SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 335

We see that the injected current amplitude is complex, indicating that the current has both a
conductive (real) and capacitative (imaginary) part. If the frequency is sufficiently low such that
wB<<

√

ω/(2Dn), the hyperbolic cotangent term may be expanded in the following manner:

αcothα=1+

α^2

3

+H.O.T. (7.5.41)

This gives us foriω(0)

iω(0) =−

eAEDnnω(0)

wB

[

1+jω

w^2 B

3 Dn

]

(7.5.42)

If we insert the expression fornω(0)from equation 7.5.38 into equation 7.5.41, we can express
iω(0)in terms of our input signalvω

iω(0) =−

eAEDnndc(0)

wB

e

kBT

[

1+jω

w^2 B

3 Dn

]

vω (7.5.43)

or

iω(0) =−

eIE

kBT

[

1+jω

w^2 B

3 Dn

]

vω (7.5.44)

whereIEis the dc emitter current.iω(0)may also be written in the form

iω(0) =−(Gs+jωCdif f)vω (7.5.45)

where

Gs=

1

re

=

eIE

kBT

(7.5.46)

is the emitter-base diode conductance , and

Cdif f=

2

3

∂QF

∂VBE

=

2

3

CB=

eAEndc(0)wB

3

e

kBT

(7.5.47)

is the diffusion capacitance measured at the emitter terminal. As was discussed in section 7.2,
the diffusion capacitance is 2/3 the value of the apparent diffusion capacitance(CB),sincefor
a short-base diode only 2/3 of the charge stored in the base is reclaimable. Finally, recognizing
thatCBcan be written related to the base transit timeτBby

τB=re·CB (7.5.48)

we may expressiω(0)as

iω(0) =−

1

re

(

1+jω

2 τB

3

)

vω (7.5.49)