On robustness of the stability of multiphase switched-capacitor two-ports

For any prescribed rational transfer function every pole of which is inside the unit circle , a set of multiphase switched-capacitor (MSC) two-ports denoted by is defined. The main theorem proved in this paper states that any MSC two-port belonging to does not have the robust stability under small perturbation of the capacitors. The presented set of MSC two-ports is so general as to include various types of SC filters designed such that they simulate the nodal equations of the analog reference ladders. In order to show the significance of the main theorem the robustness of the stability of two types of high-pass SC filters is examined. These examples show that an impedance-scaling technique does not always provide a solution to the problem of the high-pass filter realization based on the exact simulation of reactance ladders by the bilinear transformation. In the Appendix, a theorem which gives a sufficient condition for an MSC two-port to be stable in a robust sense is presented.