0195136047.pdf

8.3 BJT AMPLIFIERS 403

Rin=RB‖Ri=

RBRi

RB+Ri

(8.3.8)

in which

Ri=rπ+RW( 1 +gmrπ) (8.3.9)

where

RW=ro‖RE‖RL (8.3.10)

The voltage and current gains are given by

Av 1 =

vL

v 1

=

RW( 1 +gmrπ)

rπ+RW( 1 +gmrπ)

(8.3.11)

Ai=

iL

iS

=

vLRin

v 1 RL

=

Rin

RL

Av 1 =

RinRW( 1 +gmrπ)

RL[rπ+RW( 1 +gmrπ)]

(8.3.12)

rois generally large enough so that the following results hold. Forro→∞,

Ri∼=rπ+( 1 +gmrπ)(RE‖RL) (8.3.13)

Av 1 ∼=

( 1 +gmrπ)(RE‖RL)

rπ+( 1 +gmrπ)(RE‖RL)

∼= 1 (8.3.14)

Ai∼=

( 1 +gmrπ)(RE‖RL)RB

RL[rπ+RB+( 1 +gmrπ)(RE‖RL)]

(8.3.15)

Note that the voltage gain of the CC amplifier is about unity, but never exceeds unity. The current
gain, on the other hand, is large sinceRin>> RLtypically.

Common-Base (CB) Configuration

The common-base (CB) amplifier is shown in Figure 8.3.3(a), in which the base forms the common
terminal between the input and output circuits, and resistorsR 1 ,R 2 ,RC,andREare selected through
biasing. CapacitorsCB,CC,andCEare chosen large enough to act as short circuits at the lowest
frequency of interest in the input signalvS. The output voltagevLis taken from the collector across
resistorRL. The small-signal ac equivalent circuit of the amplifier is shown in Figure 8.3.3(b),
whose analysis yields the following results:

RH=RC‖RL=

RCRL

RC+RL

(8.3.16)

Ri=

rπ(ro+RH)

rπ+RH+ro( 1 +gmrπ)

(8.3.17)

Rin=RE‖Ri=

RERi

RE+Ri

=

(rπ‖RE)(ro+RH)

ro+RH+(rπ‖RE)( 1 +gmro)

(8.3.18)

The voltage and current gains are given by

Av 1 =

vL

v 1

=

vL

−vπ

=

RH( 1 +gmro)

RH+ro

(8.3.19)

Ai=

Rin

RL

Av 1 =

RH(rπ‖RE)( 1 +gmro)

RL[ro+RH+(rπ‖RE)( 1 +gmro)]

(8.3.20)

Forro→∞,