PROBLEM 033 · Easy · The base-emitter voltage
Cold Diode
A diode-connected PNP: a voltage that falls with temperature
The problem
Build a bias branch with one bipolar PNP: a Current source from VDD into its emitter, and its base on ground (the collector is the chip’s substrate, also ground). The emitter net is called “vbe”. Choose the current and the emitter area (the multiplier on the part) so that the voltage on “vbe” is between 0.60 V and 0.64 V at 27 °C.
A junction’s voltage follows Vbe = (kT/q)·ln(I/Is). Is grows very fast with temperature, so Vbe falls: about −1.5 to −2.2 mV per °C near room temperature. This complementary-to-absolute-temperature (CTAT) voltage is half of every bandgap reference. A larger area or a smaller current lowers Vbe.
The test bench
- Supply: VDD = 1.8 V.
- The test bench repeats the simulation at 0 °C, 27 °C and 85 °C and reports the voltage of “vbe” at each, and its slope in mV per °C. The bipolar is a generic substrate PNP model typical of a CMOS process, not a SKY130 PDK cell.
Numbers to hit
- Vbe at 27 °C between 0.6 V and 0.64 V
- Slope with temperature between -2.4 mV/°C and -1.4 mV/°C
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.
Sign in or create a free account →More on references and bias
- Poor Man's BiasThe simplest reference: a resistor feeds a diode-connected transistor, which a second transistor copies. See how badly it follows the supply.
- Diode DuoStack two diode-connected transistors under a resistor: a bias voltage that follows the supply only a fraction as much.
- BootstrapLet the circuit bias itself: a loop that sets the current from a resistor and the transistor ratio, almost ignoring the supply.
- Just EnoughA cascode transistor’s gate must sit one Vgs above its source node, which should itself sit one overdrive above ground. Generate that voltage.
- Hot CurrentTwo junctions of different area at the same current differ in Vbe by (kT/q)·ln(ratio): put that voltage across a resistor.
- Thermal ZenAdd a PTAT voltage to a CTAT voltage with the right weight and the temperature coefficient cancels.