Is g_m (and thus device f_T) independent of overdrive voltage (Eq. [9.57])

in nanometer (or long-channel) CMOS?

Both g_m and f_T vary greatly with the overdrive voltage. See Eq. (9.55)

(or, for long-channels, Eq. [9.36]) and Fig. 9.33.

The most important aspect of this dependence is that to increase CMOS

device speeds (f_T) you need to increase the overdrive voltage. This is

one of the reasons why we bias with the BMR (it's easy to set overdrive

voltage with changes in temperature and process).

The confusion comes from claims that short channel devices' f_T

does not vary with overdrive voltage because of saturation velocity effects

(as seen in Eq. (9.57) if v_sat is constant). v_sat isn't constant and does

depend on both V_GS and V_DS as indicated on page 299 (clearly g_m does

increase with overdrive as seen in Fig. 9.33). The reasons for the

variations in v_sat are outside the scope of the book (e.g. velocity

overshoot).

Biasing is often a neglected topic when learning to design CMOS analog ICs.

This is unfortunate because it is the MOST IMPORTANT topic in analog IC

design. When I look at someone else's design the first things I look at

are the threshold voltage of the process and then V_GS so I can determine

overdrive. If the V_GS is close to the threshold voltage (so overdrive

is close to zero) then I know that the design will be inherently slow (and

operating in weak inversion).

If the overdrive voltages vary from device to device then the design isn't

optimized for speed (it's that simple). If I need more speed, in a two stage

op-amp, I simply decrease the compensation capacitor (to push the unity gain

frequency, f_un = g_m/2pC_c, out to a higher frequency) and increase the widths

of the output buffer (keeping the overdrives constant, with an increase in

current). This pushes f₂ (see Eq. [24.24]) to a higher frequency (because

of the increase in g_m2 with the increase in device widths) so that f₂ > f_un.

Again, for general design set overdrives to 5% of VDD. For high-speed designs

set overdrive voltages to 10% of VDD or more.

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