[![enter image description here][1]][1][![enter image description here][2]][2]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?
 


  [1]: https://i.sstatic.net/jVSyH.png
  [2]: https://i.sstatic.net/ldqqz.png