High-Frequency Semiconductors Power Devices

[ 5 ] Device Features in Detail
Figure 1.2 shows the frequency locus of α. When actually measuring α, the difference between
theoretical and measured values increases as the frequency approaches f α . This is because the
Early’s equivalent circuit is based on an first approximation of physical phenomena.
To correct it, Thomas-Moll introduced excess phase m and offered the equation.
α ⎛ ⎞
α = 0 f
exp⎜
⎟
− jm
..........................................................................(9)
f
+ ⎝ f
1 j
α ⎠
fα
m
π
4
R e (α)
0.5
α
α = 0
f
1+
j
fα
1.0
−j 0.5
α
α =
0
f
1+
j
fα
⎛ f
exp⎜
− jm
⎝ fα
⎟ ⎞
⎠
Im (α)
f α
Figure 1.2 Frequency Locus of α
The above equation agrees well with measured values in frequencies less than f α .
r bb’: Base diffusion resistance
This is resistance from the center of the base area to the external base terminal, which
actually contributes to transistor action. It is determined according to the shape and dimensions
of the transistor, and the base specific resistance.
rbb’ ∼
q B 8 πW
.......................................................................................(10)
− ( Ω)
where,
qB: Specific resistance of base area (Ω・m)
DC Current gain (β) at the common emitter is represented as follows:
β =
α0
1
β
= 0
1 − α0
1 + jωCb'erb'e
1 + jωCb'erb'e
The β-interrupting frequency f β is defined as the frequency at which the absolute value of β
becomes β 0 2 . f β is represented similarly to f α , as:
1
fβ
=
2 πC b' erb'e
therefore,
β
β = 0 ...............................................................................................(11)
f
1 + j
fβ
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