1) In Ch. 20, on page 629 in Fig. 20.22, I am unclear of the reason Vreg is
connected to the gate of M2. Without that connection it would still work.
2) There is also a second feedback due to the cross-coupled MOSFET. What
is the function? How would that affect the DC operating point and stability?
Vreg is connected to the gate of M2 to make Vreg a low impedance node. In Fig.
20.19 Vreg is a high impedance node (meaning only drain connections). By diode
connecting M2 (connecting the gate and drain of M2 together so that its small
signal resistance is 1/gm) we only have one high-impedance node (in Fig. 20.22),
that is, Vbiasp. The reason for doing this is to make the feedback in the circuit
easier to make stable. The circuit in Fig. 20.19 is a two stage op-amp, a diff-amp
and a common-source amplifier made with M4. These topics are discussed in detail
in Ch. 24.
The reason we put that circuit in Ch. 20 instead of waiting until after we discuss
those topics, in Ch. 24, is so that we have a practical biasing circuits for
designing amplifiers and current mirrors in Chs. 21-23. Practical biasing allows
us to use real circuits for analysis and design.
The second cross-coupled MOSFET is used so that we have something to compare to
Vreg. We want the drains of M1 and M2 to be the same potential to minimize the
effects of VDD variations.