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 startup circuit is effective at eliminating undesired stable equilibrium points in the presence of process and temperature variations. This approach is demonstrated by considering the well-recognized inverse Widlar bias generator/temperature sensor as an example.