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 um and
longer, the square-law equations don’t model
the
devices well. Even for the 1 um
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 um 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.