2026-08-24
The Brokaw bandgap reference, invented by Paul Brokaw at Analog Devices in 1974, solved the biggest weakness of the Widlar bandgap: it produces its reference voltage at a high-impedance summing node that you can buffer and scale independently, and it forces equal collector currents in its two transistors through elegant use of an op-amp feedback loop. This architecture is the foundation of the AD580, AD584, LT1009, and countless modern references.
How it works: Two BJTs Q1 and Q2 have an emitter area ratio of N:1 (typically 8:1). Their collectors tie to matched resistors R feeding a positive supply. An op-amp senses the two collector voltages and drives the common emitter node through R2, forcing the collector voltages — and therefore the collector currents — to be equal. Because Q1 and Q2 carry identical currents but have different emitter areas, they develop a ΔVBE across the emitter degeneration resistor R1:
The VBE term has a negative tempco (~-2 mV/°C) and the PTAT term has a positive tempco. Choose R2/R1 so the two cancel, and you land near 1.25 V with tempco under 10 ppm/°C.
Rule of thumb: For N=8 emitter area ratio, ln(8) ≈ 2.08, and VT = 25.85 mV at 27°C, giving ΔVBE ≈ 53.8 mV. You need the PTAT contribution at VREF to reach ~525 mV to balance VBE's ~650 mV negative-slope term. That requires 2·(R2/R1)·53.8 mV = 525 mV, so R2/R1 ≈ 4.88.
Why it beat Widlar: The Widlar's output sits on top of a BJT collector — noisy, current-limited, and hard to buffer without disturbing the bias loop. Brokaw's output is a proper op-amp node with low output impedance and easy scaling. Want 2.5 V or 5 V? Just add a gain resistor in the op-amp feedback path.
Real-world example: The AD580 (still in production 50 years later) is a straight Brokaw cell trimmed for 2.5 V ±0.4% with 10 ppm/°C tempco in a TO-52 can — it powers instrumentation amps in medical monitors and 4-20 mA transmitters where you cannot afford calibration drift over a 20-year deployment.