I have some questions about the section 6.3.1(conversion gain) in chapter 6 (mixer) of the book rf microelectronics (2nd) by Razavi.

The equation where I marked with the comment is derived with the condition that M3 is cutoff and that current is flowing into one branch, and with this condition, the min Vx is derived as in equation (6.63). however, in equation (6.64), the max DC voltage acorss Rd is derived accordingly. But as the marked condition is valid under the condition that M3 is cutoff and all the current is flowing through M2, how can (6.64) become valid for DC?

Another problem is that in the following example (6.12), LO swing is given as 300mV. And in the solution, equation 6.67 is used. But equation 6.67 is valid under the marked condition, yet the LO swing and overdrive of M2 violate the condition. So why can the equation still be used here?

Thanks!

PS: attach is the page I mentioned. Due to the limitation of the size of the uploaded document, I cannot do more.