PROBLEM 034 · Hard · The PTAT current
Hot Current
A current proportional to absolute temperature
The problem
Build a PTAT core. Two matched PMOS current sources from VDD (gates on the net “gate”, which the test bench drives) feed two branches. Branch 1 is a PNP with its emitter on the net “x”. Branch 2 is a resistor from the net “y” to the emitter of a PNP eight times larger. Both bases are on ground. The test bench forces “x” and “y” to the same voltage with an amplifier acting on “gate”, so the resistor carries the difference of the two Vbe’s: I = (kT/q)·ln(8)/R. Choose R for about 10 µA at 27 °C.
The two junctions carry the same current, but the larger one needs less Vbe: ΔVbe = Vt·ln(8) = 54 mV, and Vt = kT/q rises linearly with temperature. The current through the resistor is therefore proportional to absolute temperature (PTAT): about +0.33% per °C. Adding it to a CTAT voltage with the right weight is how a bandgap reference cancels the temperature coefficient.
The test bench
- Supply: VDD = 1.8 V.
- The test bench drives “gate” with an amplifier that forces “y” equal to “x” (the loop that makes both branch voltages match), and repeats the run at 0 °C, 27 °C and 85 °C. It reports the branch current at 27 °C and the ratio of the current at 85 °C to that at 0 °C. The bipolar is a generic substrate PNP model.
Numbers to hit
- Branch current at 27 °C between 8 µA and 12 µA
- Current at 85 °C ÷ current at 0 °C between 1.25 × and 1.38 ×
- Power at most 80 µW
Design it yourself
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- 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.
- Cold DiodeA forward-biased junction has a voltage of about 0.65 V that falls by about 2 mV for every degree. Set it with area and current.
- Thermal ZenAdd a PTAT voltage to a CTAT voltage with the right weight and the temperature coefficient cancels.