I have some questions about the SF gain calculations on page 670 and 691
As I am going through Ch. 21, I have a question on the Av calculation for the
SF Amp on page 691. If I use the earlier approach in calculating the gain,
shouldn't it be something like
vout = (1/gmn || ron)id (the resistance looking into the source, 1/gmn, in parallel with ron)
vin = (1/gmn + ron)id (vin = vgs + vds)
Therefore, vout/vin = (1/gmn)/(ron + 1/gmn) which is different from the Av in the book (and
close to zero). What am I doing wrong?
On page 670 the load is a gate-drain connected device with a small-signal
resistance of approximately 1/gmn so what you've written for vout above
is correct for Fig. 21.15. On page 691 the load is infinite (that is why
we've included the body effect on pages 691-692). So for vin in the NMOS
SF on page 670, and assuming 1/gmn << ron, we get
vin = vgs2 + id(1/gmn) = id(1/gmn + 1/gmn)
knowing vout = id/gmn leads to Eq. (21.33). You likely already understand
this so let me try and answer your question a different way.
In Fig. 21.40 note that the MOSFET’s output resistance isn't included in the
calculation. The ron ends up having a small effect compared the body effect. If
you think of the MOSFET’s output resistance going from drain to source of the
MOSFET (drain is at AC ground) then you shunt the ideal DC current source
Now, you can write, neglecting body effect,
vout = idron
vin = vgs + idron = id(1/gmn + ron)
vout/vin = ron/(1/gmn + ron)
which is approximately 1 and what we derived for the SF with current source
load, Fig. (21.39) and Eq. (21.89).
Why wasn't ron included in the calculation on page 691? Because with body
effect we get a gain of, for example, 0.7 while with the MOSFET’s output
resistance included in the gain calculation, with no body effect, we get to 0.98.