Dominant-Node Theory and Monitoring-Rescue Method for Eliminating Undesired Operating Points in the Self-Biased Reference Generators

A self-biased voltage/current reference (VCR) generator provides bias for its embedded operational amplifier simply by itself. But during the power-up process, it is prone to be trapped into an undesired operating point called Trojan state (TS-UOP) that a conventional startup circuit (CSC) is unable to handle. This paper firstly simulates the power-up process of a self-biased VCR generator and discovers the dominant node that plays the leading role in the power-up convergence. Then, a dominant-node theory is proposed to find the dominant node based on the voltage-vertex directed dependency graph (DDG) and the Weight-Flow algorithm. In order to rescue the dominant node, a Monitoring-Rescue method is proposed as a general approach to enhanced startup circuits (ESCs) to eliminate TS-UOPs. An example of ESCs is designed in a 28-nm CMOS process. The measurement results verify that the ESC successfully helps the self-biased VCR generator converge to the desired operating point (DOP) regardless of the power-up ramping time range of $\mathrm {100~ \mu \text { s} }$ to $\mathrm {100~ \text {m} \text { s} }$ and the temperature range of $\mathrm {-45~ ^{\circ}C}$ to $\mathrm {115~ ^{\circ}C}$ .