PROBLEM 035 · Expert · The bandgap voltage reference
Thermal Zen
A bandgap reference: 1.2 V that ignores temperature
The problem
Extend the PTAT core into a bandgap reference. Add a third PMOS current source (source on VDD, gate on “gate”) whose drain is the output net “vref”, followed by a resistor R2 from “vref” to the emitter of a unit-area PNP (base on ground). The three PMOS carry the same current, so “vref” = Vbe3 + R2·I, with I the PTAT current of the core. Choose R2 so that the output sits near 1.2 V and does not move with temperature.
Vbe falls about 1.8 mV/°C, and R2·I rises with temperature: with the right R2/R1 ratio the two cancel to first order and the output is the silicon bandgap voltage, about 1.2 V. The test bench measures the output at 0 °C, 27 °C and 85 °C, and the spread is what you minimise.
The test bench
- Supply: VDD = 1.8 V.
- The test bench drives “gate” with an amplifier that forces “y” equal to “x” and repeats the run at 0 °C, 27 °C and 85 °C. It reports the output voltage at 27 °C and the difference between the highest and the lowest output over the three temperatures. The bipolar is a generic substrate PNP model.
Numbers to hit
- Reference at 27 °C between 1.1 V and 1.3 V
- Spread over 0 to 85 °C at most 20 mV
- Power at most 150 µW
Design it yourself
Draw the circuit on a schematic canvas, size every transistor, and see it simulated in your browser with ngspice and the SkyWater SKY130 models. Every transistor lights up green, gold or red by operating region as you move the sliders.
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