Synthesis of Configurable Voltage-Mode Biquads via Augmented NAM Expansion and Symbolic Mapping

A systematic synthesis framework based on augmented nodal admittance matrix expansion and symbolic mapping for configurable voltage-mode biquadratic filters that guarantee orthogonal control over the quality factor and pole frequency is presented. The methodology builds upon an established denominator polynomial to ensure high selectivity stability and easy adjustment of filter parameters. By formulating an augmented $3\times 3$ core admittance matrix embedded with two symbolic control variables, the proposed framework can be used to derive various filtering functions by using nodal admittance matrix expansion technique. The low-pass, high-pass, band-pass, notch, and all-pass responses are systematically extracted from this single hardware core with five input and two output voltage ports. Since the pole-generating matrix core remains completely invariant, the orthogonal parameter tunability of the active network is preserved for all extracted filter types. These synthesized filter functions are realized with current conveyors and the non-ideality of active devices is explored. The workability of the obtained multiple-input multiple-output filter is verified through HSPICE simulations using TSMC 0.18 μm CMOS technology, demonstrating the feasibility of the proposed method.