A bandgap voltage reference is a temperature independent voltage reference circuit widely used in integrated circuits, usually with an output voltage around 1.25 V, close to the theoretical 1.22 eV bandgap of silicon at 0 K. This device was first published on by David Hilbiber in 1964. Bob Widlar, Paul Brokaw and others followed up with other commercially successful versions.
The voltage difference between two p-n junctions (e.g. diodes), operated at different current densities, is used to generate a proportional to absolute temperature (PTAT) current in a first resistor. This current is used to generate a voltage in a second resistor. This voltage in turn is added to the voltage of one of the junctions (or a third one, in some implementations). The voltage across a diode operated at constant current, or here with a PTAT current, is complementary to absolute temperature (CTAT—reduces with increasing temperature), with approx. −2 mV/K. If the ratio between the first and second resistor is chosen properly, the first order effects of the temperature dependency of the diode and the PTAT current will cancel out. The resulting voltage is about 1.2–1.3 V, depending on the particular technology and circuit design, and is close to the theoretical 1.22 eV bandgap of silicon at 0 K. The remaining voltage change over the operating temperature of typical integrated circuits is on the order of a few millivolts. This temperature dependency has a typical parabolic behavior.
Because the output voltage is by definition fixed around 1.25 V for typical bandgap reference circuits, the minimum operating voltage is about 1.4 V, as in a CMOS circuit at least one drain-source voltage of a FET (field effect transistor) has to be added. Therefore, recent work concentrates on finding alternative solutions, in which for example currents are summed instead of voltages, resulting in a lower theoretical limit for the operating voltage (Banba, 1999).
Note that sometimes confusion arises when using the abbreviation CTAT, where the "C" is incorrectly taken to mean "constant" rather than "complementary". To avoid this confusion, although not in widespread use, the term constant with temperature (CWT) is sometimes used.
Brokaw bandgap reference
^ D.F. Hilbiber (1964), "A new semiconductor voltage standard", 1964 International Solid-State Circuits Conference: Digest of Technical Papers 2: 32–33