Current-Gain Cutoff Frequency
How Transit Time and Capacitance Set fT
Every transistor has a finite speed at which it can move charge between its terminals. The current-gain cutoff frequency captures that speed in a single number: it is the frequency where the small-signal current you can extract at the output equals the current you inject at the input, so the current gain has decayed to one. Below fT the device multiplies current; at fT it merely passes it through; above fT it attenuates. Because the current gain h21 rolls off as a clean single pole at 20 dB per decade across most of the RF band, fT also equals the gain-bandwidth product of the current gain, which is why it is such a convenient figure of merit.
Physically, fT is set by the total emitter-to-collector (or source-to-drain) charge-handling delay τec through the relation fT = 1 / (2πτec). That delay sums several pieces: the time to charge the emitter and collector junction capacitances through the transconductance, the base or channel transit time, and the collector depletion-region transit time. Shrinking the base width in a bipolar device or the gate length in a field-effect device cuts the transit term, while reducing junction area cuts the capacitive charging term. This is the engineering reason mature processes chase ever-smaller critical dimensions: each reduction directly buys higher fT.
fT is bias-dependent. As collector or drain current rises, transconductance increases and the charging time shrinks, so fT climbs to a peak at a specific current density. Push past that and fT collapses through the Kirk effect, where the high mobile charge density widens the effective base and lengthens transit time. Datasheets therefore always quote fT at a stated current and voltage, and amplifier designers bias near the peak-fT current density to extract maximum high-frequency gain.
Governing Equations
|h21(fT)| = 1 (0 dB)
Single-pole rolloff:
|h21(f)| ≈ fT / f (for f >> fβ)
Transit-time relation:
fT = 1 / (2π × τec) where τec = (Cbe + Cbc)/gm + τb + τc
Link to fmax:
fmax ≈ √( fT / (8π × Rb × Cbc) )
Where gm = transconductance, Cbe/Cbc = base-emitter/base-collector capacitance, τb = base transit time, τc = collector transit time, Rb = base resistance. Example: τec ≈ 0.32 ps → fT ≈ 500 GHz.
Typical fT by Device Technology
| Device technology | Typical fT | Typical fmax | Critical dimension | Common use |
|---|---|---|---|---|
| Silicon BJT (RF) | 20 to 80 GHz | 30 to 100 GHz | 0.2 to 0.5 μm base | Sub-6 GHz radios |
| SiGe HBT | 200 to 350 GHz | 250 to 450 GHz | ~0.1 μm base | mmWave radar, 5G |
| GaAs pHEMT | 80 to 150 GHz | 150 to 300 GHz | 0.15 μm gate | LNAs, switches |
| GaN HEMT | 30 to 100 GHz | 100 to 200 GHz | 0.15 to 0.25 μm gate | High-power PAs |
| InP HBT | 350 to 600 GHz | 400 to 700 GHz | <0.25 μm emitter | mmWave, THz front ends |
Frequently Asked Questions
How is fT measured from S-parameters?
fT is the frequency where |h21| = 1 (0 dB). Since a true RF short circuit is impractical, h21 is derived from measured S-parameters via h21 = −2·S21 / ((1−S11)(1+S22) + S12S21). In the single-pole region |h21| falls 20 dB/decade, so you measure it there and extrapolate the line down to unity gain. Report it with the bias point, because fT peaks at a specific current density.
What is the difference between fT and fmax?
fT is the unity current-gain frequency and reflects how fast the device moves charge. fmax is the unity power-gain (maximum oscillation) frequency and reflects the highest frequency at which it delivers power gain. They relate as fmax ≈ √(fT/(8πRbCbc)), so a device can show high fT but poor fmax if base/gate resistance is large. For PAs and oscillators, fmax is the more relevant figure.
Why does fT drop at high collector current?
fT climbs with current as transconductance rises and charging time shrinks, peaking at a set current density. Beyond that it falls due to the Kirk effect (base pushout): high mobile charge in the collector widens the effective base and lengthens transit time. High-level injection and self-heating add to the rolloff, which is why datasheets specify fT at a defined current and voltage and designers bias near that peak.