Please comment on the definition of VOH and VOL for the inverter, Ch. 11?


In your Fig. 11.2 you define VOH, for example, as the maximum inverter output

voltage and VOL as the minimum inverter output voltage. However, I've seen a few

others, including, that define VOH (VOL) as the output voltage

when the input is at VIL (VIH).


Good question. Defining VOH (VOL) when the inverter's input is VIL (VIH) is more

exact for specifying the noise margins, Eqs. (11.1) and (11.2). However, if you

look at the difference in a practical inverter the numerical difference between

the two methods is minor. It's much easier (and more practical) to determine

VOH and VOL using the definitions presented in Ch. 11.


For example, looking at the short channel inverter VTC in Fig. 11.4 the inverter's

VIL = 350 mV (at this voltage VOH = 944 mV) and VIH = 514 mV (at this voltage VOL

= 65 mV). So


NMH = VOH - VIH = 430 mV


NML = VIL - VOL = 285 mV


Now using the book's definitions, VOH = VDD = 1 V and VOL = 0 V we get


NMH = 486 mV (difference of 56 mV)


NML = 350 mV (difference of 65 mV).


However, let's look at how much VIL and VIH vary for VTC slopes changing from -0.5

to -1.5 instead of just looking at the values when the slope is -1. In this range

VIL varies from 300 to 370 mV (70 mV) and VIH varies from 500 to 555 mV (55 mV).

This variation is comparable to the difference seen using the two different methods.


Perhaps this minor difference is why most books use the engineering approximation of

VOH /VOL corresponding to the max/min inverter output voltages. Again, good question.


One last comment; CMOS is a unique logic family where the logic outputs can swing

from VDD to ground. In many logic families the outputs don't swing all the way to

the power supply rails. VOH isn't equal to VDD and VOL doesn't equal ground as

discussed in the book.