PROBLEM 031 · Expert · The self-biased (beta-multiplier) reference
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Self-biased current reference
The problem
Build a beta-multiplier reference. Two NMOS share a gate: M1 is diode-connected (its drain on the gate net), M2 is four times as wide (use four times the multiplier) and has a resistor from its source to ground. Two matching PMOS (sources on VDD, gates joined) force the two branches to carry equal currents: M3 is diode-connected on M2’s drain and M4’s drain is M1’s drain.
The equal branch currents make M1’s Vgs larger than M2’s by exactly I·R: the current is set by R and the transistor ratio, not by VDD. A circuit like this has a second stable state with no current at all, so add a start-up path: a resistor of about 20 MΩ from VDD to M1’s gate net is enough to kick it into the right state without disturbing it.
The test bench
- Supply: VDD = 1.8 V.
- The test bench reports the supply current (the sum of the two branches) at 1.8 V and sweeps the supply from 1.4 V to 2.2 V, so you can see how little the current moves.
Numbers to hit
- Supply current at 1.8 V between 25 µA and 70 µA
- Supply sensitivity at most 20 %/V
- Power at most 140 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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