7.3 BIPOLAR JUNCTION TRANSISTORS 361npn C(a)EiEvBEiBiC= iB + iC = iB + iC− +
vCB
B − +pnp C(b)EiEvEBiBiC+ −
vBC
B + −Figure 7.3.2BJTs biased in the active region.(a)npnBJT (iB,iC, andiEare positive).(b)pnpBJT (iB,iC,
andiEare negative).
With varying but positive base current, as seen from Figure 7.3.4(a),vBEstays nearly constant at
thejunction threshold voltageVγ, which is about 0.7 V for a typical silicon BJT.
TheEarly effectand theEarly voltage−VA(whose magnitude is on the order of 50 to
100 V) for a typicalnpnBJT are illustrated in Figure 7.3.5, in which the linear curves are
extrapolated back to thevCE-axis to meet at a point−VA. The Early effect causes the nonzero
slope and is due to the fact that increasingvBEmakes the width of the depletion region of the
CBJ larger, thereby reducing the effective width of the base.ISEin Equation (7.3.1) is inversely
proportional to the base width; soiCincreases according to Equation (7.3.2). The increase iniC
can be accounted for by adding a factor toISEand modifying Equation (7.3.2) such thatαiEis
replaced byαiE( 1 +vCE/VA).
The common-emitter collector characteristics for a typicalpnpBJT are shown in Figure
7.3.6.
Asmall-signal equivalent circuitof a BJT that applies to bothnpnandpnptransistors and is
valid at lower frequencies (i.e., ignoring capacitance effects) is given in Figure 7.3.7, where the
notation is as follows:
iC=gm vBE+ vCE
ro(7.3.6)in which
Transconductancegm=∂iC
∂vBE∣ ∣ ∣ ∣ ∣ Q
=ICQ
VT(7.3.7)Reciprocal of output resistance1
ro=∂iC
∂vCE∣ ∣ ∣ ∣ ∣ Q
=ICQ
VA(7.3.8)The derivatives are evaluated at the quiescent or operating pointQat which the transistor is biased
to a particular set of static dc currents and voltages. Notice the dependence ofiCon bothvBEand
vCE. Considering a small base-current change iBoccurring due to vBE, one can define
rπ= vBE
iB∣ ∣ ∣ ∣ ∣ Q
= iC
iB vBE
iC∣ ∣ ∣ ∣ ∣ Q
∼=∂iC
∂iB∣ ∣ ∣ ∣ ∣ Q
1
gm=β
gm(7.3.9)and
vπ= vBE=rπ iB (7.3.10)
Thelarge-signal modelsof a BJT for the active, saturated, and cutoff states are given in Figure
7.3.8. Note that in Figure 7.3.8(a)iE∼=βiB=iCifβ>>1. In Figure 7.3.8(b) the collector
battery may be replaced by a short circuit when the small value ofVsatcan be neglected. In Figure