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 π (g m - s C μ)

g m r π = β 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):

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

ω T = β o ω β

f T = β o f β

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

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

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