Regulated Cascode TIA using a voltage amplifier with negative gain
Notice that Δv is an AC signal, a small-signal voltage component at the gate of M1. Accordingly, all the other small-letter signals (-AΔv etc.). Whereas in your analysis (&quot;VY must be larger than VX to keep M1 and M3 in saturation. So, when VX increases --&gt; VY decreases --&gt; v_gs M1 decreases --&gt; ID M1 decreases&quot;), you are talking mostly about DC signals (VX, VY, ID), occasionally mixing DC with AC (v_gs).
You carry out the DC analysis to find out the quiescent points of non-linear devices (transistor, diodes). To calculate linear parameters of your circuits (gains, input/output impedances, etc.), you perform AC analysis in small-signal approximation.