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.
About the Bandgap Reference Calculator
Bandgap Reference Calculator is a quick, free tool for electronics and circuit design. It works in your browser and keeps everything on your device. Design a temperature-compensated bandgap voltage reference. Computes Vref, PTAT current scaling, and resistor ratios for first-order temp compensation.
How it works
Enter your figures and the result appears instantly, updating the moment you change anything. There is no submit button and nothing to wait for, so it is easy to try a few what-if numbers and compare the results. Just check each box holds the kind of value it expects.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
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.
How do I use the Bandgap Reference Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
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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