Some information about the Gm/ID design methodology. Useful as a handout for students or a cheat sheet.
Enz, C.C., Krummenacher, F. & Vittoz, E.A. An analytical MOS transistor model valid in all regions of operation and dedicated to low-voltage and low-current applications. Analog Integr Circ Sig Process 8, 83–114 (1995). https://doi.org/10.1007/BF01239381
Seems to be the origin of the gm/id parameter. This parameter is first proposed as a indicator of inversion strength. SPICE simulation models such as BSIM3 and BSIM4 use this parameter and you can see it in the output of a DC sweep.
Boris Murmann popularized a design methodology based on the gm/id parameter: https://github.com/bmurmann/Book-on-gm-ID-design
https://web02.gonzaga.edu/faculty/talarico/EE406/documents/gmid.pdf
Eric Yeh's videos on how to use gm/id for design, and how to extract the designing curves from a SPICE simulation: https://www.youtube.com/watch?v=horLp7FMTeA&list=PLQBJZzLTgobt8BlTD0spy4pPi2bccxw54
| gm/id | Region | Description |
|---|---|---|
| < 5 | Strong Inversion | High \(V_{OV}\), High speed, high power. |
| 5 ~ 20 | Moderate Inversion | Most Analog Circuits |
| 20 ~ 30 | Weak Inversion | Low Power |
| > 30 | Subthreshold | Ultra Low Power, Very Slow |
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| Parameter | Trend (typical) | Why |
|---|---|---|
| \(g_m\) @ fixed \(I_D\) | \(\uparrow\) | \(g_m=\eta I_D\) |
| Current @ fixed \(g_m\) | \(\downarrow\) | \(I_D=g_m/\eta\) |
| Power @ fixed \(g_m\) | \(\downarrow\) | \(P\propto I_D\) |
| Intrinsic gain \(g_m / g_{DS}\) | \(\uparrow\) then \(\downarrow\) | \(g_{DS} \uparrow\) due to short channel effects |
| \(f_T\) | \(\downarrow\) | caps grow + weak inv slower |
| Small-signal BW of a stage | depends | \(g_m\) \(\uparrow\) but caps \(\uparrow\) |
| Slew rate | no change @ fixed \(I\) | \(SR=I/C\) |
| Thermal noise | improves @ fixed \(I\) | Current Noise \(\propto 1/g_m\) |
| 1/f noise, mismatch | usually improves | Larger \(W\cdot L\) |