414 CHAPTER 8. FIELD EFFECT TRANSISTORS
If the capacitance charging time is the limiting factor,atthecutofffrequencythegatecurrent
IinisequaltothemagnitudeoftheoutputchannelcurrentgmVGS. The input current is the
current due to the gate capacitor, and for a small-signal sinusoidal signal we have
Iin=jωCGVGS (8.8.4)Equating this togmVGSatω=2πfτ, we get for the cutoff frequencyfτ=gm
2 πCG=
1
2 πttr(8.8.5)
wherettrrepresents the transit time of the electrons through the channel. The frequency response
is therefore improved by using materials with better transport properties and shorter channel
lengths. If we assume that the carriers are moving at a saturated velocity, the transit timettris
simply
ttr=Δt=L
vs(8.8.6)
and the cutoff frequency becomes
fτ=vs
2 πL(8.8.7)
It may be noted that the source resistanceRShas an effect of reducing the effective transcon-
ductance of the device. In the presence of a source resistance the gate bias isV
′
GSsince a part of
the input voltage drops across the resistanceRS. The drain current is
ID=gmV′
GS (8.8.8)Also we have
VGS=V
′
GS+(
gmV′
GS)
RS=(1+gmRS)V′
GS (8.8.9)The drain current now becomes
ID=gmVGS
1+gmRS=g′
mVGS (8.8.10)whereg
′
mis the extrinsic transconductance and is smaller thangm.The transistor provides the maximum power gain when both the input and output are conju-
gate matched to the generator and load impedance respectively figure 8.40(c)). This maximum
available power gain (MAG)isgivenby,
MAG=
Pload
Pav,gen=
G^2 mRds
16 π^2 f^2 Cgs^2 Ri≡
(
fmax
f) 2
, (8.8.11)
where
fmax=fτ
2√
Ri/Rds