Miller Time Constant Approach

Equation (4.19) tells us that the effect of the Miller capacitor can be easily approximated by finding the midband gain, and the value of the pole p. An easy way to determine the value of p is to notice that

$$p=\frac{-1}{R_MC_M}$$ (85)

Where R_M is the resistance seen by the Miller capacitor C_M.

$$R_M=R_{in}\vert\vert R_S=R_B\vert\vert(r_{\pi}+\beta R_E)\vert\vert R_S$$ (86)

In summary, we've been trying to show that the overall strategy for approximating the effect of the Miller capacitor, is to determine the midband gain, and then multiply that gain by the expression for a first order low pass filter, with pole determined by $\frac{1}{R_MC_M}$.