Linear dropout voltage transfer function
I have actually some troubles to understand why Rds is in parallel with the capacitor Cb.


When we're working out the equivalent resistance of some network, we treat ideal voltage sources as shorts. In this analysis we're assuming the input (\$V_i\$) is being provided by an ideal voltage source. Therefore the source terminal of the PMOS is connected to ground, for the purpose of this analysis. 

Since \$C_b\$ is also connected between the output terminal and ground, that puts \$C_b\$ and the drain-source branch of the MOSFET in parallel.