Dominik Przyborowski
Advanced Member level 4
If you don't want to read heresy skip this paragraph.
[oozing the venom mode on]
I have read a lot of books (in various fields) and I can conclude, I understood idea behind burning them.
Square law is a result of very strong simplification, weak assumptions and basically does not work in region of interest of analog design.
In this particular OTA example, only these PMOS devices can has close values changes by doubling current and/or decreases W/L ratio - they are already far in strong inversion (and velocity saturation effect in PMOS is experienced a bit later than in NMOS).
Commonly academics are repeating it during lectures, because nowadays academia has nothing common with science and principles which was standing long time ago behind it. So, Mr professors are uses argument "ad auctoritatis" , because one or other "a great scientist is/was" and barely investigates what they are teaching.
[oozing the venom mode off]
Above is an harmful generalization of academia society and I am aware that there is a lot of good faithful scientists believing in they mission.
However, cancer cells doesn't need to be in majority to kill organism.
The only application for square law may be somehow useful is to estimate on-resistance of highly overdriven switch with high tolerance.
[oozing the venom mode on]
I have read a lot of books (in various fields) and I can conclude, I understood idea behind burning them.
Square law is a result of very strong simplification, weak assumptions and basically does not work in region of interest of analog design.
In this particular OTA example, only these PMOS devices can has close values changes by doubling current and/or decreases W/L ratio - they are already far in strong inversion (and velocity saturation effect in PMOS is experienced a bit later than in NMOS).
Commonly academics are repeating it during lectures, because nowadays academia has nothing common with science and principles which was standing long time ago behind it. So, Mr professors are uses argument "ad auctoritatis" , because one or other "a great scientist is/was" and barely investigates what they are teaching.
[oozing the venom mode off]
Above is an harmful generalization of academia society and I am aware that there is a lot of good faithful scientists believing in they mission.
However, cancer cells doesn't need to be in majority to kill organism.
I don't remember this book, so I don't know whether there is information about range of application of square law relation. On the figure (f) is marked that such relation is not true in all regions, so maybe somewhere in book it was mentioned. I believe author is aware about limitations and are using square law to show trends and mnemotechnic which might be useful for beginner (this book was published ca 2000, so EKV and ACM were already succesfully used, and leading processes like 0.5µ, 0.35µ, 0.25µ already showed limitations of square law).
This book of Allen and Holberg was published in mid-80s. If you look on perspective these times, you may find that BSIM was not known, or just started development (i'm not sure publication year) and considering load and compensation capacitances are (the most probably) much higher than gate capacitances (notice tox in 0.35 is in order of 7nm, while for 80s process like 2.5µm it was ca 100× more). So, it simplifies design considerations. First, effect of Cgs was negligible, second, verification with spice models was like applying square law equations. Also, with 5-10V of supply it was not a problem to going into IC>100.
The only application for square law may be somehow useful is to estimate on-resistance of highly overdriven switch with high tolerance.