Novel stabilising functions for configuring stability-guaranteed and low-quantisation-sensitivity biquad-cascaded tunable filters
Tian–Bo Deng · International Journal of Electronics Letters · 2025
This paper reveals five novel below-unity (BU) functions for stabilising a recursive biquad-cascaded tunable filter. The tunable filter is configured by serially connecting multiple biquad blocks, and guaranteeing the stability of the entire configuration requires each serially-connected biquad to be stable. This is accomplished by exploiting the BU functions to express the biquad parameters as the BU functions. As compared with the existing functions needing a factor to scale the expressions, the novel BU functions drop the factor and thus simplify the expressions. After revealing those functions, this paper further investigates an algorithm for designing the biquad-cascaded tunable filter based on the least L1-norm-error metric, aiming to minimise the mean-absolute-error of the gain response. This novel design exploits both biquad-cascaded structure and the simplified coefficient expressions, leading to a biquad-cascaded tunable filter with definitely ensured stability and mitigated quantisation errors in the practical hardware configurations. Simulating the design of a tunable band-stop filter demonstrates that the band-stop tunable filter can implement the ideal band-stop response with a significantly small L1-norm-error while always remaining stable during the band-stop tuning.