Improving Absolute Accuracy of Integrated Resistors With Device Diversification

This brief employs an unorthodox optimization approach inspired by portfolio diversification to improve the absolute accuracy of integrated resistors. The similarity between minimizing resistor variation and maximizing expected returns-a classic problem investigated in modern portfolio theory-allows us to exploit the idea of diversification. We analytically demonstrate that a weighted combination of different types of resistors can form an optimal composite resistor that exhibits less variation than the fabrication tolerance of its constituent resistors. The proposed technique is validated by both the simulations in 250-, 180-, 130-, 90-, and 65-nm CMOS technology and the measurements in Taiwan Semiconductor Manufacturing Company 65-nm CMOS process. Data obtained from 80 test chips fabricated in two wafer runs show 60% lower resistor variation and 2× improved accuracy, compared with the baseline single resistor of the same value and area. This method can simultaneously compensate for the temperature variation of integrated resistors as well.