Dynamic modelling of analog integrated filters for the stability study of on-chip automatic tuning loops

Continuous-time filters with automatic tuning loops are feedback nonlinear systems with potential instability. If a stability study is to be carried out, even if it is at least local, the appropriate linear dynamical modelling of the filter should be obtained. This modelling is mandatory if an improved design of the loop controllers is to be carried out. This work presents the dynamic modelling of a CMOS continuous-time analog filter with automatic tuning capability. The analysis leads to an equivalent small-signal linearised incremental model from which transfer functions between output variables and control voltages are obtained. The dynamic modelling of both the phase-shift between input and output signals as well as the output amplitude, required to properly tune both frequency and quality factor parameters, is presented. The analysis leads to the design of a compensated loop with enhanced stability and dynamic performance.