User:Msiddalingaiah/BJT transition frequency

From Millman and Grabel second edition, page 465


 * $$I_b = V_\pi \left [ \frac{1}{r_\pi} + s (C_\pi + C_\mu) \right ]$$


 * $$I_c = V_\pi (g_m - s C_\mu)$$


 * $$g_m r_\pi = \beta_o$$


 * $$\beta(s) = \frac{I_c}{I_b} = \frac{\beta_o (1 - \frac{s C_\mu}{g_m})}{1 + s (C_\pi + C_\mu) r_\pi}$$


 * $$\beta(s) = \frac{\beta_o (1 - \frac{s}{\omega_z})}{1 + \frac{s}{\omega_\beta}}$$


 * $$\omega_z = \frac{g_m}{C_\mu}$$


 * $$\omega_\beta = \frac{1}{r_\pi (C_\pi + C_\mu)}$$

Assuming single pole response (ignore the zero):


 * $$\beta(s) = \frac{\beta_o}{1 + \frac{s}{\omega_\beta}}$$


 * $$\omega_T = \beta_o \omega_\beta$$ $$f_T = \beta_o f_\beta$$


 * $$f_T = \frac{g_m}{2 \pi (C_\pi + C_\mu)}$$


 * $$g_m = \frac{I_{cq}}{V_T} = \frac{I_{cq}}{26 mV}$$


 * $$f_T = \frac{I_{cq}}{2 \pi (C_\pi + C_\mu) V_T}$$