344 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS
Zo CBC
1
ωTCBC
Figure 7.20: Equivalent circuit representation of the intrinsic device with the dominant extrinsic
elements outside.
is also in parallel to the ac components in figure 7.19 but is typically very small compared to the
ac conductance. The transistor can now be represented as an intrinsic device with the dominant
extrinsic elements outside, as shown in figure 7.20.
Power gain is always calculated for the case of a conjugately matched loadZL=Z∗oto
enable maximum power transfer to the load. The conjugately matched loadZLfor the output
impedance shown in figure 7.19 is illustrated in figure 7.21. Since the output current in the load
is one-half of the short circuit current,
iC
iB=
iC(short)
2·
1
iB=
β
2(7.5.87)
The power gain can be written as
G=
Pload
Pin=
|iC|^2 Rload
|iB|^2 Rin=
(
iC
iB) 2
·
1
ωTCBC·
1
rb(7.5.88)
or
G=|β|^2
4·
1
ωTCBC·
1
rb(7.5.89)
Substituting|β|=ωT/ω(equation 7.5.82) and usingω=2πf,weget
G=
fτ
8 πrbCBC·
1
f^2(7.5.90)
fmaxis defined as the frequency at whichG→ 1. This gives us
fmax=√
fτ
8 πrbCBC(7.5.91)
whererbis the total base resistance of the device including contact resistance, sheet resistance
of the extrinsic base, and the intrinsic base resistance of the device.