Explain the design of a precision bandgap voltage reference with curvature compensation.

Basic bandgap combines PTAT (proportional to absolute temperature) voltage from delta-VBE of two transistors at different current densities with CTAT (complementary to absolute temperature) VBE. Reference Vref = VBE + K*delta_VBE where K is chosen to cancel first-order temperature dependence, yielding approximately 1.25V (silicon bandgap). Curvature compensation addresses higher-order terms: Techniques include adding nonlinear current source (exponential or squared PTAT), using beta-compensated VBE subtraction, implementing piecewise-linear correction, or employing trimmed resistor ratios. Advanced designs achieve < 5ppm/C temperature coefficient. Also address: supply rejection, noise, and start-up circuits.