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 A_v calculation for the

SF Amp on page 691. If I use the earlier approach in calculating the gain,

shouldn't it be something like

v_out = (1/g_mn || r_on)i_d   (the resistance looking into the source, 1/g_mn, in parallel with r_on)

v_in = (1/g_mn + r_on)i_d   (v_in = v_gs + v_ds)

Therefore, v_out/v_in = (1/g_mn)/(r_on + 1/g_mn) which is different from the A_v 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/g_mn so what you've written for v_out 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 v_in in the NMOS

SF on page 670, and assuming 1/g_mn << r_on, we get

v_in = v_gs2 + i_d(1/g_mn) = i_d(1/g_mn + 1/g_mn)

knowing v_out = i_d/g_mn 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 r_on 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 r_on.

Now, you can write, neglecting body effect,

v_out = i_dr_on

v_in = v_gs + i_dr_on = i_d(1/g_mn + r_on)

v_out/v_in = r_on/(1/g_mn + r_on)

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 r_on 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.

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