2026-08-19
In 1971, Bob Widlar published a deceptively simple circuit that changed analog IC design forever: a voltage reference built from just two BJTs and three resistors, producing a temperature-stable output around 1.25 V without needing a Zener diode. Every LM317, LM385, and countless op-amp bias networks trace their DNA back to this circuit.
The core trick is exploiting the difference between two BJT base-emitter voltages (ΔVBE) operating at different current densities. A single VBE has a negative tempco of roughly −2 mV/°C. But ΔVBE between two transistors running at a current ratio N has a positive tempco proportional to absolute temperature (PTAT):
Sum a properly scaled ΔVBE (positive tempco) with a VBE (negative tempco) and the temperature terms cancel. What's left is the silicon bandgap voltage extrapolated to 0 K — approximately 1.205 V.
The Widlar topology: Q1 runs at high current density, Q2 at low density (typically via a large emitter resistor R2). The voltage across R2 equals ΔVBE. This PTAT current flows through R3, developing a PTAT voltage that adds to Q2's VBE. Choose R3 so this sum equals ~1.25 V, and you have zero tempco at your design temperature.
Design example: For a 10:1 current ratio (N=10), ΔVBE ≈ 26 mV · 2.3 = 60 mV. To cancel a −2 mV/°C VBE tempco with a +0.2 mV/°C ΔVBE tempco, you need a gain of 10. So develop 600 mV of PTAT voltage across R3, added to a 600 mV VBE, giving 1.2 V out. If your PTAT current is 10 µA, then R3 = 60 kΩ.
Real-world example: The LM113 (Widlar's own 1971 part) uses this exact topology to produce a 1.22 V reference with 100 ppm/°C drift, powered from as little as 500 µA. It became the guts of the LM10 op-amp and the biasing core of the μA741's successors. Modern parts like the LM4041 still use recognizable Widlar descendants.
Rule of thumb: First-order Widlar references drift about 20–50 ppm/°C over commercial temp range. To do better, you need curvature correction (a covered topic) to cancel the residual T·ln(T) term. Also: match transistor pairs tightly — 1 mV of VBE mismatch translates directly to output error.