Brokaw bandgap reference

Brokaw bandgap reference is a voltage reference circuit widely used in integrated circuits, with an output voltage around 1.25 V with only little temperature dependence. This particular circuit is one type of a bandgap voltage reference, named after the author of its first publication.[1]
The theoretical circuit of a Brokaw bandgap

Like all temperature-independent bandgap references, the circuit maintains an internal voltage source that has a positive temperature coefficient and another internal voltage source that has a negative temperature coefficient. By summing the two together, the temperature dependence can be canceled. Additionally, either of the two internal sources can be used as a temperature sensor.

In the Brokaw bandgap reference, the circuit uses negative feedback (e.g., an operational amplifier) to force a constant current through two bipolar transistors with different emitter areas. By the Ebers–Moll model of a transistor,

The transistor with the larger emitter area requires a smaller base–emitter voltage for the same current.
The base–emitter voltage for either transistor has a negative temperature coefficient (i.e., it decreases with temperature).
The difference between the two base–emitter voltages has a positive temperature coefficient (i.e., it increases with temperature).

The circuit output is the sum of the base–emitter voltage difference with one of the base–emitter voltages. With proper component choices, the two opposing temperature coefficients will cancel each other exactly and the output will have no temperature dependence.

See also

Bandgap voltage reference
LM317

References

^ Brokaw, P., "A simple three-terminal IC bandgap reference", IEEE Journal of Solid-State Circuits, vol. 9, pp. 388–393, December 1974.

External links

Original IEEE paper (pdf) – This is the 1974 paper describing the circuit.
A Transistor Voltage Reference, and What the Band-Gap Has To Do With It – This 1989 video features Paul Brokaw explaining his bandgap voltage reference.
ELEN 689-602: Introduction to Bandgap Reference Generators – Includes detailed description and analysis of Brokaw bandgap reference.
The Design of Band-Gap Reference Circuits: Trials and Tribulations — Robert Pease, National Semiconductor (shows Brokaw cell in Figure 3)
ECE 327: LM317 Bandgap Voltage Reference Example – Brief explanation of the temperature-independent bandgap reference circuit within the LM317. The circuit is nearly identical, but the document discusses how the circuit allows different currents through matched transistors (rather than a single current through different transistors) can set up the same voltages with opposing temperature coefficients.