SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 339

B

rπ

Cπ CBE

CBC

gmVBE

R 0

C

E

Element

re

rπ

Cπ

R 0

IE

kBT

b 0 re

Value

IC

VA

re

tB+tC

Figure 7.16: Small-signal model of a bipolar transistor.

Inserting our expressions from , we get

iB=−

vω

re

[(

1+jω

2 τB

3

)

−

(

1 −jω

τB

3

−jωτC

)]

(7.5.68)

where we have assumedωto be small so that

iC

−

vω

re

[

1 −jω

(τB

3

+τC

)]

(7.5.69)

Simplifying equation 7.5.57 gives us foriB

iB=−jω

(τB+τC)

re

vω=−jωCπvω (7.5.70)

where

Cπ=

τB+τC

re

(7.5.71)

which illustrates how collector delay adds to the input capacitance.