PROBLEM 006 · Medium · Weak inversion and area
Barely On
Weak inversion: the most gm per microamp
The problem
Connect one NMOS with its source at ground, its drain on VDD and its gate driven by an Input source named “in”. The drain current is the supply current.
Biased near or below threshold, a transistor is in weak (or moderate) inversion: Id grows exponentially with Vgs and gm/Id reaches its theoretical maximum of about 1/(n·kT/q), near 25 per volt. This is how micropower circuits get gain from nanoamps, but it needs a very wide device, so area is the price.
The test bench
- Supply: VDD = 1.8 V.
- The test bench reads the supply current, and sweeps the source named “in” from 0 V to 1 V. The gate area is the sum of W·L·M over your transistors.
Numbers to hit
- Drain current between 4.75 µA and 5.25 µA
- Gate voltage Vgs at most 0.52 V
- Efficiency gm/Id at least 18 1/V
- Gate area W·L·M at most 150 µm²
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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