode (TIM) and trans admittance-mode (TAM) circuits are required to satisfy this criterion. The voltage differencing gain amplifier (VDGA) has emerged as an alternative active component in recent years for a wide range of analog generation circuits and signal processing tasks [13; 29; 30]. The VDGA generally has three voltage-controlled current sources, each possessing the requisite number of outputs, which are internally interconnected sub-circuits. Active components with multiple adjustable characteristics are especially advantageous in circuit design and synthesis. The resulting circuit solutions frequently enable electronic control of many parameters.