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

with ron.


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.