Source follower input/output swing

Question

I found in this book at the page 271 a definition of the source follower input/output swing ( that i didn`t know as:

$$ V_{in-pp} = V_{dd} - ( Vt + 2.V_{ds-sat} )$$

I tried to understand how to calculate this paramater (I've tried to consider the condition for having the MOSFET in saturation V_ds > V_d-sat and active V_gs > V_t), but I didn`t arrive to the same result. Considering: V_ds > V_d-sat

and

V_in= V_out + V_GS

I obtained

V_out < V_dd - V_d-sat

or equivalently

V_in < V_dd +V_gs - V_d-sat

Can somebody help me?

Book Name: Analog/RF and Mixed-Signal Circuit Systematic Design (pag271) Schematic:

Answer 1

We can arrive at their answer by adding the following assumptions, which are reasonable enough though not universally true:

1. \$V_{in}\$ can never go above \$V_{DD}\$ or below ground.
2. The current source \$I_b\$ needs headroom of at least \$V_{dsat}\$.
3. We can approximate \$V_{gs} = V_{dsat} + V_{t} \$

Then the maximum value of the input is just \$V_{DD}\$.

The minimum value of the output is \$V_{dsat}\$, so:

$$V_{in,min} = V_{GS} + V_{out,min} = (V_t + V_{dsat}) + V_{dsat}$$

Thus:

$$V_{in,pp} = V_{DD} - (V_t + 2 V_{dsat})$$