7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 341
This expression reduces to
Io(jω)
Iin(jω)
=
rπ
re
[
1 −jωCBCre
1+jωrπ(Cin+CBC)
]
(7.5.77)
Neglecting the zero introduced byreCBC,sincereandCBCare both small,β(jω)can be
written as
β(jω)=
β 0
1+jωrπ(Cin+CBC)
=
β 0
1+jωβ 0 re(Cin+CBC)
(7.5.78)
or
β(jω)=
β 0
1+jβ 0
(
ω
ωT
) (7.5.79)
where
ωT=
1
re(Cin+CBC)
(7.5.80)
It is readily seen that
1
ωT
= re(Cin+CBC)=re[(Cπ+CBE)+CBC]
= re(CBE+CBC)+τB+τC (7.5.81)
= τEC
whereτECis the total delay from the emitter to the collector.
Let us examine our expression forβ(jω)in equation 7.5.79. Whenω<ωT/β 0 , the denomi-
nator in equation 7.5.79 is approximately equal to 1, and|β(jω)|is given by the dc current gain
β 0 .Onceω>ωT/β 0 , we can ignore the 1 in the denominator, andβ(jω)is approximately
given by
β(jω)
ωT
jω
(7.5.82)
So we see that atω=ωT,|β|=1, or the current gain is unity.ωTis the transit frequency and
determines the current gain cutoff frequency asωT=2πfτ,or
fτ=
1
2 πτEC
(7.5.83)
Maximum frequency of oscillationfmax
fτis a very important figure of merit because it is determined by the intrinsic delay in the de-
vice and is therefore related intimately to material parameters such as carrier velocity, lifetimes,
etc. However, when used as an amplifier, in many cases the device can amplify power beyond
fτ, because often voltage gain can be achieved at frequencies higher thanfτ. The maximum
frequency of operation beyond which the power gain is less than 1 is termedfmax. Beyond this
frequency, the device dissipates more power than it outputs.