I wanted to make an comparator with cascade of amplifiers of equal gain, output impedance etc. We know that we can approximate it as single pole system , thus a resistor and a capacitor in the output will do the approximation. I was able to calculate the gain for first stage i.e $$-g_m * R_o * \frac{t }{R_o C_o} $$

This is when t<< time constant. Now as stages increases , I want to derive the speed and delay. Can someone help me or share materials that contain this derivation?