gm = sqrt (2 k_n' (W/L) I_D)
    = sqrt (2 * 20e-6 * (30/10) * 100e-6)
    = 110 uA / V₂
f_T = gm / (2 * pi * (Cgs + Cgd))
    = 110e-6 / (2 * pi * (0.08 + 0.01)*1e-12)
    = 194.5 MHz

w_T = gm / (Cgs + Cgd)
For Cgs >> Cgd and the overlap component
of Cgs negligibly small, Cgs ~= (2/3) W L Cox, and
w_T ~= gm / ( (2/3) W L Cox)
substituting for gm from
gm = sqrt (2 * u_n Cox (W/L) I_D)   results in
w_T = (3/2)sqrt(2 u_n Cox (W/L) I_D) / (W L Cox)
    = (3/2) sqrt (u_n I_D / (2 Cox W L))
note that:
1) to increase w_T, the device should be operated at a higher ID.
2) w_T is greater for devices with smaller dimensions