In short: A bandgap reference produces a stable voltage near 1.2 V that barely drifts with temperature. It does this by adding a voltage that falls with heat (CTAT) to one that rises with heat (PTAT) in just the right ratio, so the two slopes cancel.
A bandgap reference is an analog circuit that generates a fixed, predictable DC voltage that stays almost constant across temperature, supply voltage, and process variation. The name comes from the output value, roughly 1.2 V, which tracks the extrapolated bandgap energy of silicon (about 1.22 eV at 0 K). Almost every data converter, voltage regulator, oscillator, and power-management IC leans on one of these references to define "what a volt is" for the rest of the chip.
The core challenge is temperature. A plain diode or resistor divider drifts by thousands of parts-per-million per degree Celsius. A bandgap reference instead deliberately combines two temperature behaviours that pull in opposite directions, so their drift cancels to near zero over the operating range.
Two complementary temperature coefficients do the work:
Here k is Boltzmann's constant, q is electron charge, T is absolute temperature, and N is the ratio of current densities (set by emitter-area ratio or current mirror ratio). The term kT/q is the thermal voltage VT, about 26 mV at room temperature, and it rises predictably with T.
The output is built as:
VREF = VBE + M · ΔVBE
VBE contributes about −2 mV/°C. ΔVBE contributes roughly +0.085 mV/°C per unit, so it must be multiplied by a gain factor M (set by resistor ratios and the current-density ratio N) until its positive slope is about +2 mV/°C. When the two slopes are equal and opposite, the first-order temperature coefficient of VREF becomes zero.
At that balance point, the two voltages add up to the silicon bandgap voltage extrapolated to 0 K, which is why the result lands near 1.2 V rather than any arbitrary value. The magic is not the number itself but the fact that a material constant falls out of two measurable, opposing transistor behaviours.
Paul Brokaw's 1974 topology uses two bipolar transistors with an emitter-area ratio of N:1, an op-amp forcing equal collector currents, and two resistors. ΔVBE appears across one resistor to set a PTAT current; the IR drop across a second resistor provides the PTAT term, which stacks on one VBE to form the reference. It is compact and widely taught.
This version uses an op-amp to force equal voltages at two nodes feeding diode-connected transistors of different area. The op-amp's virtual-short action fixes the current-density ratio, and resistor ratios scale the PTAT contribution. It is the form most common in CMOS designs, often with substrate PNP transistors.
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Explore CourseTron Courses →Because at the temperature-balanced point, VBE plus the scaled PTAT term equals the silicon bandgap voltage extrapolated to absolute zero, about 1.2 V. The value is set by physics, not by resistor trimming.
PTAT voltage rises linearly with absolute temperature (it comes from ΔVBE), while CTAT voltage falls with temperature (it is the VBE of a forward-biased junction). Summing a scaled PTAT with a CTAT cancels the temperature dependence.
The self-biased loop has two valid operating points: the useful one and a degenerate state with zero current. A start-up circuit injects a small current at power-on to force the loop into the correct point, then disengages.
Yes. Sub-bandgap or current-mode references generate PTAT and CTAT currents, sum them, and drop the result across a chosen resistor, giving any target voltage (for example 0.6 V) suitable for low-voltage supplies.
Related: current mirror circuit · Glossary · all courses.