Bandgap Reference Calculator
Design a temperature-compensated bandgap voltage reference. Computes Vref, PTAT current scaling, and resistor ratios for first-order temp compensation.
How to Use
- Enter target reference voltage (typically 1.2-1.25 V for silicon bandgap).
- Enter PTAT current and BJT emitter area ratio N (typically 8).
- Tool computes resistor values for first-order temperature compensation.
Show Work
Formulas
History of the Bandgap Reference
Bob Widlar at Fairchild Semiconductor invented the first practical bandgap reference in 1971 (the LM113), exploiting the predictable ~2 mV/C negative TC of a forward-biased diode and the matching positive TC of delta-Vbe between two transistors at different current densities. The sum lands near the silicon bandgap energy (~1.2 eV at 0 K). The LM399 (1970s), LTZ1000 (1984), and modern LM4040/REF5025 references all trace their topology to Widlar's 1971 design - extended with curvature correction and on-chip trim to achieve sub-1 ppm/C in the best references.
About This Calculator
Enter target Vref (1.2-1.25 V typical for silicon), PTAT current, emitter area ratio N (typically 8), and temperature. The tool computes ΔVbe = Vt·ln(N), resistor R1 = ΔVbe/I_PTAT, and R2/R1 ratio needed to make Vref = Vbe + (R2/R1)·ΔVbe.
This is a first-order bandgap. For production ICs, add curvature correction and on-die trim for < 5 ppm/°C performance. Classic discrete bandgap references like the LM431 (TL431) use this topology but are factory-trimmed to 1% initial accuracy. Everything runs client-side.
Frequently Asked Questions
Why 1.25 V?
Silicon bandgap voltage extrapolated to 0 K ≈ 1.205 V. A bandgap reference sums a negative-TC Vbe (~-2 mV/°C) with a positive-TC PTAT voltage to cancel to first order, landing at ~1.2-1.25 V.
PTAT?
Proportional-To-Absolute-Temperature. Created by the Vbe difference between two BJTs at different current densities: ΔVbe = Vt·ln(N) where N is emitter area ratio. At 300 K with N=8: ΔVbe ≈ 54 mV.
Temperature range?
Simple first-order bandgap: 20-50 ppm/°C over 0-70 °C. Trimmed second-order (curvature-corrected): < 5 ppm/°C over -40 to +125 °C. Precision buried-Zener references (LTZ1000): 0.05 ppm/°C.
Common Use Cases
ADC Reference
12-bit+ ADCs use internal bandgap for conversion reference. 1.235 V nominal across most MCUs.
LDO Regulator
LDO output = Vbg × (1 + R2/R1) — feedback around error amp.
DC/DC Setpoint
Buck converter target voltage sensed via voltage divider against bandgap.
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