I
have a question about the MOS switching resistance calculation for the book’s
long-channel process
discussed in Sec. 10.1. Using Eq. (10.6) a value of
4.72k •L/W
is calculated but, as seen in Table 10.1, the value calculated from
Fig.
10.5 is 15k •L/W. Why the large
difference?
Equation
(10.6) assumes a constant value of KP,
constant threshold voltage, and
that the devices
follow the square-law equations...they don't. The results will be (are)
different from the
results we get when KP is varying (from,
for example, velocity
saturation). This
equation is useful to understand where the model comes from but in
all practical cases it's better to
use simulations to determine the effective switching
resistance since the
results come from measurements (the MOSFET models are
determined empirically).
Note that this question was already answered immediately
following
Fig. 10.6 and Eq. (10.6) on page 314.
It’s
important to understand that unless the CMOS technology you are dealing with is
very old, say
channel lengths 5 mm and longer, the square-law equations
don’t model
the devices well. Even for the 1 mm devices
discussed in the book using the square-law
equations to model their
electrical behavior is questionable. For example, the NMOS
output resistance
plotted in Fig. 9.24 varies from 2.5 to 7 MW with changes in
VDS
even though VGS is constant. The equation
for the output resistance derived from the
square-law equations, Eq.
(9.6), predicts a constant output resistance. Again though,
as mentioned in the preface,
mathematical rigor is needed when learning circuits so
even though the
square-law equations have limited practical use it’s still a good idea
to use them so that the students
can derive various parameters and equations governing
circuit operation. It
just needs to be clear that the results will not match the silicon (or
the simulation results) but rather
just be close (for L of 1 mm and longer,
square-law
equations are useless in
nanometer CMOS technology and so the graphical approach
presented
in the book must be used when designing).
Note
that we could have avoided comparing simulation results, like the ones seen in
Fig.
9.24 and literally dozens of other figures in the book, to hand calculations or
simply used a Level 1
SPICE model (the model derived from square-law equations)
instead of real devices
and models. Both of these approaches are very, very common
in textbooks. Unfortunately though
both are impractical if at some point the engineer’s
or student’s calculations have to
be used as a starting point to design real silicon circuits.
Fiddling
with a design in SPICE until it works, under one set of conditions, with no
concrete starting point
or understanding of the circuit’s operation and limitations, isn’t
wise. Simulate what
you think will work based upon your calculations and then
investigate any significant
differences between your understanding and the simulation
results.