Transistor fT / fmax
The transition frequency fT — where the short-circuit current gain falls to unity — is the headline speed figure of an RF transistor. It is set by the transconductance and the input capacitances. The maximum oscillation frequency fmax, where the power gain reaches unity, additionally depends on the parasitic gate resistance and feedback capacitance.
Equations & Parameters ▸
\(f_T = \dfrac{g_m}{2\pi\,(C_{gs} + C_{gd})} \qquad f_{\max} \approx \sqrt{\dfrac{f_T}{8\pi\,R_g\,C_{gd}}}\)
| gm | Transconductance (mS = mA/V). |
| Cgs | Gate–source (input) capacitance (pF). |
| Cgd | Gate–drain (feedback / Miller) capacitance (pF). |
| Rg | Effective gate resistance (Ω), optional — needed for fmax. |
| fmax | Maximum oscillation frequency (unity power gain). The simplified form shown assumes gate-resistance-limited operation. |
References: T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed., Cambridge, 2004. · B. Razavi, RF Microelectronics, 2nd ed., Prentice Hall, 2012.
Inputs
mS
mA/VpF
Input cappF
Feedback capΩ
For fmaxResults
Speed figures
Transition freq. fT—
Max osc. freq. fmax—
Detail
Total input C—
Diagram