Performance verification of start-up circuits in reference generators

A new approach for identifying the number of stable equilibrium points in supply-insensitive bias generators, references, and temperature sensors based upon self-stabilized feedback loops is introduced. This provides a simple and practical method for determining if these circuits require a "start-up" circuit and, if needed, for verifying that the start-up circuit is effective at eliminating undesired stable equilibrium points in the presence of process and temperature variations. This approach is demonstrated by considering the wel-lrecognized inverse Widlar bias generator/temperature sensor as an example.