CMOS Voltage References: An Analytical and Practical Perspective

7

High Order Curvature Correction

In theory, the voltage reference circuit can obtain a near-zero TC voltage by the mutual compensation of properly scaled CTAT and PTAT voltages. In practice, the CTAT and PTAT voltage sources are seldom precisely linearly proportional to temperature. To understand the temperature dependency of various voltage sources, let’s consider the Taylor series expansion of the CTAT voltage V_BE(T) in the opamp based β-multiplier bandgap voltage reference circuit at T_(nom) as shown in Equation 7.1 in a sequel. We can observe that the V_BE(T) voltage has high order temperature dependent terms. The opamp based β-multiplier bandgap voltage reference circuit considered in previous chapters generates the reference voltage by linear combination of the CTAT and PTAT voltages will be able to achieve mutual compensation of the first order temperature dependent terms of the CTAT and PTAT voltages. As a result, the opamp based β-multiplier bandgap voltage reference circuit is said to be a voltage reference circuit with first order temperature compensation. Using a similar argument, most of the temperature compensated voltage reference circuits presented in previous chapters are first order temperature compensated voltage reference circuits. Since the first order temperature compensated voltage reference circuit does not compensate the high order temperature dependent terms of the CTAT and PTAT sources, as a result, when the PTAT and CTAT terms are nonlinear functions ...