Analog CMOS - Small-signal, DC, bias, large-signal

Question

I have a question about this page from this book - Design of Analog CMOS Integrated Circuits.

The author isn't being very clear on distinguishing what is small-signal and what is large-signal. In the point marked (1), a step is applied at Vin,CM. Is this small-signal or large-signal. From the point marked (2), I believe it should be a small-signal step since the author is using g_m for the gain. However, in the point marked (3), he is stating that bias points are affected.

I'm confused. Is the Vin,CM step supposed to be treated as small-signal or large-signal? If it is large-signal, then g_m cannot be assumed to be fixed?

Or is the author just using this to gain intuition and not being rigorous.

Answer 1

"Gain" is, almost exclusively, a small-signal parameter.

However, even if you think about large-signal behavior, what you should note is the overall magnitudes of the different parameters.

In most VLSI circuits, 1/(2g_m) is quite a bit less than R_SS which means that the common mode gain is roughly proportional to R_D/R_SS. Designers tend to make R_SS greater than R_D, so the common mode gain is fairly insensitive to even large-signal changes (until the transistors drop out of saturation) as the common mode gain is less than 1 (generally by quite a bit).

Compare this to the differential gain which is proportional to -g_m * R_D which is quite a bit more sensitive large-signal features.

Hope this helps.