What is the fT and fmax of a transistor and how do they determine the maximum operating frequency?
fT and fmax in RF Transistors
Understanding f_T and f_max is fundamental for selecting the right transistor technology and predicting circuit performance at high frequencies.
Frequently Asked Questions
Can I operate above f_T if the gain is still positive?
f_T is the current gain unity frequency, not the power gain unity frequency. A transistor can provide useful power gain above f_T if f_max > f_T. Between f_T and f_max: the current gain is < 1 (< 0 dB), but the power gain (MAG or MSG) can still be positive because the output impedance is high enough that the power gain exceeds unity despite the current gain being below unity. Example: a SiGe HBT with f_T = 300 GHz and f_max = 500 GHz: at 350 GHz (above f_T): current gain = negative dB, but power gain ≈ 3-5 dB (usable for multi-stage amplification). In this case: f_max is the true upper limit for useful operation (not f_T). However: for practical amplifier design, operating above f_T is only done when absolutely necessary (the circuit becomes very sensitive to parasitics and layout).
Why is f_max often higher than f_T?
f_max depends on both f_T and the gate (or base) resistance: f_max ≈ f_T / √(4×R_gate×2×pi×f_T×C_gd). If R_gate is very small (good metallization, short finger widths) and C_gd is small: f_max >> f_T. This is especially true for InP HEMTs: the high electron mobility and short gate give high f_T, and the low feedback capacitance (C_gd) gives even higher f_max. Example: InP HEMT with f_T = 600 GHz: if R_gate = 0.5 Ω, C_gd = 3 fF: f_max ≈ 600 / √(4×0.5×2×pi×600e9×3e-15) = 600/√(22.6e-3) = 600/0.15 = 4000 GHz. Too high because this simplified model neglects other parasitics, but it shows the trend. Actual f_max for InP HEMT: 1.0-1.5 THz (2.5× f_T). Conversely: GaN HEMTs often have higher R_gate (due to wider gate for power) and higher C_gd, so f_max/f_T ratio is 1.5-2.5 (lower than InP).
How do I extract f_T from S-parameter data?
Step-by-step: (1) Measure S-parameters from 1 GHz to the maximum frequency of your VNA (40-67 GHz for standard VNA, 110+ GHz for mmWave VNA). (2) De-embed the fixture parasitics (subtract pad capacitance and probe contact inductance using open/short structures). (3) Convert S-parameters to H-parameters: h21 can be computed from the S-parameter matrix. (4) Plot |h21|² in dB vs log(frequency). It should follow a -20 dB/decade slope (20 dB per decade decrease). (5) Fit a straight line to the -20 dB/decade region (avoid frequencies near the VNA noise floor and frequencies below where the gain saturates). (6) Extrapolate the line to 0 dB. The frequency at the 0 dB crossing is f_T. Note: the slope should be exactly -20 dB/decade (6 dB/octave). If the slope is steeper: there may be additional parasitic poles (second-order effects). If the slope varies: the transistor may have non-ideal behavior at certain frequencies (substrate coupling, feedback resonance). Use the portion of the curve with consistent -20 dB/decade slope for the extrapolation.