PROBLEM 079 · Medium · Thermal noise and gm
Quiet, Please
Noise of a common-source stage
The problem
Build a common-source amplifier: an NMOS with its source on ground and its gate on an Input source named “in”, with a resistor from VDD to the drain “out”. The test bench measures its noise referred to the input, integrated from 10 Hz to 1 MHz.
The channel’s thermal noise referred to the gate is √(4kT·γ/gm), with γ near 2/3: a larger gm means less input-referred noise. The load resistor adds 4kT·R_D at the output, which is small at the input if the gain is high. Flicker (1/f) noise adds at low frequencies and shrinks with the gate area W·L.
The test bench
- Supply: VDD = 1.8 V.
- The test bench hangs a 200 fF load capacitor from “out” to ground, applies the AC stimulus to “in”, and runs a noise analysis from 10 Hz to 100 MHz with “out” as the output and “in” as the reference input.
- Input-referred noise is the output noise divided by the gain: what an ideal noiseless amplifier would need at its input to produce the same output noise.
Numbers to hit
- Gain at least 10 dB
- Input-referred noise, 10 Hz to 1 MHz at most 15 µV
- Power at most 300 µW
- Every transistor in saturation
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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